Paul Weingartner Omniscience

From a Logical Point of View

P h i l o s o p h i s c h e A n a l y s e P h i l o s o p h i c a l A n a l y s i s

Herausgegeben von / Edited by

Herbert Hochberg �x Rafael Hüntelmann �x Christian Kanzian Richard Schantz �x Erwin Tegtmeier

Band 23 / Volume 23

Paul Weingartner

Omniscience

From a Logical Point of View

ontos

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Preface The main task of this book is to clarify the concept of omniscience and to reject attacks which are based on false or very questionable premises or on invalid argumentation. The book thereby defends the possibility to attribute omniscience to God in a consistent way. The method is to divide the main task into 12 chapters which are formulated as basic questions. Each chapter begins with arguments pro and contra. Then a detailed answer is proposed which contains a systematic discussion of the question. This is the repective main part of the chapter. These arguments pro and contra express different positions concerning the concept of omniscience and attacks against a consistent formulation of it. These problems are discussed and clarified in the commentaries to the objections at the end of the chapters. It has to be emphasized however that what is expressed in the pros and contras is not the opinion of the author. It is sometimes the opinion of other scholars as shown by quotations. The opinion of the author is expressed in the main part of the chapters and in the commentary to the objections. The last chapter 13 contains a theory of omniscience formulated as an axiom system. It is to show that theism claiming an omniscient God, who knows everything about himself and about his creation (including the universe) is possible in a consistent way. It should be observed moreover that this book is not a book about the existence of God; but about the possibility of a consistent concept of omniscience which can be attributed to a presupposed object of religion (God) which is usually understood as a most perfect being and as creator of this world (universe). This does not mean that this book is only readable for theists. Any reader interested in the topics of omniscience may study the book, accepting the assumptions which seem questionable to him only conditionally. Aknowledgements: The author wants to thank Ursula Stranzinger, Eva Stieringer and Albert Anglberger for providing the typoscript and the layout. Further thanks go to Dr. Rafael H�ntelmann of Ontos Verlag for the efficient cooperation. Salzburg, March 7, 2007 Paul Weingartner

Contents

1. Whether Everything is Ttrue What God Knows..........................................1

1.1 Arguments Against................................................................................1 1.2 Argument Pro........................................................................................3 1.3 Proposed Answer...................................................................................3

1.31 Analysis of the Concept of Knowledge.............................................3 1.32 Further Support: Logical and Deductive Omniscience......................5 1.33 Further Support: Logical and Deductive Infallibility........................6 1.34 Further Support: God's knowledge of logic is not restricted to PL1..6 1.35 Further Support: God's knowledge comprises also the facts of the world (universe).......................................................................................7 1.36 Further Support: In God there is no Belief........................................7

1.4 Answer to the Objections.......................................................................9 1.41 The Divine Liar (to 1.11)..................................................................9 1.42 True Justified Belief (to 1.12).........................................................13 1.43 Belief not different from Knowledge (to 1.13)...............................14 1.44 Necessity of Contingency (to 1.14).................................................15

2. Whether God Necessarily Knows Whatever He Knows...........................19 2.1 Arguments Against..............................................................................19 2.2 Argument Pro......................................................................................20 2.3 Proposed Answer.................................................................................20 2.4 Answer to the Objections.....................................................................22

2.41 GodÕs Knowledge is Complete (to 2.11).........................................22 2.42 l Kp ! Kl p (to 2.12)......................................................................22 2.43 GodÕs knowledge and will concerning necessity (to 2.13)..............23

3. Whether God Knows Something at Some Time........................................25 3.1 Arguments Pro.....................................................................................25 3.2 Argument Contra.................................................................................25 3.3 Proposed Answer.................................................................................25

3.31 Knowing at some time and knowing that something happens at some time........................................................................................................26 3.32 Analysis of Time............................................................................26

3.321 Time of this world (universe)....................................................26 3.322 Time as a Chronological Order..................................................29 3.323 Time as Biological and Psychological Time..............................33

3.4 Answer to the Objections.....................................................................35 4. Whether God Knows All Past and Present Events....................................37

4.1 Arguments Against..............................................................................37 4.2 Arguments Pro.....................................................................................37 4.3 Proposed Answer.................................................................................38 4.4 Answer to the Objections.....................................................................39

5. Whether God's Knowledge Exceeds His Power........................................41 5.1 Arguments Against..............................................................................41 5.2 Arguments Pro.....................................................................................42 5.3 Proposed Answer.................................................................................42

5.31 Definition of Omnipotence (God's power)......................................43 5.32 God's knowledge exceeds his power...............................................47

5.4 Answer to the Objections.....................................................................50 6. Whether God Causes Everything What He Knows...................................53

6.1 Arguments Pro.....................................................................................54 6.2 Arguments Contra................................................................................55 6.3 Proposed Answer.................................................................................55

6.31 The knowledge need not to be a sufficient condition for causing something...............................................................................................55 6.32 The statement "God causes everything what he knows" leads to absurd consequences...............................................................................56 6.33 The thesis "God causes everything what he knows" excludes cooperation and learning processes in creatures......................................56 6.34 If God causes everything what he knows, then he is normative and volitive inconsistent................................................................................57 6.35 If God causes everything what he knows, then he causes everything................................................................................................................58 6.36 The thesis of the allcausing God and transitivity .............................59

6.4 Answer to the Objections.....................................................................61 6.41 GodÕs knowledge Ð a necessary cause (ad 6.11)..............................61 6.42 GodÕs knowledge Ð not a sufficient cause (ad 6.12)........................61 6.43 Omniscience and Freedom (ad 6.13)...............................................62

7. Whether God Knows Singular Truths?......................................................67 7.1 Arguments Contra................................................................................67 7.2 Arguments Pro.....................................................................................68 7.3 Proposed Answer.................................................................................69 7.4 Answer to the Objections.....................................................................73

7.41 Discursive Knowledge (to 7.11)......................................................73 7.42 Irrelevant truths (to 7.12)................................................................73 7.43 God knows A-propositions? (to 7.13).............................................74

8. Whether God's Knowledge of Singular, Contingent Truths Implies the Mutability of God.........................................................................................79

8.1 Arguments Pro.....................................................................................79 8.2 Arguments Contra...............................................................................79 8.3 Proposed Answer.................................................................................80

8.31 The underlying principle................................................................. 80 8.32 Principle KCH is not generally valid..............................................80 8.33 God does not need to change his knowledge..................................81

8.4 Answer to the Objections.....................................................................83 9. Whether God Knows What Is Not.............................................................85

9.1 Arguments Against..............................................................................85 9.2 Arguments Pro.....................................................................................85 9.3 Proposed Answer.................................................................................86

9.31 God's knowledge extends also to that what is not in the sense of what is either impossible or incompatible with laws of nature or accidentally not, but possible.....................................................................................86 9.32 GodÕs knowledge extends to things that are not actual...................89

9.4 Answer to the Objections.....................................................................90 9.41 What is not can be interpreted in two ways (to 9.11)......................90 9.42 Truly negated (to 9.12)...................................................................91 9.43 Does ÒGod cannot know something falseÓ imply that he is not omniscient? (to 9.13)..............................................................................91 9.44 Does God know counterfactuals (9.14)?.........................................92

10. Whether Knowledge or Truth Can Change the Status of a State of Affairs.....................................................................................................................97

10.1 Arguments Pro...................................................................................97 10.2 Arguments Contra..............................................................................98 10.3 Proposed Answer...............................................................................98

10.31 Different Kinds of States of Affairs..............................................99 10.32 The necessary status cannot be changed by truth or knowledge..102 10.33 Can the status "contingent" be changed by truth or knowledge?.104

10.4 Answer to the Objections................................................................. 112 10.41 Only closed proposition can be true (ad 10.11)...........................112 10.42 Truth does not destroy contingency (ad 10.12)...........................112 10.43 The reason for truth is the obtaining fact, not the other way round (ad 10.13).............................................................................................112 10.44 GodÕs knowledge does not change the ontological status of a state of affairs (ad 10.14)..............................................................................113

11. Whether God Knows Future States of Affairs.......................................115

11.1 Arguments Contra............................................................................115 11.2 Arguments Pro.................................................................................117 11.3 Proposed Answer.............................................................................117

11.31 God knows the future states of affairs of the universe and of the creatures belonging to it by knowing their causes.................................117 11.32 God knows his power and the power of the creatures including man..............................................................................................................120 11.33 God might have a possibility to know future states of affairs in their actual states...........................................................................................122

11.4 Answer to the Objections.................................................................127 11.41 ÒPresentÓ or Òactual eventÓ is ambiguous (to 11.11)...................127 11.42 Future events ! determinate events (to 11.12).............................128 11.43 ÒForeknowsÓ is inadequate for God (to 11.13)............................128 11.44 ÒIs a factÓ is ambiguous (to 11.14)..............................................129 11.45 Does foreknowledge destroy free will decisions? (to 11.15).......129 11.46 Is knowledge of contingent future propositions inconsistent? (to 11.16)...................................................................................................131 11.47 Free actions ! non-causal actions (to 11.2).................................133

12. Whether God Knows Everything That is True......................................135 12.1 Arguments Contra............................................................................135 12.2 Arguments Pro.................................................................................136 12.3 Proposed Answer.............................................................................136

12.32 God's knowledge about himself..................................................138 12.33 God's knowledge about his creation............................................140 12.34 God's knowledge about Logic and Mathematics.........................141

12.341 Leibniz's idea of human knowledge concerning Logic and Mathematics......................................................................................142 12.342 The limitations discovered in the 20th century........................144

12.4 Answer to the Objections.................................................................150 13. A Theory of Omniscience.....................................................................153

13.1 Introduction......................................................................................153 13.2 Theory of Omniscience....................................................................154

13.21 Definitions of Omniscience and of Omnipotence........................155 13.22 GodÕs Knowledge.......................................................................160 13.23 GodÕs Knowledge of the Universe..............................................161 13.24 GodÕs Knowledge and Will.........................................................165 13.25 GodÕs Knowledge and Will in Relation to Moral Evil................166 13.26 God knows his activities.............................................................170

Literature ...................................................................................................173 Subject Index .............................................................................................183 Name Index ...............................................................................................187

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1. Whether Everything is True What God

Knows The above question "whether everything is true what God knows" expressed in other words reads: Does it hold that if God knows something (say that some state of affairs obtains) then this (that some state of affairs obtains) is true. If we translate this question into the language of Epistemic Logic then it can be expressed more precisely thus: If g (God) knows that p (is the case) then p is true. Here 'p' stands for a proposition representing states of affairs. Symbolically: gKp " Tr(p) or: gKp " p This question can also be expressed by asking whether God is infallible. Because some person may be called infallible if it cannot happen that this person knows something which would not be the case.

1.1 Arguments Against

1.11 If everything is true what God knows, then he has to believe all and only truths. But as Grim says there can be no such being. For suppose there is, and consider a sentence we might term the Divine Liar: God believes that (8) is false (8) "On the supposition that (8) is true, it is true that God believes that (8) is false. But we are supposing here that (8) is true, and thus we are forced to conclude that God holds a false belief. On such a supposition he cannot then qualify as omniscient. On the supposition that (8) is false, it is not the case that God believes that (8) is false. But our supposition here is that (8) is false, and thus there must be a truth Ð that (8) is false Ð that God does not believe and hence does not know. Here again he fails to qualify as omniscient. If (8) is either true or false, then, God is not omniscient. But, of course, God is not alone in this respect: a similar argument will hold for any being

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proposed as omniscient. It appears that there simply can be no omniscient being."1 This argument is also applicable if 'believes' is replaced by 'knows'. Thus on the supposition that (8') (God knows that (8') is false) is true, God knows a proposition which is false. But if everything is true what God knows, then he has to know all and only truths. Therefore it does not seem to hold that everything is true what God knows. 1.12 The thesis "everything is true what God knows" seems to presuppose (as a necessary condition) a concept of knowledge which is defined as true justified belief. But as Gettier has shown there are some cases where all the three conditions: truth, justification, and belief are satisfied though one cannot speak of knowledge such that this definition is not satisfied. Therefore the thesis "everything is true what God knows" does not seem to hold. 1.13 If everything is true what God knows, then the presupposed concept of knowledge seems to imply true belief. But in God there is no belief. Therefore it does not seem to hold that everything is true what God knows. 1.14 It cannot hold that everything is true what God knows. This can be shown by the following indirect proof: 1. Assumption to the contrary: Everything is true what God knows. Symbolically: gKp " p. Now this premise of infallibility must necessarily hold for God such that we can assume the stronger premise: 2. Necessarily: Everything is true what God knows. Symbolically: l (gKp " p) 3. Instantiation: We substitute for 'p': the world exists, such that we get: Necessarily: if God knows that the world exists then the world exists. Symbolically: l (gK that the world exists " the world exists). 4. By a distribution law of Modal Logic the necessity operator 'l ' can be distributed on the parts of the implication: l gKp " l p or: If it is necessary that God knows that the world exists then it is necessary that the world exists. Symbolically: l gK that the world exists " l the world exists. 5. But we can generally assume Ð since God's knowing belongs to God's essence and actuality Ð that he necessarily knows whatever he knows. Symbolically: gKp " l gKp. 1 Grim (1991, IUN) p. 8.

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T hus w e ha ve w . r . t. this insta nc e : N e c e ssa r ily: G od k now s t ha t the w or ld e xists. A nd f r o m 4. a nd 5. it f ollo w s ( o n the a ssum pti on tha t G od know s tha t the w or ld e xist s, gKp) : 6. T he r e f or e : N ec e ssa r ily the w or ld e xist s. 7. But tha t the w or ld e xi sts i s c onti nge nt a nd not ne c e ssa r y. 2 8. T he r e f or e it doe s not se e m to ho ld tha t e ve r ything i s tr ue w ha t G od know s.

1. 2 A rg u me nt P r o

D e nying t ha t e ve r ythin g is tr ue w ha t G od know s w ould me a n to de ny tha t gKp → p. But t his me a ns tha t G od w oul d know tha t p i s the c a se a lthough p is not the c a se , i. e . f or some p : gKp a nd ¬ p. But thi s se e ms to be im pos sib le f or a pe r f e c t be ing. T he r e f or e it se e ms to hold: E ve r ythi ng i s tr ue w ha t G o d know s, i. e . gKp → p. 1. 3 P r opo se d A n sw e r

E ve r ythin g w ha t G o d know s is tr ue . O r : I f G od know s tha t p ( i s the c a se ) the n p is tr ue . Symb olic a l ly : gKp → p. T h a t this hol ds c a n be substa nt ia te d a s f ollow s:

1.31 Analysis of the Concept of Knowledge I t is suppor te d by a n a na lysis of the c onc e pt of know le dge it se lf . T he a r gume nt is th is: I f a str ong c onc e pt of know le dge – in the se ns e tha t know in g tha t p i mp lie s the tr uth of p – is a ppl ic a ble a lr e a dy to me n' s know le dge , a ll the m or e it mus t be a ppl i c a ble to G od' s kn ow le dge . B ut a s w ill be show n sub se que nt ly a s tr ong c o nc e pt of k now le dge ( in t he a bove se n se ) c a n be a pplie d to me n's kno w le dge . T he c onc e pt of me n's know le dge is usu a lly un de r stoo d in suc h a w a y tha t i t imp lie s tha t w ha t is kno w n is tr ue . O r : I f pe r son a know s tha t p ( is the c a se ) the n p ( is the c a se ) , w he r e ' p' s ta nd s f or a ny me a ningf ul sta te me n t or pr oposi tio n r e pr e se ntin g a sta te of a f f a irs. Symb olic a l ly thi s is e xpr e sse d a s: 2 Premise 2. and assumption 5. have been used (together with 4. ) by Charles Hartshorne to derive conclusion 6. The Argument 1. 14 originates in Thomas Aquinas (STh) I, 14, 13 objec tion 2. The answer of Thomas Aquinas is however different from ours given below 1. 44.

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K T aKp → p T he r e f or e the tr a ditiona l de f i nit ion o f know le dge c onta ins tr u th in the de f inie ns: know le dge is tr ue , jus tif ie d be lie f . 3 Sinc e aKp → p i s log ic a lly e quiva le nt to ¬ p → ¬ aKp w ha t is e xpr e sse d by it c a n a ls o be sta te d i n the f ollow ing w a y : I f it is no t t he c a se tha t p ( is tr ue ) the n p is not know n. T ha t is, the r e is n o kno w le dge of so me thi ng f a ls e . T hough the r e mi ght be know le dge that so me pr opos iti on is f a lse . Be c a use tha t some p r opo sit ion i s f a lse c a n be tr ue a nd in this se nse the r e c a n be know le dge of it. T he pr inc ip le K T c a n be f ur the r de f e n de d by inve s tiga t ing its ne ga ti on or a sking : w ha t is the c la i m of so me bod y w ho de n ie s t ha t aKp → p ? I t is the c la im tha t the ne ga t ion of it i s tr ue . I ts n e ga tion i s: aKp ∧ ¬ p ; tha t is "pe r son a know s tha t p ( is the c a se ) a nd ( but) ¬ p ( i. e . p i s n ot the c a se ) ". T h is is a situa t ion w hic h w e w oul d vie w a s i mpo ssib le ; i. e . f or the u sua l u nde r sta nd ing of the c onc e p t of know le dge i t i s imp ossib le t ha t s ome one is sa id to kn ow some t hing ( sa y tha t the sun is s hin ing) w he n this i s f a lse ( w he n the sun is no t shin ing) . Fr o m th is c on side r a tio n it f o ll ow s w . r . t. the usua l un de r sta ndi ng of know le dge tha t the a bove pr inc iple K T i s tr ue . T he r e is a lso a d isc u s sio n of th is pr in c iple in E pis te mic L ogic . S ome ha ve c la ime d tha t suc h a str ong c onc e pt of know le ge is not de f e nsi ble . But i t c a n e a sily be sh ow n by a lo t of e xa mp le s tha t s uc h a c onc e pt of know le dge i s de f e nsible : 4 T he r e w ould be a w ide spr e a d or ma ybe e v e n c omple te a gr e e me nt unde r sc ie ntis ts tha t w e know in t he str ong se nse of the a bove pr inc ip le K T sim ple pr opo sit ions of f in ite nu mbe r t he or y, simp le the or e ms of lo gic ( of Pr opo sit iona l L og ic a nd of F ir st O r de r P r e dic a te L ogic ) , si mple f a c ts of se nse pe r c e ption, si mp le f a c ts of our ow n i nne r e xpe r ie nc e ( tha t w e f e e l joy or a nge r or sa tisf a c ti on … e tc . ) the r e sults of ve r y w e l l c or r obor a te d e xpe r ime nta l te s ts in d if f e r e nt sc ie nc e s … e tc . T his a gr e e me nt is a f a c t, thoug h m ost of t he sc ie nt ist s t oda y a r e ve r y c a r e f ul w ith usi ng t he c onc e pt of know le dge or know ing. T ha t me a ns the y a r e ve r y muc h a w ar e of the dist inc ti on be tw e e n str o nge r c onc e pts s uc h a s "know " a nd w e a ke r one s suc h a s "be lie vin g", "a sse r t ing ", "a ssum ing " a nd "c onje c tur in g". Bu t sti ll the r e is a gr e e me nt tha t w . r . t. spe c ia l a r ea s a str ong c onc e pt of know le d ge is de f e nsible . A nd si nc e a str ong c onc e pt of know le dge i n the se nse t ha t tr ut h is

3 Concerning the question whether there are exceptions to this definition see the answer to the objection 1. 12. 4 Also Chisholm (1966, ThK) ch. 2 and 3 and Hintikka (1962 , KaB) p. 43ff. defended such a strong concept of knowledge.

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a ne c e ssa r y c ondition f or k now le dge ( K T ) is a pplic a b le to hu ma ns, a ll the mor e it mu st be a pplic a ble to G od.

1.32 Further Support: Logical and Deductive Omniscience O bse r ve how e ve r tha t a gr e e me nt w . r . t. a str ong c o nc e pt of k now le d ge in the a bove se nse doe s not i mpl y a gr e e me nt w ith s tr ong f ur t he r a xioms a bo ut huma n k now le d ge suc h a s "l ogic a l omn isc ie nc e " a nd "de d uc tive omni sc ie nc e ": L ogic a l O mn isc ie nc e ( L O ) : "L ogic a l O mni sc ie nc e " ha s so me one w ho know s a ll the tr ut hs of lo gic ( sa y a ll the the or e ms of Fir st O r de r Pr e dic a te Ca lc ulu s w ith I de nti ty ( PL 1) ) . D e duc tive O mn isc ie nc e ( D O ) : "D e duc t ive O mni sc ie nc e " ha s so me one w ho know s a ll the va l id inf e r e nc e s of logic ( PL 1) . Ca n hu ma ns p osse s s L O ? T o a n sw e r th a t que sti on w e ha ve t o di sti ngui sh a n imp lic it k now le d ge of the the or e ms of P L 1 a nd a n e xplic i t one . Sinc e PL 1 is a c omple te sy st e m, by know ing a c omp le t e se t of a xioms + de r iva tio n r ule s, w e ma y sa y tha t o ne c a n ha ve a n implic i t know le dge of the the or e ms of P L 1. A nd i n this i mp lic it se nse hu ma ns c a n ha ve L O w . r . t. P L 1. But hu ma ns c a nnot ha ve a n e xp lic it kn ow le dge of a l l the the or e m s of PL 1 si mpl y be c a use the y a r e inf inite in nu mbe r . Ca n hu ma ns po sse ss D O ? A s im ila r a ns w e r c a n be give n he r e too. Sinc e PL 1 is a c omple te syste m, by know i ng a c omple te se t of r ule s e ithe r in a ddit ion to a c omple te se t of a xi om s or w it hout us i ng a xi oms ( i f the s yste m is buil t up a s a syste m of de r iva t ion r u le s) w e ma y sa y tha t one c a n ha ve a n i mpl ic it know le dge of the de r iva tio n r ule s of PL 1. O n the othe r ha nd huma ns c a nnot ha ve a n e xplic it know le dge of a ll the de r iva tion r u le s w hic h a r e va lid r ule s in PL 1 . 5 For G od h ow e ve r it w ou ld be im pe r f e c t to ha ve L O or D O only in the i mpl ic it se nse like me n. T he r e f or e w e ha ve to sa y tha t he mus t ha ve bo th L O a nd D O in the imp lic i t a nd in the e xplic i t se nse .

5 There are systems of Epistemic Logic which (claim to) describe human knowledge and have LO and DO as their consequences. This is the case for example with the system of Hintikka in his (1962, K aB). Such systems can be accepted however only as describing an ideal(istic) concept of knowledge or as describing a kind of implicit knowledge in the above sense. For a criticism of LO, DO (and LI, DI, see below) as properties of human knowledge cf. Weing artner (1982, CRC). There a system for the concepts knowledge, belief and assumption is proposed which does not have these idealistic properties.

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1.33 Further Support: Logical and Deductive Infallibility A str on g c onc e pt of know le dge w h ic h sa tisf ie s K T d oe s no t ho w e ve r im ply logic a l i nf a lli bil ity ( L I ) or de duc t ive inf a llibi li ty ( D I ) . L ogic a l inf a l lib ili ty ha s some one w h o ne ve r c ommi ts a n e r r or w . r . t. logic a l the or e ms use d. A nd de duc tive inf a l lib ili ty ha s so me one w ho ne ve r c ommits a n e r r or w . r . t. logic a l de duc tion ( i. e . the va lidit y of inf e r e nc e s) use d. O bse r ve tha t a lthou gh L I f ollow s f r om L O a nd D I f r om D O the opposi te doe s not hold. T hu s the se pa ir s of c onditio n s ( L O a nd L I ; D O a nd D I ) a re not e quiva le nt, sinc e the a bil ity no t to c om mit a n e r r or ma y be r e str ic te d just to those tr ut hs or inf e r e nc e s w hic h a r e in f ac t inve sti ga te d. I t w ill be e a sily unde r st ood tha t a ls o L I a nd D I ar e not huma n pr ope r tie s. I t ha s be e n a n old e xpe r ie nc e of ma nkin d tha t to e r r is hu ma n. T he r e is no logic ia n or ma t he ma tic ia n w ho w oul d not c omm it so me e r r or some ti me s. T he r e f or e L I a nd D I do not hold f or huma ns. 6 O f G od on t he othe r ha nd w e c a nnot s a y tha t he c ould c o mm it a n e r r or of logi c w hic h w oul d v iola te L I or D I . H i s pe r f e c tion mu st e a si ly c o mpr e he nd L I a nd D I . A c c or din g t o T homa s A qu i na s a lr e a dy a nge l s ha ve the a bi li ty of L I a nd D I , the y a r e a ble to un de r sta nd a ll lo gic a l c onse q ue nc e s of so me th ing know n w i thou t a ny disc ur s ive pr oc e s s: "Bu t if f r om the k now le d ge of a k now n pr inc i ple t he y w e r e str a ig htw a y to pe r c e ive a s know n a l l i ts c o nse que n t c onc lusio ns, t he n the r e w oul d be no disc ur si ve pr oc e ss a t a ll. Suc h is the c on diti on of the a nge l s … T he r e f or e the y a r e ca lle d inte lle c tua l be i ngs … ". 7 I f T homa s A qu ina s is r igh t w i th thi s de s c r iption of the a nge l s t he n a lr e a dy the a nge ls c a nnot c o mm it l ogic a l e r r or s a n d thus it i s i mpos sib le tha t G od w ho ha s c r e a te d the m c ould c ommi t a n e r r or in ma tte r s of log ic .

1.34 Further Support: God's knowledge of logic is not restricted to PL1 W he n de f inin g L O a n d D O , a nd L I a n d D I a bove w e ha ve r e f e r r e d to PL 1. But a num be r of tr uths of logic w e r e ski ppe d tha t w a y: ( 1) Me ta lo gic a l the or e ms a bou t PL 1 ( f or e xa mp le tha t i t i s c o nsi ste nt, c omple te , not de c ida ble … e tc . ) . ( 2) T he or e ms of H ighe r O r de r L ogic s + the ir me ta log ic a l the r e ms a bout H ighe r O r de r L ogic .

6 LI and DI are nevertheless consequences of some systems of Epistemic Logic, like that of Hintikka (1962, KaB ) and Lenzen (1980, GWW). Cf. note 5 above. 7 Thomas Aquinas (STh) I, 58, 3.

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( 3) T he or e ms of logic s w h ic h a r e w e a ke r tha n Cla ssic a l L o gic ( like M ini ma l L ogic , I nt uit ioni st ic L og ic , I nte r me d ia te L og ic s) + the ir m e ta l ogic a l the or e m s a bout the se w e a ke r logic s. A ll the se the or e m s a nd me ta t he or e ms a r e inf inite in n umbe r . Me n ( log ic ia ns) c a n ha ve a t most some i mp lic it k now le dge of the se the or e m s a nd me ta the or e m s. A c c or ding to T ho ma s A quina s a lr e a dy the a n ge ls ma y posse s s L O , D O a nd L I , D I unr e str ic te dly ( i. e . w ithou t r e str ic ti on to PL 1) . A ll the mor e G od w ho ha s c r e a te d the se in te lle c tua l be in gs mus t po sse ss L O , D O a nd L I , D I unr e str ic te dly. Fr om w ha t ha s be e n sa i d i n 1. 32 – 1. 34 it f o llow s t ha t the f o llow ing pr inc i ple holds f or G o d: I f some thin g i s l ogic a ll y tr ue ( in the br oa d se nse ind ic a te d by the the or e m s of PL 1 a n d by the c ond it i ons ( 1) – ( 3) a bove ) the n G od know s tha t it is so. O r : I f p is a tr uth of L ogic ( p ∈ L) the n G od know s t ha t p . Sy mbol ic a lly : L K p ∈ L → gKp

1.35 Further Support: God's knowledge comprises also the facts of the world (universe) I f w e a ssume t ha t G o d c r e a te d the w o r ld the n his know le dge of the w or l d mus t be pe r f e c t. T hus he mu st know a ll the f a c ts a bo ut his c r e a t ion. A nd i t i s impo ssi ble tha t he c om mit s e r r or s a bout f a c ts of the w or ld. T h is i s of c our se c ompa ti ble w i th t he f a c t tha t he c r e a t e d the li ving or ga nis ms a s le a r ning or ga nis ms, i. e . a s or ga nisms w hic h i mpr ove a nd de ve lope via tr ia l a nd e r r or . 8

1.36 Further Support: In God there is no Belief Conc e r nin g the r e la tion of be lie f to k now le dge w e ha ve to disti ngui sh ( a t le a st) tw o dif f e r e nt k inds of be l ie f , a str onge r a nd a w e a ke r one : the s tr onge r w ill be c a lle d know le dge - e xc lu sive be l ie f ( a bbr e via te d a s G - be li e f ) a nd the w e a ke r w ill be c a lle d know le dge - inc lu si ve be lie f ( a bbr e via te d a s B - be lie f ) . T he f or me r ( G - be lie f ) is c ha r a te r iz e d by the c ond it ion, tha t if so me one be lie ve s s ome t hing, the n he doe s not kn ow it a nd if he kn ow s it, he doe s n ot ( or ne e d not) be lie ve it. W he r e a s t he se c ond ( B - be lie f ) i s c ha r a c te r iz e d by the c ondit ion, tha t if so me one kno w s so me t hing, he a lso be lie ve s i t, but if he doe s not be lie ve it, he a lso doe s not k now it. 8 The necessary learning process is emphasized strongly by many contemporary biologists. Cf. Dobzhansky (1937, GOS), Maynard - Smith (1982, ETG).

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T he se c onditi ons c a n be e xpr e sse d mor e pr e c ise ly a s f ollow s: aGp → ( ¬ aKp ∧ ¬ aK¬ p ) aKp → ¬ aGp aKp → aBp aK¬p → ¬aGp aGp → aBp ¬ aBp → ¬aKp E xa mple s f or G - be lie f : Be f or e the pr oof of the inde pe nde nc e of the Con tinu um H y pothe s is ( f r om the a xi oms of se t the or y) w a s gi ve n, v. N e uma nn be lie ve d ( but he did n't kn ow ) , tha t the Contin uu m H y pothe s is is inde pe nde nt. A f te r G öde l pr ove d th e f ir st pa r t, i. e. tha t the G e ne r a l Con tinu um H yp othe s is ( G CH ) c a n be c oniste nt ly a dde d to the a xio ms of N e uma nn - Be r na y s - G öde l - Se t T he or y ( e ve n if ve r y str ong a x iom s of inf i nit y a r e use d) , v. N e uma nn w r ote : "T w o sur mise d the or e ms of se t the or y, or r a the r tw o pr inc i ple s, the s o - c a lle d ' Pr inc i ple of Ch oic e ' a nd t he so - c a lle d 'Con tin uu m - H ypo the si s' r e siste d f or a bout 50 ye a r s a ll a tte mp ts of de mons tr a tio n. G öde l pr ove d, tha t ne i t he r of the tw o c a n be dispr ove d w ith ma the ma t ic a l me a ns. For o ne of the m w e kn ow tha t it c a nnot be pr o ve d e ithe r , f or the othe r the sa me se e ms lik e ly, a lthoug h i t doe s n ot se e m li ke ly, tha t a le sse r ma n tha n G öde l w il l be a ble to pr ove this. " 9 But a f te r the pr oof of the se c ond pa r t – tha t a lso the ne ga tion of G C H c a n be c onsis te ntl y a dde d to t he a xio ms of Se t T he or y ( it hol ds f or both sy ste m s, tha t of Z e r me lo - Fr a e nke l a nd tha t of N e um a nn - Be r na ys - G öde l) – w a s give n by Pa ul Cohe n in 1 963, von N e uma nn did n't a ny mor e be lie ve it, but kne w t ha t G CH w a s inde pe nde n t ( f r om the a xiom s of Se t T he or y) . I n ge ne r a l w e c a n sa y tha t sc ie n tif ic be l ie f ( be lie f in sc ie n tif ic hypo the se s) – be it in ma t he ma tic s or in na tur a l sc ie n c e – is a lw a ys G - be lie f : one doe s not ye t ha ve know le dge in the str o ng se nse of K T . E xa mple s f or B - be l ie f : N o spe c ia l e xa mple s f or B - be l ie f a r e ne ce ssa r y sinc e B - be lie f ma y be in te r pr e te d in the f ollow ing w a y : T o B - be l ie ve tha t some t hing ( p) is the c a se me a ns just to t hink tha t p is tr ue ( va lid) , to hol d tha t p is tr ue ( va lid) , to st r on gly a ssu me tha t p is tr ue ( va lid) e tc . T hus if some one know s tha t c hr om oso me s d upl ic a te , th e n he a lso B - be lie ve s it a n d a ls o if some one G - be lie ve s tha t G CH is ind e pe nde nt ( f r om the a xi oms of Se t T he or y) , the n he a lso B - be lie ve s it. Re lig iou s be lie f – li ke sc ie nt if ic be lie f – is a lw a y s kn ow le dge - e xc lu sive , i. e . is a lw a ys f ir st of a ll G - be l ie f . Sinc e if one be lie ve s r e ligio usly – f or in sta nc e tha t C hr ist c a me f or t he sa lva ti on of ma nkind or tha t t he r e w ill be so me ki nd

9 v. Neumann (1969, TbG).

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of c onsc ious l if e a f te r de a th – one d oe s not know i t ( a nd know s t ha t one doe s not k now it) . A n d th is hol ds f or a ll r e l igi ous be l ie f s e ve n if no t ne c e ssa r il y f or a ll the sta te me nt s of the c r e e d of some spe c ia l r e ligion. S inc e the sta te me nt s of the c r e e d migh t not be a ll l ogic a ll y i nde pe nde nt o f o ne a nothe r suc h tha t some be lie ve r ma y inf e r o ne pr op osi tio n of t he c r e e d f r om some othe r s. A nd in thi s c a se he know s tha t one is a c ons e que nc e of the othe r . Suc h inf e r e nc e s ma y be a lso do ne by the ol ogic a l a r g ume nta t ion. S til l the pr op osi tio ns so de r ive d a r e not know n but be lie ve d, a s know n c onse que nc e s of othe r s w hic h a r e be lie ve d. 1 0 N ow G od doe s ha ve ne ithe r B - be lie f n o r G - be lie f . Sinc e B - be lie f i s a w e a ke r c onse que nc e of know le dge , if he posse s se s know le d ge he doe s not pos se ss B -be lie f , e xc e pt in a n in c lusi ve w a y in the se nse tha t if he know s so me th ing he inc lus ive ly a l so th inks tha t t his i s tr ue . But "th ink ing t ha t it i s tr ue " c a nno t be inte r pr e te d in a w e a ke r se nse tha n kn ow i ng – a s i t c a n be in te r pr e te d in ma n if some one th inks tha t so me th ing is tr ue but doe s n ot ye t know it. Mor e ove r G od c a nnot ha ve G - be lie f e i the r . Si nc e G - be lie f is know le dge - e xc lus ive th is w ould me a n tha t G o d la c ks some know l e dge w . r . t. a c e r ta in a re a a nd ha s only be lie f the r e . So me ha ve c la i me d thi s f or those f utur e c on tinge nc ie s w h ic h a r e de pe nding on me n's f r e e de c isions. T hi s dif f ic ult que s tio n w ill be tr e a te d in c ha pte r 11. be low . But the ma in p oin t he r e is tha t G od c a nn ot c om mi t a ny e r r or ; sinc e t his w ou ld be inc o mpa tib le w i th his pe r f e c tion. T hus inde pe nde n tly in w ha t se nse h is r e la tion t o f utur e c on tin ge nc ie s i s e xpr e sse d, he c ould ne ve r ha ve a be l ie f w hic h is f a lse . 1. 4 A ns w e r to th e O b jec t io ns

1.41 The Divine Liar (to 1.11) G r im thi nks tha t the a ssu mpt ion : e ve r y thing w ha t G od kn ow s ( be lie ve s) is tr ue – gKp → p – le a ds to a c on tr a dic ti o n by c o nstr uc t ing a L ia r se n te nc e a nd the r e f or e c a nnot be tr ue . T o be mor e a cc ur a te ly G r im ne e ds f or the c ontr a dic tio n a ls o the oppo site im plic a tion: e ve r ythi ng w h ic h i s tr ue G od know s ( p → gKp) . T hi s la tte r pr i nc iple w ill be d isc us se d in c h. 12. A l tho ugh it be lo ngs to t he c onc e pt of o mn isc i e nc e this que stio n w i ll ha ve to be a na lyz e d in de ta il, be c a use of i ts d if f ic ult subq ue sti ons : D oe s G od kn ow a ll pa st e ve nts, a ll f utur e c ont inge nc ie s, a ll tr uth a bout the w or ld, a bout hi m se lf 1 0 For sim ilarities and differences between scientifc and religious belief see Weingartner (1994, SRB).

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… e tc . T he se que st ions w i ll be de a lt w i th i n t he su bse que nt c ha pte r s. I n a ny c a se G r im's ma in poi nt is tha t the L ia r c a n be a pplie d to G od's kn ow le dge ( a nd be lie f ) a s it is show n in 1. 11 T o t he quote d a r gume nt of G r im w e sha ll sa y thr e e thin gs: ( 1) I t is c e r ta inly not n e c e ssa r y tha t G od w o uld ha ve s uc h a n a mbigu ous be lie f ( or know le dge ) a s e x pr e sse d in a L ia r se nte nc e . ( 2) T he r e a r e ma ny dif f e r e nt sol utio ns of th is a n d othe r L ia r se n te nc e s w h ic h s how tha t c ontr a dic tio ns c om ing up w i th L ia r se nte nc e s a r e not una voida ble . ( 3) O ne c a n give a n e xpl ic it so luti on of G r i m' s D ivine L ia r . T he r e f or e the c o nc lus ion dr a w n by G r im ( tha t the r e c a nnot be a n omni sc ie nt be in g) is not pr ove d. a d ( 1) T he spe c ia l c on str uc t ion of the L ia r se nte nc e in 1. 11 u se s se lf r e f e r e nce , like si mila r c on str uc t ions ; o n e of the s hor te st is "( 8) is f a l se … … ( 8) ". I n bo th ( in thi s a nd G r i m’ s) c on st r uc tions '( 8) ' is use d in tw o d if f e r e nt me a nings : O n the one ha nd '( 8) ' me a ns a pa r tic ula r se nte nc e ( not me ntione d) w hic h is f a l se ; o n the o the r ha nd '( 8) ' m e a ns the se nte nc e : "( 8) is f a l se " or i n G r im' s e xa m ple i t me a ns the se n te nc e : "G od be lie ve s tha t ( 8) is f a l se ". But tha t e quivoc a t ions a nd e xp lic it a m big uitie s le a d to f a lse a nd so me ti me s c ontr a dic tor y c onse q ue nc e s is a n old e xpe r ie nc e ; a lr e a dy A r isto tle e mpha siz e d tha t e qu ivoc a ti on is t he ma i n sour c e of f a lla c ie s. A nd w hy should w e a ssume tha t a most pe r f e c t be ing sho uld ha ve suc h a mbig uous be l ie f s? a d ( 2) T he r e a re ma ny dif f e r e nt solu ti ons f or L ia r se nte nc e s kno w n to da y. O ne is tha t of T a r sk i w h ic h is ba se d on the d ist inc ti on be tw e e n ob je c t la ngua ge a nd me ta la ngua ge . T hi s di sti nc tion u nma s ke s the a m big uit y ( the tw o d if f e r e nt me a ning s of '( 8) ') sho w n a bove . T he olde st s olu tion se e ms to be tha t of Pa ul us V e ne t us w ho u se d a n e xte nsi on of T a r ski' s tr u th c on dit ion. 1 1 T he r e a r e non - T a r skia n pr oposa ls like t ha t of K r ipke or H in tik ka w hic h c a n solve L ia r pa r a doxe s. 1 2 A sim ple pr opo sa l w hic h i s ba se d o n a n e xte nsi on of T a r ski's tr u th c on dit ion w a s ma de e l se w he r e by myse lf . 1 3 T he r e by T a r sk i's tr uth c on dit i on " s i s tr ue if f p " ( w he r e ' s' is the me ta lin gui stic na me of a se nte nc e a nd ' p' is the tr a ns la tion o f the r e spe c tive se nte nc e into the me ta la ngua ge ) is e xte nde d b y tw o e xpl ic it c omp one nt s or c ondit ions w h ic h a r e implic i t in T a r sk i's f or ma l a ppa r a tus of his e s sa y on tr u th. 1 4 T he f ir st c ondit ion ( a bbr e via te d a s MC) i s tha t ( u nde r nor ma l c ond iti ons) a n ind ic a tive se nte nc e s i s in te r pr e te d in suc h a w a y t ha t s me a ns i ts c on te nt ( its pr opo sit ion p) ; th us 'sn ow i s w h ite ' me a ns tha t sn o w is w hi te . T he se c on d i s tha t ( u nde r nor ma l c ond iti ons) a n ind ic a tive se nte nc e s is inte r pr e te d in suc h a w a y tha t s 1 1 For details cf. Weingartner (2000, BQT) ch. 7.361. 1 2 Kripke (1975, OTT), Hintikka (1996, PMR) ch. 6 and 7. 1 3 Cf. Weingartner(2000, BQT) p. 129ff. and Weingartner (2006, SDT) 1 4 Tarski (1935, WBF), translated in Tarski (1956, LSM), pp. 152 – 278.

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sa ys of it se lf ( of s ) t ha t it is so a s it s a ys ( i. e . tha t s is tr ue ) ; thu s ' Ca e sa r c r osse d the Rub ic on' is i nte r pr e te d in su c h a w a y tha t it sa ys of itse lf tha t it is so a s i t sa y s ( or tha t th is is tr ue ) . T his c ondit ion is c a l le d a lso the p osi tive ( or se r ious) usa ge of la ngua ge ( a bbr e via te d a s PS) . P S ma y be vi ola te d in t he ir onic a l ( un se r ious) w a y of ta lk ing ( s o me ti me s ma r ke d by a s mile , bu t mor e hidde n in w r i tte n te x ts) . I t i s a lso vio la t e d in l ie s f or the lia r hi mse lf ( w h o is a w a r e of the lie ) but pur por ts ( non viola ti on of ) PS to t he a ddr e sse e . I f w e e xte nd now T a r sk i's tr ut h c ondi ti on by MC ( f or shor t : s me a ns t ha t p) a nd P S ( f or shor t: s sa ys tha t s is tr ue ) w e r e c e ive the f ollow in g tr u th c ondit ion T M P* : T MP * I f s me a ns tha t p the n: s is tr ue if f p a nd s sa ys tha t s is tr ue I nste a d of T M P* one c a n ha ve a tr u th c ondit ion w hic h pla c e s P S a l so in the a nte c e de nt: I f MC a nd PS the n: s i s tr ue if f p a nd PS ( T M P + ) . O r one c a n e ve n dr op P S a lt oge the r , t houg h i n t his c a se a n i mpor ta nt c o mpo ne nt is m iss ing. N e ve r the le ss it c a n be s how n tha t w i t h a ll thr e e e xte nde d tr u th c ond it ions ma ny know n ve r sion s of sim ple a nd c omplic a te d L ia r s ( a s c yc lic one s, str e ngthe ne d L ia r s, L ia r e quiva le nc e s e t c . ) ca n be solve d. 1 5 a d ( 3) Soluti on of the sim ple a nd the D i vine L ia r ( a ) Soluti on of the sim ple L ia r T he simp le L ia r is of te n sta te d thu s: ( s) is f a lse ( s ) But thi s i s a r a the r unc le a r w a y of e xp r e ssing the L ia r s inc e the f unc tion of '( s) ' on the si de is not pr e c ise . T he r e f or e w e sha ll e xpr e ss the shor t L ia r se nte nc e thus: L s me a ns tha t s is f a lse . Mor e ove r if w e a dd a lso PS w e sha ll e x pr e ss the f ull L ia r se nte nc e L * thus: L * s me a ns tha t s is f a lse a nd s sa ys tha t s is tr ue .

1 5 For details see Weingartner (2000, BQT) pp. 121 – 140. The name ‘TMP*’ is used accordingly in my book (2000, BQT) ch. 7.

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U sing L a s the f ir st pr e mi se w e a pply ( w ith the r e spe c tive sub sti tut ion f or p ) the e xte nde d tr uth c ond iti on T M P* a s th e se c ond pr e mise : T MP * I f s me a ns tha t s is f a l se the n : s is tr ue i f f s is f a lse a nd s sa y s t ha t s is tr ue . T he sol uti on i s n ow t he f oll ow in g: Si nc e the e quiva le nc e ( in t he c onse que n t of the i nsta n tia te d T M P* w hic h c a n be de r ive d f r om L a nd T M P* by Mo dus Pone n s) ha s the f or m p ↔ (¬p ∧ q) this i s ( by Pr o pos iti ona l L og ic ) e quiva le nt t o ¬p ∧ ¬q. T ha t i s, the sol ution r e a ds thu s: s is f a lse a nd no t: s sa ys ( of itse lf ) tha t s is tr ue ( P S) . I f w e use the f ull L ia r L * w e ha ve to use T MP + a s tr uth c ondi tion, si nc e T MP + c onta ins P S in the a nte c e de nt. T he c onc lusio n ( sol uti on) is t he n the sa me a s in the c a se o f the shor t L ia r . Sim ila r solu tion s c a n be r e c e ive d f or ma n y ve r s ions of L ia r se nte nc e s inc lu ding ve r y c ompl ic a te d a nd soph ist ic a te d one s. I n a ll the se c a se s no c ontr a dic ti on f ollow s. ( b) Solut ion of the D iv ine L ia r I nste a d of : "G o d b e l ie ve s tha t ( 8) i s f a l se …… ( 8) " w e use t he mor e pr e c ise f or m D L ( r e pla c ing '( 8) ' by ' s') in or de r t o a void the me nt ione d a mb igui tie s : D L s me a ns tha t G od be lie ve s tha t s is f a lse . By a ddin g P S w e r e c e ive the f ull D ivine L ia r se nte nc e D L * D L * s me a ns t ha t G od be lie ve s tha t s is f a lse a nd s sa ys tha t s is tr ue . D L ( D L *) is the f ir st pr e mise . T he se c ond pr e mise w ill be a ga in the insta n tia te d e xte nde d tr u th c ondi tio n: T MP * I f s me a ns tha t G od be lie ve s tha t s is f a ls e the n: s is tr ue if f G od be lie ve s tha t s is f a lse a nd s sa ys tha t s is tr ue . T he solut ion i s now a s f ollow s: A s sa i d a bove it mus t hold t ha t G od be lie ve s ( know s) tha t s is f a lse if f s is f a lse . T he r e f or e ‘ G od be lie ve s tha t s is f a lse ’ c a n be r e pla c e d by ‘ s is f a l se ’ . T hus the c onc lus ion ( so lu tio n) i s: s i s f a lse a nd not: s sa ys t ha t s is tr ue

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W he n usin g the f ul l D iv ine L ia r ( D L *) a nd a pplyi ng T M P* the n t he solu tio n is the sa me . I n both inte r pr e ta t ions D L a nd D L * of the D iv ine L ia r t he so luti ons a r e a s f ollow s: T he posi tive ( se r ious) usa ge o f la ngua ge is viola te d ( by a pply ing a mis le a ding or c he a tin g usa ge : no n - P S) a nd s is f a lse . But n o c ontr a dic t ion f ollow s. Sinc e the r e a r e othe r solu tio ns of L ia r se nte nc e s the r e w ill be a ls o othe r solu tion s of the D ivi ne L ia r . T he solu tion g ive n a bove a nd pos sib le othe r solu tion s show q uite c le a r ly tha t G r im' s c la im tha t o mni sc ie nc e is im pos sib le be c a use of the ( a lle ge d unso lva bi lit y of t he ) D ivi ne L ia r is w r ong. 1 6 T he r e f or e the c onc lusio n in obje c t ion 1. 11 is n ot pr ove d. O n a mor e ge ne r a l p oin t of vie w it se e ms r a t he r i mpor ta n t t o be ve r y c a r e f ul not to pr oje c t to the a ttr ib ute s of G od a ll ( or a pa r t of) the ma ny pa r a doxe s, inc ons iste nc ie s a n d c onf us ions ma n pr oduc e s be c a use of his im pe r f e c t a nd r e str ic te d min d.

1.42 True Justified Belief (to 1.12) T o this ob je c tio n one c a n sa y tw o things : ( 1) T he de f in iti on of k now le dge a s true justified belief i s a r e a sona b le de f init ion of huma n know le dge f or ma n y a pplic a t ions ( thou gh no t f or a ll ; se e ( 2) be low ) . But it is n ot a r e a sona ble d e f init ion f or G od's know le dge . T his c a n be se e n a s f o llow s: Fir st be c a use the r e is no be lie f in G od a s ha s be e n substa n tia te d a bo ve ( se c tion 1. 36) . Se c o ndly t he r e is no ne e d f or jus tif ic a ti on in G od' s know le dge be c a use he doe s not know c e r ta in pr opos it ions be c a use of othe r s in the se n se f or e xa mp le tha t so m e a r e mor e e vide nt or tr a nspa r e nt t ha n othe r s or f unc ti on a s a n e xp la na tion f or othe r s. Fur t he r jus tif yi ng pr op osi tion s w ith the he lp of othe r s im plie s t ha t the know le dge is d isc ur si ve w hic h is a lso not t he c a se w ith G od' s know le d ge . T o this poi nt T ho ma s A qu ina s sa ys: "I n o ur kn ow le dge the r e is a tw of o ld d isc ur si on; one is a c c or ding to suc c e ssion onl y, a s w he n w e ha ve a c tua lly unde r s tood a nyt hing, w e tur n our se lve s to unde r s ta nd some thin g e l se ; w hile the o the r mode of d isc ur si on is a c c or ding to c a usa lit y, a s w he n thr ough pr inc iple s w e a r r ive a t the know le dge of c onc lusion s. " 1 7 1 6 See Simmons (1993, AAO) who also stresses that there are many ways out of Liar and other paradoxes and criticizes Grim' s attacks of omniscience from some other aspects. 1 7 Thomas Aquinas (STh) I, 14, 7. Cf. (SCG) I, 57.

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T homa s A qu ina s t he n ju stif ie s t ha t bo t h kin ds of disc ur s ion c a nn ot h old f or G od. Fr o m the se c ons ide r a tio ns i t f oll o w s tha t t he de f in it ion of know le dge a s true justified belief i s not a de qua te ( a pplic a ble ) to G od. Bu t si nc e the de f init ion of kno w le dge a s true justified belief doe s n ot a ppl y to G od 's know le dge the c o nc lus ion in the obj e c tion 1. 1 2 i s n ot pr ove d by thi s a r gume nt. ( 2) I nde p e nde nt ly of tha t one ma y a s k w he the r the tr a diti ona l de f ini tion ( w hic h goe s ba c k to Pla to) of know le dg e a s true justified belief w he n a p plie d to hu ma n kn ow le dge i s a lw a ys sa ti sf ie d . T he a nsw e r to th is q ue sti on i s th is: A ltho ugh th is de f ini tio n is sa t isf ie d i n ma ny c a se s of both c om mon a nd sc ie ntif ic kn ow le dge i t is no t sa ti sf ie d i n a ll c a se s. T ha t the r e a r e e xc e ptions ha s be e n show n by G e t tie r in a pa pe r of 1963 1 8 w hic h ha s be e n disc us se d w ide ly sinc e . Bu t G e t tie r use s t w o ve r y a r tif ic ia l e xa mp le s a s c ounte r e xa mple s a nd the f ir st one doe s n ot se e m to be a ge nu ine c ounte r e xa mple a t a ll. H ow e ve r i t i s ve r y e a sy to give so me r e a l ( non a r tif ic ia l) c ounte r e xa mp le s f r om the h i stor y of sc ie nc e . 1 9 I n f a c t e ve r y w e ll just if ie d sc ie nt if ic c onje c tur e w hic h is c or r e c t is true justified belief a lthou gh no sc ie nt ist w o uld c a ll it kn ow le dge be f or e the c onje c tur e is pr ove d or e xpe r ime nta l ly c onf ir me d. O ne e xa mple , v. N e uma nn's c onje c tur e c onc e r ning the inde pe n de nc e of the Co nti nuu m H ypothe s is, ha s be e n gi ve n a bove ( se e se c tion 1. 36) . A nothe r is Fe r ma t 's f a mo us c onje c tur e w hic h ha s be e n pr ove d by W i le s i n 19 94 or Poinc a r é ’ s c on je c tur e w hic h ha s be e n pr ove d by Pe r e lma n in 2006, a ga i n o the r e xa mple s a r e E ins te in' s thr e e f a mous c onje c tur e s ( or pr e dic t ions) of hi s G e ne r a l T he or y of Re la ti vit y in 191 5 a bou t the pe r ihe lion of Me r c ur y, the de via tio n of ligh t due to gr a vi ta tiona l f ie lds, the r e d - shif t of the ligh t f r o m d ista n t s ta r s. T he y ha ve be e n w e ll c onf ir me d e ve r sinc e 1919. T his sh ow s t ha t the c onc e pt of hu ma n know le dge c a nno t be c omple te ly c ompr ise d b y the de f ini tion of kn ow le dg e a s true justified belief, a lthoug h thi s de f init ion ha s a w ide f ie ld of a pplic a tio n a lso in the sc ie nc e s.

1.43 Belief not different from Knowledge (to 1.13) T he c onc e pt of the kno w le dge of G od d oe s not i mp ly tr ue be l ie f in the se n se tha t t he r e c ould be be lie f i n hi m w hic h w ould dif f e r f r om his know le dge . T hi s 1 8 Gettier (1963, JTB). 1 9 For a discussion of Gettiers counterexamples and for more detail s on genuine counterexamples see Weingartner (1996, NGP).

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w a s show n i n se c tion 1. 3 6. T he r e f or e the f ir st pr e mise of 1. 13 i s not c or r e c t w he ne ve r be lie f ( in G od) me a ns so m e thing d if f e r e nt tha n know le dge ( in G od) ; but w i thou t suc h a dif f e r e nc e the se c ond pr e mise ( a lso inte r pr e ti ng be lie f a s dif f e r e nt f r om know le dge ) w ou ld ha ve no po int. T he r e f or e , sinc e the f ir st pr e mise is n ot tr ue the c onc lus ion in 1. 13 is not pr ove d.

1.44 Necessity of Contingency (to 1.14) I n or de r to disc u ss obje c ti on 1. 14 in a pr e c ise w a y w e a sk tw o que st ion s: I s the a r gume nt ( inf e r e nc e ) va lid, i. e . doe s the c onc lus ion f o llo w log ic a lly f r o m the pr e mise s? A nd se c on dly : A r e a ll pr e m ise s tr ue ? O nly if bo th que s tio ns c a n be a nsw e r e d positive l y the c onc lusi on is pr ove d by thi s a r gume nt. A s to the f ir st que st ion o ne c a n se e e a sily tha t the a nsw e r is po sit ive , i. e . the a r gume nt is l ogic a ll y va lid. Conc e r nin g the se c ond que st ion w e sha ll go ove r the pa r tic ula r pr e mise s : Pr e mi se 1 a nd 2 c a n be a c c e pte d sinc e p r e mise 1 w a s de f e nde d i n se c tio n 1. 3. w ith dif f e r e nt r e a sons. Pr e mi se 2 is a s tr e ngthe ni ng of pr e mi se 1 w h ic h c a n a lso be a c c e pte d o n the gr oun d tha t G o d's k now le d ge be lon gs to h is e s se nc e . Pr e mi se 4 is a the or e m of Mo da l L ogic w hic h is va lid in ve r y ma ny dif f e r e nt Moda l L o gic s suc h tha t it c a n be ge ne r a lly a c c e pte d. Pr e mise 5 c a n be de f e nde d inde pe nde nt ly suc h t ha t it c a n be a c c e pte d too. I t w ill be de f e nde d in c h. 2. be low . Pr e mi se 7 c a n a lso be a c c e pte d a s tr ue . Sinc e 6 a nd 8 a r e c onc lusio ns, t he on ly pr e mise le f t is n umbe r 3 w hic h se e m s t o be ha r mle ss be c a use it is a substi tut ion in sta nc e of pr e mise 2 w hic h is a c c e pte d. But on a c lose r loo k 3 is onl y a ha lf tr uth. T his c a n be se e n a s f ollow s: Me n' s know le dge is of te n inc om ple te be c a use it se le c ts one a spe c t or pr ope r ty a nd doe s not me n tion a n othe r a t the sa me t i me . T his ma y ha ve d if f e r e nt r e a sons. So me ti me s the r e a son is jus t tha t not a ll a spe c ts or p r o pe r tie s a r e c ompr e he nsi ble f or us a t t he sa me t ime ; ma y be be c a use the y a r e too ma ny or be c a use of de e pe r r e a sons like in the c a se of qua n tu m me c ha nic a l ob je c ts of w hic h n ot a ll pr ope r tie s a r e a va ila ble to us b y s ha r p me a s ur e me nt a t t he sa me time . O r t he r e a son ma y be si mp ly i gn or a nc e , like in t he c a se tha t w e k now some pr ope r tie s of a ne w e le me nta r y pa r tic le but no t the othe r s. N ow a ll the se dif f e r e nt k inds of inc o mp le te ne ss a nd a d dit iona l othe r one s a r e impo ssi ble f or G od' s k now le d ge . S in c e he ha s c o mpl e te know le dge of e ve r ything w ha t he ha s c r e a te d. T he r e f or e he doe s know not o nly tha t a thi ng e xists bu t in one a c t of know le dge a lso how it e xis ts. W he r e a s w ith us it of te n ha ppe ns tha t w e know on ly tha t so me th ing e xis ts be c a use w e disc ove r some

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c a usa l e f f e c t on othe r things w i thou t a ny know le dge of w ha t it e xa c tly is a nd how ( w i th w h ic h pr o pe r tie s e tc . ) it e xis ts. Fr o m this c ons ide r a tion it is c le a r tha t pr e m ise 3 is ins uf f ic ie nt a n d inc or r e c t w . r . t. G od's kn ow le dge . I t is impo ssi ble f or G od' s kn ow le dge t ha t he know s tha t the w or ld ( w hic h he c r e a te d) e xists w ith out k now i ng tha t the w or ld e xis ts c ont inge nt ly be c a use he know s th is in o ne a c t of know ing ( w hic h mor e ove r inc lude s a ll othe r pr ope r tie s of the w or ld) . T he r e f or e w e ha ve to r e vise pr e mise 3 by ma k in g a mor e c omple te in sta nt ia tio n 3* of pr e mi se 2: 3*. N e c e ssa r ily: if G od kn ow s tha t t h e w or ld e xis ts c on tinge n tly the n t he w or ld e xist s c onti nge nt ly. Sy mbol ic a lly : l ( gK tha t the w or ld e xi sts c on tin ge ntl y → the w or ld e x ist s c ontinge n tly ) . 3* c a n be ob ta ine d a ls o in the f o llow ing w a y. W e ins ta ntia te pr e mise 2 by l ( gKCon t( p) → Co nt( p ) ) w he r e 'Cont( p ) ' me a ns 'c on tin ge ntl y p'. For ' p ' w e c a n the n subst itu te 'the w or ld e xist s' w hic h le a ds dir e c tl y to 3*. L e a ving a ll othe r pr e mise s unc ha ng e d w e c onc lude t he n a s t he ne w c onc lusio n 6*: 6*. N e c e ssa r ily: the w or ld e xis ts c ont ing e ntly. Con tinge nc y c a n be de f ine d i n dif f e r e nt w a ys. U sua ll y one d is ting uis he s the f ollow ing tw o k inds w h ic h ha ve be e n use d impl ic itl y a lr e a dy by A r istot le : 2 0 Con t( p ) ↔ m¬ p ↔ ¬l p Con t( p ) ↔ ( m p ∧ m ¬p ) ↔ ( ¬l ¬p ∧ ¬l p) But w i th bot h de f ini tion s of c ontinge nc y w e obta in the r e vise d c onc lusio n 6*. Mor e ove r i t s houl d be me n tione d tha t i f Cont(p) is inte r pr e te d a s ¬l p the r e is a n a xio m, w hic h le a ds f r o m the moda l s yste m T ( Fe y s or v. W r ight) to S5 ; it ha s the f ollow ing f or m : ¬l p → l ¬l p. T hus thi s a xiom le a ds dir e c tly to the c onc lu sion 6 * w he n ‘ p ’ is insta nt ia te d by ‘ the w or ld e xis ts’ . T he r e ply to obje c ti on 1. 14 i s the r e f or e thi s: Pr e m ise 3 i s i nc or r e c t w . r . t. the know le dge of G o d be c a use it me nt io ns on ly one pa r t of t he tr u th. But know in g on ly one pa r t of so me tr ut h is i mp oss ible f or G od's kno w le dge . T he r e f or e the c onc lus ion s 6 a nd 8 a r e not pr ove d b y t his a r gume n t. I f

2 0 Cf. Hintikka (1973, TaN) ch. 2, especially p. 34.

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how e ve r w e c or r e c t pr e mise 3 by 3* the n the r igh t c onc lu si on 6* c a n be de r ive d f r om the se pr e mise s.

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19

2. Whet her God N ece ss ar i l y Knows Wh at ever

He Know s T his que st ion c a n a ls o be e xpr e sse d a s f ol low s : D oe s i t h old, tha t if G od know s so me thin g, the n he ne c e ssa r il y know s it? O r : D oe s it h old f or e ve r ything G od k no w s t ha t he ne c e ssa r ily know s it? Sy mbol ic a lly : ∀p ( gKp → l gKp) ? 2. 1 A rg u me nt s A g ai ns t

2. 11 I n c ha pte r 1. it w a s show n tha t w ha te ve r G od know s is tr ue . T his c e r ta inly hol ds ne c e ssa r ily. Sym bol ic a ll y: l ( gKp → p ) . N ow a c c or ding to a n a xiom of Moda l L o gic ( w hic h is va lid i n ve r y ma ny dif f e r e nt Moda l L ogic s) l c a n be distr ibu te d to the pa r ts of the i mpl ic a tion suc h t ha t w e ge t: l gKp → l p ; w h ic h me a ns: if G od ne c e ssa r ily kno w s tha t p, the n ne c e ssa r ily p. T hus if i t ho lds tha t w ha te ve r G od k now s he ne c e ssa r ily k now s, the n w e c a n r e pla c e ' gKp' by ' l gKp'. T hu s b y mo dus pone ns it f o llo w s t ha t p is ne c e ssa r y, symbo lic a ll y l p, f or e ve r y pr opo sit ion p of w h ic h G od ha s know le dge . Con se que nt ly the r e a r e onl y ne c e ssa r y f a c ts ( e xpr e sse d b y ' l p ') or G od know s onl y the ne c e ssa r y f a c ts. Both c o nse que nc e s a r e a bsur d. T he r e f or e it is not c or r e c t to sa y tha t G od ne c e ssa r ily kno w s w ha te ve r he know s. 2. 12 G od's k now le dge i nc lude s kn ow le dge a bout hi mse lf a nd a bou t his c r e a tion ( a bout the uni ve r se ) . Sinc e G od is a ne c e ssa r y be ing he ne c e ssa r ily know s e ve r y thin g w ha t he kn ow s a bout hi mse lf . B ut s inc e the w or ld ( unive r se ) is no t a ne c e ssa r y, but a c ontinge n t be in g, it se e ms tha t w ha t he know s a bo ut t he uni ve r se , he doe s not n e c e ssa r ily know . T he r e f or e it d oe s not se e m to hold ge ne r a lly t ha t G od ne c e ssa r ily know s w ha te ve r he know s. 2. 13 G od doe s no t ne c e ssa r il y w ill e ve r ything w ha t he w ill s. T ho ugh he ne c e ssa r ily w ill s his ow n go odne s s, h e w ills th ings a pa r t f r om hi mse lf ( f or e xa mple the c r e a tion of the w or ld) not n e c e ssa r ily, but f r e e ly. "A c c or ding ly, a s to t hin gs w ille d by G o d, w e mu st o bse r ve tha t

he w il ls so me thi ng of a bso lute ne c e ssit y: b ut thi s i s n ot tr u e o f

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a ll tha t he w i lls. F or the div ine w il l ha s a ne c e ssa r y r e la tion to the div ine go odne s s, sinc e t ha t i s i ts pr ope r obje c t. H e nc e G o d w ill s H is ow n good ne ss ne c e ssa r i ly, e ve n a s w e w il l our ow n ha ppine ss ne c e ssa r il y. . . But G od w i lls t hin gs a pa r t f r om hi m se lf insof a r a s the y a r e or de r e d to his ow n g oodne ss a s the ir e nd. . . H e nce , sinc e the G oodne ss of G od i s pe r f e c t a nd c a n e xist w it hou t othe r thin g s ina sm uc h a s no pe r f e c tion c a n a c c r ue to hi m f r o m the m, i t f ollow s tha t hi s w il lin g thi ngs a pa r t f r om him se lf is no t a bsolu te ly ne c e ssa r y. " 2 1

But bo th G od 's w il l a nd G od's k now le dg e be long to his na tur e . T he r e f or e it se e ms a lso to hold f or G od's kn ow le dge tha t he doe s no t ne c e ssa r ily know w ha te ve r he know s. 2. 2 A rg u me nt P r o

A ltho ugh the un ive r se ( G od’ s c r e a tio n) is c onti nge nt G od’ s know le d ge a bout his c r e a tion ne e d no t to be c on tinge n t t oo. A nd sinc e hi s kn ow le dge be long s to his e sse nc e it mus t be ne c e ssa r y. T he r e f or e it se e ms to hold t ha t w ha te ve r G od know s he ne c e ssa r ily kn ow s. 2. 3 P r opo se d A n sw e r

G od ne c e ss a r ily know s w ha te ve r he kno w s. Sy mbo lic a lly : ∀p ( gKp → l gKp ) . T ha t this i s tr ue c a n be se e n by the f ollow ing ind ir e c t pr oof : ( 1) A ssu me tha t this i s not so, i. e . tha t f or some p, G od know s tha t p bu t not

ne c e ssa r ily know s t ha t p; i. e . symbo lic a l ly: ∃p ( gKp ∧ ¬l gKp) . ( 2) Fr om th is it f ol low s by m oda l log ic th a t ∃p( gKp ∧ m¬gKp) , i. e . tha t f or

some p , G od know s t ha t p, but poss ibl y he doe s not know tha t p. ( 3) But th is is i mpos sib le ( i. e . ( 2) m ust be f a lse ) a s c a n be se e n b y t he

f ollow ing c ons ide r a tion : ( a ) Sinc e G od k now s t h a t p ( gKp) , p must b e tr ue ( a cc or ding to the r e sul t of

Q ue stio n 1) be c a use othe r w ise it w ou ld not be the c a se tha t G od know s tha t p ( a nd the n m¬gKp w o uld of c our se be tr ue ) .

( b) I f 'possib le ' ( m) is inte r pr e te d w it h the he lp of time , the n ( 2) w ould sa y tha t G o d know s t ha t p a nd f or a t le a st so me ( pe r iod of ) t ime he d oe s n ot know t ha t p. Bu t th is inte r pr e ta ti on i s i mpos sib le f or tw o r e a son s: Fir s t,

2 1 Thomas Aquinas (STh) I, 19, 3.

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be c a use G od is ou tside ti me , a s w e a ss ume he r e . Si nc e w e a ssu me in a c c or da nc e w ith the T he or y of Re la tiv i ty t ha t t i me is the ti me of o ur unive r se . A nd sinc e G od c r e a te d t he unive r se , he c r e a te d time by c r e a ting movin g a nd c ha nging ma te r ia l obje c ts. Se c ond be c a use this w ould me a n tha t his k now i ng ( a nd thi nking) w o uld be onl y pa r tia ll y a c tua l a nd pa r tia lly po te ntia l or l ike a ha bitus. B ut w e a ssume he r e tha t the r e is no pote nc y or ha bitu s in G od. 2 2 In c ontr a dist inc ti on to tha t, f or ma nkin d's know le dge bot h is tr ue : t ha t so me thi ng is know n a t so me time but no t a t a nothe r ( f or e xa mp le e a r lie r ) ti me a nd tha t kn ow le dge is ha bi tua l a nd no t a lw a ys a c tua l.

( c ) I f 'poss ible ' ( m) is inte r pr e te d w . r . t. the doma in of kno w le dge , the n ( 2) w ould sa y tha t t he r e is a doma in ( i. e . f or some pr op osi tion s p) , w he r e G od ha s know le dge b ut c on tin ge nt k now le dge in the se nse tha t he possi bly d oe s not k now . N ow th is ha p pe ns f r e que ntly w i th ma n : F ir st his know le dge is r e str ic te d to a spe c ia l doma in a nd se c ond w i thin t his doma in he of te n ha s o nly c ont inge n t kn ow le dge ; th us he know s a pr oof f or a ma the ma tic a l the or e m, but pos sib l y not, i. e . he ma y ha ve f a i le d t o do the pr oof . O r he suc c e e de d to de sign a ne w e xpe r ime nt w ith a ne w r e sult, but he ma y e a sily ha ve f a ile d to d e sign it. . . e tc .

But f or G od thi s kind of c ont inge nc y is impo ssi ble . Fir s t his kno w le dge is not r e str ic te d to a spe c ia l d oma i n si nc e it inc lu de s kno w le dge a bou t him se lf a nd a bout his c r e a tion a nd a bou t thing s ( e ve n unive r se s) w hic h he c ould ha ve c r e a te d bu t di d no t c r e a te . Se c ond, if he i s a ne c e ssa r y be in g, a s w e a ssume he r e , the n he mus t ne c e ssa r ily kno w w ha te ve r he know s of him se lf ; i. e . i t is i mpo ssi ble t ha t he w o uld kn ow s ome th ing a b out hi mse lf w ha t he poss ibly d oe s not k now . Bu t th i s se e ms to be e qua l ly tr ue w . r . t. his c r e a tion; if he ha s c r e a te d a nd de signe d the un ive r se , he mus t kn ow it in a mos t c om ple te w a y a nd it is imp oss ible tha t he w ou ld k now so me thin g of the uni ve r se w ha t he pos sib ly d oe s no t ( w ould f a il t o) kn ow . T he sa me holds w . r . t. those thing s ( unive r se s) w h ic h he c ould ha ve c re a te d but did not c r e a te , be c a use his kn ow le dge c a nn ot be na r r ow e r tha n his pow e r ( c f . c ha pte r 5 be low ) . Sinc e the c ons ide r a tion s in ( 3) ( a ) - ( c ) show tha t ( 2) is f a lse a nd s inc e ( 2) f ollow s f r om ( 1) , the a ssu mp tio n ( 1) m u st be f a lse . T he r e f or e the ne ga tion of it m ust be tr ue a nd so i t mu st be tr ue tha t G od ne c e ssa r ily kn ow s w ha te ve r he know s.

2 2 This is als o defended by Thomas A quinas ( SCG) I, 56. There are som e recen t proposals for habitual or dispositi onal knowledge of God (cf. Hunt (1995, DOS)). However, the premises on which their arguments are based do not seem convincing.

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2. 4 A ns w e r to th e O b jec t io ns

2.41 God’s Knowledge is Complete (to 2.11) T he a nsw e r to th is o bje c tio n is the sa me a s tha t g ive n i n 1. 44 ( t o obje c t ion 1. 14 of c ha pte r 1) : G od' s know le dge is a lw a ys c o mple te . T ha t i s if ' p' r e pr e se nts a ne c e ssa r y tr uth, t he n G o d know s tha t a n d if i t r e pr e se nts a c ontinge n t tr ut h, the n G od w ill a l so kno w tha t. T hus i t is i mp oss ible f or hi m to kn ow t ha t p is the c a se w it hout kno w ing h ow a nd in w ha t se n se it is the c a se . T he r ef or e if ne ce ssa r ily G od kn o w s tha t p is the c a se , but it is the c a se not ne c e ssa r ily but c ont inge n tly, it f oll o w s tha t ne c e ssa r ily: p is the c a se not ne c e ssa r ily but c ont inge n tly. O r , in ot he r w or ds, the c or r e c t c onc lusion is: ne c e ssa r ily, p is c ontinge n t. A nd so the c onc lusion dr a w n in 2. 11 tha t the r e a r e only ne c e ssa r y f a c ts or t ha t G o d know s onl y ne c e ssa r y f a c ts doe s not f ollow .

2.42 l K p ≠ K l p (to 2.12) T hough the a r gu me nt in 2. 12 is log ic a ll y va lid, the th ir d pr e m ise of i t i s the pr oble ma t ic one : F ir st it sh ould be c le a r tha t the ne c e ss ity of kn ow in g s houl d not be c onf use d w ith the ne c e ssi ty of w ha t is know n. Se c ond t he r e is no la w w ith the he l p of w hic h w e c o uld c onc lud e the se c ond f r om the f ir s t or the f ir s t f r om the se c on d. T hus a c o ntin ge nt f a c t ( sa y a pr e dic tion of a n e c lip se ) c a n be pr ove d logic a l ly a nd ma the ma tic a ll y f r om a dyna mic a l la w ( dif f e r e ntia l e qua tion) pl us s ome ot he r c ontin ge nt f a c ts ( init ia l c ond iti ons : c onste l la ti on of sun, e a r th a nd moon) . N ow t he thin ki ng ( know i ng) inv olve d i n the pr oof pr oc e ss ( ste p by ste p) c a n be ne c e ssa ry know le dge th ough w ha t i s pr ove d ( pr e dic te d) is a c ontin ge nt f a c t; w he r e a s the pr e mise s a r e pa r tia ll y c ont inge nt ( the ini tia l c on dit ion s) pa r tia ll y ph ysic a l ly ( na tur a ll y) ne c e ssa r y ( the la w ) . O n the ot he r ha nd a dif f ic u l t ma the ma t ic a l the or e m ( a ne c e ssa r y f a c t) ma y be ne c e ssa r ily know n by so me ma the ma tic i a ns w ho know the de ta ile d pr oof of it but ma y be onl y c ontin ge ntl y know n b y othe r s w ho a r e le a r ning how to pr ove it. T he r e f or e in ge ne r a l w e w i ll a gr e e th a t a sc ie nti st w h o in ve nts or suc c e e ds to ma ke a r igor o us pr oof – no ma tte r w h e the r the c onc lusi on i s a ne c e ssa r y or a c ontinge n t f a c t – ha s ne c e ssa r y kno w le dge w . r . t. the pr oof pr oc e ss ( i ts de ta ile d ste ps a nd i ts log ic a l inte r r e la tio ns) . I f w e now a ssu me i nste a d of the sc ie n ti st a pe r f e c t be ing w ho ha s c r e a te d the unive r se w ith a ll i ts va r ie ty a nd mu lt ipl ic ity it w i ll no t be dif f ic ult to a ss ume tha t he c a n ne ce ssa r ily know e ve r ythi ng a bout the c ontin ge nt f a c ts of his c r e a tion. T he r e f or e nothing hin de r s th a t c ontin ge nt f a c ts of thi s w or l d a r e

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ne c e ssa r ily kn ow n by G od w ith out be i ng kn ow n to be the c a se ne c e ssa r il y. A nd the r e f or e the c onc lusion of obje c ti o n 2. 12 is not pr ove d.

2.43 God’s knowledge and will concerning necessity (to 2.13) T he r e is a dif f e r e nc e c onc e r ning G od' s know le dge a nd G o d's w il l w . r . t. t he que sti on of t his c ha p te r . T hough G od ne c e ssa r ily kno w s w ha te ve r he k now s it doe s no t ho ld tha t he ne c e ssa r ily w i lls w ha te ve r he w i lls. Be c a use he ne c e ssa r ily w i lls his ow n e x iste nc e , his ow n go odne s s a nd w ha te ve r f o llow s f r om his e sse nc e . But si nc e his c r e a tion doe s not f ollo w ne c e ssa r ily f r om his e sse nc e 2 3 , he f re e ly a nd not ne c e ssa r il y w ill s his c r e a tion. I n th is se nse T homa s A qui na s c onc lu de s hi s a r tic le " W he the r w ha te ve r G od w ill s he w i ll s ne c e ssa r ily? " a s f oll ow s: " it f o llo w s tha t G od kno w s ne c e ssa r i ly w ha te ve r he know s, but doe s n ot w il l ne c e ssa r ily w h a te ve r he w ills. " 2 4 Cons ide r ing t he a r gume n t 2. 13 i n mo r e de ta il the c onc l usi on ( of 2. 13) is ba se d on the pr e m ise "bo th G od's w i ll a nd G od ' s know le dge be l ong to h is na tur e . " Fr om th is the a r gu me nt inf e r s b y a na log y t ha t e ve r yt hing w ha t ho lds f or G od' s w ill, a l so hol ds f or G od 's kno w le dge . T o se e tha t th is is no t c or r e c t, one ha s to c ons ide r tw o d if f e r e nt pr inc iple s w he r e ne c e ssit y is invo lve d : I n one of the m ( 1) ne c e ssit y is a p plie d to G od's w ill a n d G od 's k now le d ge ; in the othe r ( 2) ne c e ssity is a pplie d t o w ha t G o d w ills or to w ha t G o d know s : ( 1a ) I f G od w ills tha t p oc c ur s, the n ne c essa r ily he w il ls tha t p oc c ur s. ( 1b) I f G od know s tha t p oc c ur s, the n ne c e ssa r ily he know s tha t p oc c ur s. Sy mbol ic a lly : ( 1a ) ∀p( gWp → l gWp) ( 1b) ∀p( gKp → l gKp) O f the se ( 1b) is tr ue a s w a s sh ow n in th e a nsw e r by a n indir e c t a r gume nt. But ( 1a ) is not ge ne r a ll y tr ue , sinc e it f a i ls in a l l the c a se s w he r e G od w ill s ( f r e e ly) some thing a pa r t f r om hi mse lf . ( 2a ) I f G od w ills tha t p oc c ur s, the n G od w ills tha t p oc c ur s ne c e ssa r ily. ( 2b) I f G od know s tha t p oc c ur s, the n G od know s t ha t p oc c ur s ne c e ssa r ily. Sy mbol ic a lly : ( 2a ) ∀p( gWp → gWl p) ( 2b) ∀p( gKp → gKl p)

2 3 At least not accor ding to the Christian D octrin e. Though this is so according to the doctrine of emanation ("necessary overflo w") of Plotinus. 2 4 (STh) I, 19, 3, ad 6.

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W . r . t. the se s e c ond pr i nc iple s, ( 2a ) a n d ( 2b) , the w i ll of G od w ou ld be ha ve in a simila r w a y a s his know le dge : B ut bot h ( 2a ) a nd ( 2b) a r e not ge ne r a lly tr ue . Be c a use f or some s ta te s of a f f a ir s onl y ( f or those be lon gin g to G od's na tur e ) he w ills a nd know s tha t the y ne c e s sa r ily oc c ur . A nd this kind of ne c e ssity is a str ong a nd unc ond iti ona l ne c e ssity. F o r othe r s ta te s of a f f a ir s w h ic h o be y la w s of na tur e ( w hic h ma y be sa i d to be physic a l ly or na t ur a lly ne c e ssa r y) he w ill s a nd know s tha t the y oc c ur na tur a lly or ph ysic a ll y n e c e ssa r y. For st ill othe r sta te s of a f f a ir s w hic h do not o c c ur ne c e ssa r ily w . r . t. both type s of ne c e ssity a bove , he w ills a nd kno w s tha t the y oc c ur c ontinge ntl y. T hus of the f our pr inc iple s a bo ve only ( 1b) is ge ne r a lly tr ue . T he thr e e othe r s only h old f or some sta te s of a f f a ir s a nd not f or ot he r s, thus not for all . I nste a d of ( 1a ) , ( 2a ), ( 2b) the f ollow ing pr inc ip l e s hold ( w he r e ' Nl p ' me a ns ' na tur a lly ( physic a ll y) ne c e ssa r y p') . ( 1a ') ∃p ( gWp ∧ l gWp) ∃p( gWp ∧ ¬l gWp) ( 2a ') ∃p ( gWp ∧ gWl p) ∃p( gWp ∧ gW¬l p) ( 2 a '') ∃p( gWp ∧ gWNl p ) ∃p( gWp ∧ gW¬Nl p) ( 2b') ∃p( gKp ∧ gKl p) ∃p( gKp ∧ gK¬l p ) ( 2b'') ∃p( gKp ∧ gKNl p) ∃p( gKp ∧ gK¬Nl p)

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3. Whet her God Kn ows S om et hi ng at S om e

T i m e T his que st ion c a n a l so be e x pr e sse d a s f ollow s: D oe s i t h old f or so me thi ng tha t G od know s tha t he know s i t a t some time ? 3. 1 A rg u me nt s P ro

3. 11 S inc e G od is e te r na l, w ha t he kn o w s a bout hi mse lf he doe s n ot know a t some ti me . Bu t s inc e the e ve n ts of t h is w or ld a r e a t so me ti me , w ha t he know s a bou t the e ve nts of this w or ld he se e ms to know a t so me t i me . T he r e f or e the r e se e ms to be some th ing t ha t he know s a t some ti me . 3. 12 I f e ve r yth ing is tr ue tha t G od kn ow s, the n G od c a nno t e r r a bou t pa s t e ve nts. Bu t to ha ve know le dge w it hou t e r r or a bout pa st e ve nts imp lie s to know a t w ha t ti me the y ha p pe ne d. N ow a s it w a s show n in c ha p te r 1. , e ve r ything i s tr ue tha t G od know s. T he r e f or e G od know s some t hing ( pa st e ve nts) a t some ti me . 3. 13 A na lo gous ly t o 3. 12 w e c a n a r gue a bout pr e se nt e ve nts, be c a use t o kn ow a bout pr e se nt e ve nts a lso i mp lie s to kn o w a t w ha t time the y ha ppe ne d. T he r e f or e G od know s some t hing ( pr e se nt e ve nts) a t some ti me . 3. 2 A rg u me nt C on tr a

A ny p oin t of ti me be long s t o ( l ie s o n ) some ti me sc a le . E ve r y t ime sc a le dist uing ishe s be t w e e n e a r lie r a nd la te r or be tw e e n pa st a nd f utur e . But e te r nity ha s no pa st or f ut ur e or e a r lie r and la te r . T he r e f or e , sinc e G od himse lf a nd his a c tivi ty like hi s know le dge is e te r na l it c a nnot be a t some time . 3. 3 P r opo se d A n sw e r

W ha t G od know s he doe s no t know a t s ome ti me . T his a ns w e r c a n be substa n tia te d a s f o ll ow s. Fir st ( 3. 31) i t be c ome s c le a r w ith the he lp of a distinc t ion. Se c ond ( 3. 32) it c a n be show n by a n a na lysis of time .

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3.31 Knowing at some time and knowing that something happens at some time T o know tha t so me th ing ha p pe ns a t so me ti me doe s no t me a n to know thi s a t some ( the sa me ) time . Mor e a c c ur a te ly: T o know t ha t p i s the c a se a t ti me t is not the sa me a s ( a nd doe s not im ply) to know a t ti me t tha t p is the c a se . Sy mbol ic a lly : aKpt is no t the sa me a nd doe s not imp ly: aKt p. N o r doe s it imp ly: aKt pt. T his c a n e a sil y be se e n f r om the f a c t tha t i n the f ir s t c a se ( aKpt) the ti me ope r a tor is a t tr ibu te d t o t he e ve nt ( or t o the pr opo sit ion de sc r ibin g the e ve nt) , w he r e a s in the se c ond c a se it is a ttr i bute d t o the kno w le dge ( or to the a c tion of kn ow in g) . Fr o m t his it is pla in tha t if G od kno w s t ha t s ome e ve nt ha ppe ns a t ti me t, it doe s not f ol lo w f r om this t ha t his a c ti on of know i ng a lso ha ppe ns a t so me time . I n othe r w or ds it w ou ld be a logic a l f a ll a c y to inf e r aKt p ( G od know s a t t t ha t p) f r om aKpt ( G od know s tha t p oc c ur s a t t) . T hus it is ve r y w e ll c ompa tib le tha t G od know s a t w ha t ti me ( of thi s w or ld) c e r ta in e ve nts oc c ur w i th the the sis t ha t his a c tio n of know in g doe s no t oc c ur a t a c e r ta in time . H ow e ve r it s hou ld be a dde d tha t c o nc e r ning h uma n know le dge it is c or r e c t tha t know ing ( in t he se nse of a c tua lly kno w ing, no t in the se n se of dispo sit iona l ly kno w ing) t ha t p is the c a se a t t1 implie s tha t t he a c tion of know in g oc c ur s a t a c e r ta in ti me t2 . I f pt1 is a c o nti nge nt e ve n t ( f a c t ) of t he e xte r na l w or ld a nd me dia tion of se nse s a nd br a in pr oc e sse s a r e ne c e ssa r y f or r e c ognitio n, the n t1 w il l no t be s imu lta ne ous w i th t2 but e a r lie r , sinc e e ve r y c a usa l pr opa ga tio n ne e ds t ime ( a c c or din g to the Spe c ia l T he or y of Re la t ivi ty) . W he the r it c oul d be si mul ta ne ous if the e ve nt a nd the a c tion of k now i ng a r e r e f le c ting me nta l pr oc e sse s, like in c a se s of intr ospe c tio n, is a n ope n que stio n.

3.32 Analysis of Time A n a na lysi s of ti me show s tha t t ime c a n be unde r stood in a th r e e f old w a y: 3. 321 a s ti me of this w or l d ( un ive r se ) , 3. 322 a s a c hr o nol ogic a l or de r in the logic a l or ma the ma tic a l se nse , 3. 323 a s biolo gic a l or psyc ho logic a l t ime .

3. 321 T ime of thi s w or ld ( uni ve r se ) T ime a s time of thi s w or l d h a s the f ollow ing c ha r a c te r ist ic s w h ic h sho w c le a r ly tha t G od c a nnot be subje c t of thi s time : ( i) I t be lon gs to th is w or ld, it is bou nd to this w or l d; i. e . the r e c a nnot be

time "o uts ide " th is w or ld or inde pe nde nt of th is w or ld. I n t his se nse

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a lr e a dy A r istot le , w ho ha d a lso a r e la ti v istic c onc e pt of pla c e 2 5 , de f ine s time a s the me a sur e of c ha nge w . r . t. e a r lie r a nd la te r 2 6 . T ha t me a ns tha t time is b ound t o c ha nge a nd move me nt in thi s w or ld in suc h a w a y tha t c ha nge or mo ve me nt a r e ne c e ssa r y c on diti ons of ti me . T hi s i s a ls o i n a c c or da nc e w ith the T he or y of G e ne r a l Re la ti vity a c c or ding t o w hic h time is a c omp one nt of spa c e ti me a nd spa c e time is de pe nde n t on the ma tte r dis tr ibu te d in the unive r se ( i. e . it is c ur ve d spa c e time ) .

( ii) T he time of t his w or ld i s no t N e w ton 's a bsol u te ti me , but i s r e la tive ; i. e . e ve r y physic a l sy ste m ( sa y a p la ne t or a pla ne ta r y sys te m or a c luste r of sta r s) w hic h i s in move me nt w . r . t. a not he r ha s its ow n ti me . A ssu min g ine r tia l sy ste m s in t he unive r se ( va li d o nly ve r y loc a ll y) unive r sa l ti me w ould sti ll be de f ina b le via Einstein Synchronisation. N e w to n tho ugh t tha t the r e i s a bso lute t ime a nd tha t a bsolu te ti me "f low s e q ua bly ": "A bso lute , tr ue , a nd ma the ma tic a l ti m e , of itse lf , a nd f r o m its ow n na tur e , f low s e q ua bly w it hou t r e la ti on t o a nyth ing e xte r na l. . . " 2 7 B ut in f a c t a s w e know f r om the T he or y of G e ne r a l Re la tivi ty, the r e is no suc h time in o ur unive r se . T he ti me of our unive r se is a c c or ding to G e ne r a l Re la tiv ity r e la t ive , it f lo w s une q ua bly, a nd it f low s w i th r e la tio n to t he distr i but ion of ma t te r a nd the f ie lds, f orc e s a nd bounda r ie s pr oduc e d by it. T his doe s not r ule ou t of c our se tha t loc a lly t ime f low s ( a ppr oxima te ly) e qua bl y. A ssu mi ng t h e Cosmological Principle o ne c ould de f e nd Fr ie d ma nn - u nive r se s w hi c h a llow a uni ve r sa l t ime . T h is a ssump tio n is how e ve r ve r y que s tiona ble ; si nc e if the r e a r e r ota ting subsy ste m s i n t he un ive r se , the n no sta nda r d sync hr o niz a tio n or unive r sa l ti me c a n be e sta blishe d.

( iii) A c c or ding to the T he or y of G e ne r a l Re l a tivit y the spa c e of the un ive r se is c lo se d ( e ve n if the un iv e r se is e xpa nding) ; tha t is, the r e a r e c lose d spa tia l c oor d ina te s or c l ose d s pa c e - like ge ode sic s. O n t he othe r ha nd, w e usua ll y a ss ume tha t t he ti me c oor d in a te is n ot c l ose d; i. e . w e a ssume tha t the r e a r e no c lose d ti me - like ge o de sic s. T hi s a ssu mpt ion ha s be e n c a lle d the c hr onology c on dit ion of spa c e time . 2 8 H ow e ve r , e ve n if the time c oor d ina te w ou ld be c lose d, a s lon g a s the pe r iod w ou ld be m uc h gr e a te r ( f or se ve r a l or de r s of ma gn itu de ) tha n the lif e t ime of the unive r se s o f a r , it w ou ld not ma ke a ny d if f e r e nc e f or a ll pr a c tic a l ( e xpe r ime nta l) pur po se s.

2 5 Cf. Jammer (1954, CSP), ch. 1. 2 6 Aristotle (Phys) IV, 220a25. Cf. Mittelstaedt/Weingartner (2005, LNt), ch. 6. 3. 2. 2 7 Newton (Princ) I, Scholium. Cf. Mittelstaedt (2008, CTP) 2 8 Cf. Hawking, Ellis (1973, LSS), p . 189.

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( iv) T ime a s ti me of thi s w or l d i s me a sur e d in u nit s. T he se u nit s a r e ta ke n f r om tw o ki nds of phy sic a l pr oc e sse s ( c ha nge s) w hic h ha ve a c e r ta in r e gula r ity: pe r io dic pr oc e sse s w he r e the sta te of the syste m r e pe a ts i tse lf a f te r a f inite pe r iod of ti me a nd mono to ne pr oc e sse s. E xa mp le s f or the f ir st a r e da y, ye a r , pe ndulum, c r ysta l c l oc k, a tomic c loc k ( w h ic h give s the mos t e xa c t me a sur e me nt of ti me units s o f a r ) . E xa mple s f or the se c ond is the unif or m mo ve me nt of a body on a str a igh t line ( e qua l dista nc e s in e qua l t ime s) . T he ma in po i nt to r e c ognise c onc e r ning un its of ti me is tha t the y a r e c onve nti ona l to some e x te nd – a s w a s obse r ve d by Poi nc a r é a nd Ma c h – a nd mor e impo r ta ntly tha t t he y a r e r e la tive a nd not a bsol ute . T hus the mos t e xa c t a tomi c c loc k ha s to be re f e r re d to se a le ve l be c a use of i ts de pe nde nc e on gr a vita ti on. I n a dd iti on f a st c loc k tr a nspor t c ha nge s the uni ts of ti me ( se e (v) ) be low .

( v) L ike t he r e is no a bsol ute or un ive r sa l uni t of t ime , t he r e is a lso no a bs olu te or unive r sa l c o nc e pt of si mul ta ne ity, e xc e pt f or ine r t ia l syste ms. T hu s t he r e c a n be dila ta t ion of ti me de pe ndi ng o n the ve loc it y of the ph ysic a l sys te ms ( pa r ts of the w o r ld) r e la tive t o e a c h othe r . I n a sim ila r w a y the un its of d ista nc e a nd of ma ss a r e no t a bs olute , b ut the r e ma y be c ontr a c tion of le ngth a nd i nc r e a sing of ma ss de pe ndin g on move me n t. I n ge ne r a l: T he r e a r e no f r e e ly mo va ble me a sur ing r od s or c loc ks w hic h a r e r igid, i. e . re sista nt a ga i nst c ha nge ( move me n t) . 2 9

Fr om th is a na ly sis of "r e a l " ti me , i. e . of the ti me of our unive r se , i t is c le a r tha t th is t ime c a nno t be a ttr i bute d to G o d or to G o d's k now le d ge . T his c a n be se e n by c onside r ing pr ope r t ie s ( i) to ( v) of the time ( of this un ive r se ) : a d ( i) : I f ti me is a pr o pe r ty of this uni ve r se a nd G od ha s c r e a te d t his unive r se , the n he ha s c r e a te d time by c r e a ting a c h a nging a nd de ve l opi ng un ive r se . T his is a ls o the vie w of the gr e a t Chr i st ia n philo sop he r s, like T ho ma s A qu ina s: " T he phr a se a bout t hing s be ing c r e a te d in the be ginn ing of time me a ns tha t the he a ve ns a nd e a r th w e r e c r e a te d toge the r w ith ti me ; i t doe s not sugge st t ha t t he be ginni ng of ti me w a s the me a sur e of c r e a tion. " 3 0 But if th is is tr ue , the n it ma ke s no se nse to a ttr ib ute thi s ( c r e a te d) time to G od or to hi s a c tions. a d ( ii) : Sinc e e ve r y s yste m of the un ive r se ( e a r th, sta r s e tc . ) ha s its ow n ti me ( de pe nding o n the dif f e r e nt m ove me nts of the s yste ms) a nd t he w hole unive r se c ou ld ha ve a t mos t a n a ve r a ge of thi s r e la ti ve t ime s, b ut c a nn ot ha ve a unive r sa l ti me , it se e ms t he mor e a bs ur d to a ttr ib ute one suc h t ime ( w hic h one ? ) to G od. 2 9 For details see any textbook on Special Relat ivity. For Space Time invariance o f laws of nature cf. Mittelstaedt/Weingartner (2005, LNt), ch. 6. 3 0 Thomas Aquinas (STh) I, 46, 1 ad 4.

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a d ( iii) : I nde pe nde n tly of w he the r the ti me c oor di na te s ( t ime - l ike ge ode sic s) a r e c lose d or no t, the y im ply the d ist inc tion of e a r lie r a nd la te r or of pa s t a nd f utur e ( e ve n if only loc a lly i n c a se the ti me - l ike ge ode sic s w e r e c lose d) . But if G od is e te r na l, pa st a nd f utur e c a nnot be a ttr ibute d to h im ( c f . 3. 3221 be low ) . a d ( iv) : I f the ti me of th is w or l d c a n be a ttr ibu te d to G od ( or to G od' s a c tion s) , the n a lso the ti me uni ts or t ime s ta nda r ds ( me a sur e d by r e gu la r pr oc e sse s of this w or ld) . N ow a s w e know f r o m the T he or y of Spe c ia l Re la tiv ity the r e is no uni ve r sa l ti me a nd n o uni ve r sa l or r i gid t ime u nit, i. e . ti me ( a nd it s un its) a r e de pe nde nt on mo ve me nt suc h t ha t the r e ma y be ti me di la ta tio n. Bu t it w ould be r a the r a bsur d to a ttr i bute s u c h a r e la tivity of ti me unit s to G od. T he r e f or e it w ould be a bsur d to a ttr ibu te the time of this w or l d to G od. a d ( v) : A n a na l ogou s c ons ide r a tio n is c o nc e r ne d w ith si mul ta ne ity : I f the ti me of this w or ld c a n be a t tr ibu te d to G od ( or to G od's a c tion s) , the n a lso sim ulta ne i ty. H ow e ve r , i t i s c le a r f r om the T he or y of G e ne r a l Re la tiv ity tha t the r e is no unive r sa l c o nc e pt of s imu lt a ne ity in a u nive r se w i th gr a v ita ti on a nd r ota ti on; th us it w oul d be r a the r a bsur d to a t tr ibu te to G od ( or t o h is a c tions) suc h a r e la tive c onc e pt of simul ta ne ity. T he r e f or e it w ould be a bsur d to a ttr ibu te the time of this w or l d to G od.

3. 322 T ime a s a Chr ono logic a l O r de r ( i) T ime a s a c hr ono logic a l or de r ( w it h a bina r y r e la t ion earlier than or

later than ) in the log ic a l or ma the ma t ic a l se nse is usua ll y de sc r ibe d by a t le a st f our pr o pe r tie s w hic h a r e f or m ula te d w ith the he lp of a x iom s: I r r e f le xivity, T r a nsi tiv ity, A s ym me tr y, i. e . Pa r tia l O r de r ing a nd D e nsity. T ime i n th is s e n se is d isc us se d in T e nse L o gic s. 3 1 I t ha s se ve r a l a dditi ona l c ha r a c te r istic s w hic h w e lis t u nde r ( ii) - ( iv) be low :

( ii) T his ki nd of c hr onolo gic a l ti me is not r e la tive in the w a y the ti me of our unive r se i s; i. e . it is a ssu me d t o "f low e qua bly " a nd not to be de pe nde nt on mo ve me nt ( ve l oc ity) or on ma t te r a nd its f ie lds. I n th is se n se it is a kind of "a b solu te " or "c onc e pt ua l" ti me . I t is a lso a s su me d tha t th is kin d of time ha s a unique ( or unive r sa l) c onc e pt of simul ta ne ity a nd c onc e ptua l c loc k s w h ic h a r e r igi d a n d w hic h a r e not de pe nde nt on gr a vita tio n or f a st tr a nspor t.

( iii) T his kind of c hr ono log ic a l ti me ma y be a pplie d to r e a l pr oc e sse s in or de r to de sc r ibe the suc c e ssive se r i e s of huma n a c tion s or othe r pr oc e sse s in na tur e a nd te c hnology of e ve r yda y lif e . I f th e doma in is

3 1 One of the first to do this with the means of Symbolic Logic was A. N. Prior. Cf. Prior (1957, TMd). For later development cf. Van Benthem (1991, LgT).

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r e str ic te d in suc h a w a y, the a spe c ts of Spe c ia l a nd G e ne r a l Re la tiv ity ha ve no impa c t be c a use of the r e str ic te d "loc a l ity ". T hu s f or ti me ta b le s of buse s a nd tr a in s a nd e ve n of a e r opla ne s ide a l or r igid c l oc ks a r e suf f ic ie ntl y a c c ur a te . But ne ve r the le ss f or a ny time me a sur e me nt one ha s to use phy sic a l or bi olog ic a l c loc k s ( e ve n if the y a r e unde r s tood a s pur por te d i de a l a nd r igi d c loc ks) w hic h r e f e r to the r e volut ion of t he e a r th or to so me ot he r a ppr oxi ma te ly c onsta n t ( a nd u sua ll y pe r io dic a l) p r oc e ss. O the r w i se c hr ono log ic a l or c o n c e ptua l t ime is no t a pp lic a ble a t a ll.

( iv) A ltho ugh c hr ono log ic a l time i s not bo u nd to the c ha nge in our un ive r se it is st ill bo und to so me kind of loc a l c ha nge . T his c ha nge might be c ha nge in our ( huma n) e nv ir onme n t o r c ha nge of our a c tions w hic h invol ve phys ic a l, physio log ic a l ( f or e xample br a in w a ve s) a nd me n ta l c ha nge s or c ha nge in a pur e ly ide a l ise d me nta l se nse . T h us a l so c hr onolog ic a l ti me ha s c ha nge a s its ne ce ssa r y c onditi on.

( v) A lso c hr ono log ic a l or c onc e ptua l ti me i nvolve s e a r lie r a nd la te r or pa st a nd f utur e . T he di sti nc tio n of pa s t a nd f utur e is ne c e ssa r y f or a ny k ind of time a nd is a l so i mpl ie d by a ny ki nd of c ha nge ( r e ca ll 2. 321( i) a nd a d ( iv) ) .

T ha t ti me in vol ve s pa st a nd f ut ur e ( e a r lie r a nd la te r ) is e vide n t f r om bot h t ime ( unde r stoo d) a s t ime of our uni ve r se a nd ti me ( un de r stood) a s c hr on olog ic a l time : E ve r y dyna mic a l la w de sc r ibe s the ti me de ve lop me nt of a p hysic a l syste m i n s uc h a w a y tha t t he sta te S1 ( t1 ) of the sys te m a t time t1 ( i n t he pa s t) c or r e sponds to a so luti on of the dif f e r e nt ia l e qua tion a nd the sta te S2 ( t2 ) of this syste m a t t2 ( in t he f utur e ) c or r e spond s to a not he r solu tio n of t he dif f e r e ntia l e qua tion. I n thi s c a se sta te S2 ( t2 ) of the f utur e c a n be pr e dic te d w ith the he lp of the dyna m ic a l la w a nd s ta te S1 ( t1 ) of the pa st. I n a si mila r w a y o the r la w s, be side s dy na mic a l a ls o sta t ist ic a l la w s , de sc r ibe the time de ve lop me nt of syste ms in t he un ive r se , e ve n if i n the c a se of sta t ist ic a l la w s the pr e d ic tio ns c onc e r n a huge e nse mble a nd not sta te s of s ingula r ob je c ts. A lso t ime in t he se nse of c hr ono log ic a l or de r invol ve s pa st a n d f utur e . T hi s i s c le a r f r om its unde r lying a xi om s ( f or exa mple pa r tia l or de r ing) a nd f r om i ts a pplic a tio n to pr oc e s se s be the y pr oc e sse s of na tur e , of te c hnol ogy or of huma n ( inc lu sive me n ta l) a c tivit y. Fr om the a bove a na ly sis of c hr onol ogic a l time it i s a lso e v ide nt tha t th is time c a nnot be a ttr ibute d to G od or to G o d's know le dge . T his c a n be se e n a s f ollow s: A c c or ding to ( i) time a s c hr onolo gic a l or de r is c ha r a c te r ise d by f o ur a xioms. N ow the a xi om of pa r tia l or de r ing imp li e s the di sti nc tio n be tw e e n e a r lie r a nd

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la te r or pa st a nd f utur e ; sinc e it sa ys tha t e ve nt A is e a r lie r ( la te r) tha n e ve nt B or B is e a r lie r ( la te r ) tha n A or A a nd B a r e simulta ne ou s. But a s it w a s sa id a bo ve , sinc e G od is e te r na l a nd a r e a sona ble c onc e pt of e te r nity doe s no t invol ve pa st a nd f utur e , c hr onologic a l t i me c a nnot be a ttr ibute d to G o d. A c c or ding to ( iv) c hr on olog ic a l ti me im plie s so me kin d of c ha nge : e ve n if it is not bo und t o the c ha nge of ( in) our unive r se , it is me a sur e d by c loc ks w h ic h a r e c ha nging in phys ic a l or biolo gic a l sy ste ms. N ow e ve r y c ha nge imp lie s the dist inc ti on of pa st a nd f u tur e ( v) . But sinc e G od is e te r na l, the r e c a nnot be pa st a nd f utur e in hi m or in hi s kn ow le dge . T his is so, sinc e a n y r e a sona ble c onc e pt of e te r ni ty i s d ist ingu ishe d f r om inf ini te ti me i n tha t i t la c ks pa st a n d f utur e , w he r e a s on the othe r ha nd e ve r y c onc e pt of ti me ( f inite or inf inite ) invol ve s pa st a nd f utur e or e a r lie r a nd late r . T he r e f or e a lso c hr onologic a l ti me c a nnot be a ttr ibute d to G o d. 3. 3221 Eternity – no succession, no past and future T ha t a r e a sona ble c onc e pt of e te r ni ty do e s not i nvol ve c ha nge nor suc c e ss ion, nor the d ist inc ti on be t w e e n e a r lie r a nd la te r or be tw e e n pa s t a nd f u tur e or be tw e e n be ginnin g a nd e nd w a s de f e nde d sinc e A ugust in a nd Boe thiu s: "T e mp us a ute m quo nia m muta b il ita te tr a nsc ur r it, a e te r nita te

im muta b ili no n pote st e sse c oa e te r num. " 3 2 "E te r ni ty, the n, i s t he to ta l a nd pe r f e c t posse ss ion of lif e w ith ou t e nd, a sta te w hic h be c ome s c le a r e r if compa r e d w ith the w or l d of ti me ; f or w ha te ve r l ive s in t ime live s in the he r e a nd now , a n d a dva nc e s f r om pa st to f utur e . " 3 3

T homa s A qu ina s a gr e e s w ith Boe th ius t ha t e te r nit y i s s im ulta ne o usly w ho le . Mor e ove r he point s out tha t it w ou ld no t be suf f ic ie nt to sa y tha t e te r ni ty ha s ne ithe r be ginn ing nor e nd ( w he r e a s t ime ha s) . Sinc e so me a ssume tha t move me n t ( in t he unive r se ) goe s on f or e ve r . U nde r suc h a n a ssumpti on t ime c ould no t be t he me a sur e of the w hole move me n t, be c a use a n inf i n ity is n ot me a sur a ble , but it c ould me a sur e f i nite pa r ts, i. e . pe r iods, r e vol utio ns, w h ic h ha ve a be ginning a nd e nd: "Be c a use gr a n te d t ha t ti me a lw a ys w a s a nd a lw a y s w ill be ,

a c c or ding to the ide a of those w ho th i nk the move me nt of the he a ve ns goe s on f o r e ve r , the r e w oul d ye t r e ma in a d if f e r e nc e be tw e e n e te r nit y a nd ti me a s B oe thi u s sa ys ( D e Cons ol. V ) , a r ising f r o m the f a c t tha t e te r n ity is sim ulta ne ou sly w hole ;

3 2 Augustine (Civ) XII, 16. 3 3 Boethius (Cons) V, 6.

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w hic h c a nnot be a pplie d to t ime . " 3 4 "T hus e te r nity is kn ow n f r om tw o s our c e s: f ir st be c a use w h a t i s e te r na l is inte r m ina ble – t ha t it ha s no be ginni ng nor e nd ( tha t is, no te r m e ithe r w a y) ; se c ond ly, be c a use e te r nity ha s n o suc c e ssion, be ing s imu lta ne ou sly w h ole . " 3 5

3. 3222 Universe – finite in time Conc e r nin g the q ue sti on w he t he r the unive r se is f ini te or inf i nite in t ime , T homa s A q uina s de f e nde d tha t our un ive r se ha s a f inite a ge . But he ga ve r e a sons tha t this f a c t c a nno t be pr ove d r igor ous ly f r om our kno w le dge a bou t the unive r se w he r e a r igor ous pr oof is unde r stoo d a s a de r iva tion f r om la w s ( in this c a se la w s of na tur e ) . I n his qua r r e l w ith Bona ve n tur a a t the U nive r sity of Pa r is he de f e nde d the vie w t ha t t he be ginni ng i n ti me of the w or ld ( unive r se ) c a nnot be pr o ve d f r om u niv e r sa l pr inc iple s ( la w s) of ( a bou t) thi s w or ld . Be c a use uni ve r sa l pr inc i ple s w hic h ha ve the ir f o unda ti on i n the e sse nc e of things ( or na t ur e ) a bstr a c t f r om hic ( pla c e ) e t nunc ( poin t of ti me ) . T ha t is, la w s of na t ur e a r e spa c e time inv a r ia nt a nd the r e f or e w e c a nnot e xtr a c t a c e r ta in point of time ( be gi nn ing of the unive r se ) or a singula r ity f r o m a la w : "T ha t the w or ld ha s no t a lw a y s e xis te d c a nno t b e

de mons tr a tive l y pr ove d, but i s he ld b y f a ith a lone . . . . T he r ea son is thi s: the w or ld c ons ide r e d in itse lf of f e r s no gr ounds f or de mons tr a tin g tha t i t w a s onc e a ll ne w . For the pr inc iple f o r de mons tr a tin g a n obje c t is its de f in iti on. N ow the s pe c if ic na tur e of e a c h a nd e ve r y obje c t a bstr a c ts f or th e he r e a nd now , w hic h i s w hy un ive r sa ls a r e de sc r ibe d a s be in g everywhere and always. H e nc e it c a nno t be de m ons tr a te d t ha t ma n or the he a ve ns o r stone did no t a lw a ys e xis t. " 3 6

I n th is c o nne c tion I w a n t to me nt ion tha t the q ue sti on w he the r i t c a n be de mons tr a te d tha t the w or l d ha s a lw a ys e xiste d or tha t it ha s a be ginnin g in ( w ith) ti me – a nsw e r e d dif f e r e ntly by c o mpe t ing t he or ie s of the u nive r se – is a que stion a bout t he c omple te ne ss of t he la w s of na tur e . Or a t lea st of tha t la w s w e know . A sy ste m of la w s L a bout a c e r ta in pa r t P of r e a lity is c omple te if a nd on ly if e ve r y tr uth a bo ut P is pr ova b ly ( de r iva ble ) f r o m L. T homa s A qui na s' s ta ndpo int w a s tha t t h e unive r sa l la w s of na tur e ( a bout t his w or ld) a r e not c omple te w it h r e spe c t to a ll que sti ons ( a ll tr u ths) a bou t thi s w or ld. I t is not jus t our insuf f ic ie n t kno w le dge of the la w s of na tur e w ha t he 3 4 Thomas Aquinas (STh) I, 10, 4. 3 5 Ibid. 10, 1. 3 6 Thomas Aquinas (STh) I, 46, 2.

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ha s in min d, but the tr ue la w s itse lf a r e inc omple te a c c or ding to hi m w it h r e spe c t to s ome spe c ia l que s tio ns. T ha t me a ns tha t the r e a r e so me sta te me nts a bout thi s w or ld w hic h c a nn ot be de c ide d w i th the he l p of the la w s a b out th is w or ld. O r in mor e mode r n te r ms : the la w s of na tur e a r e inc omple te w it h r e spe c t to some i mpor ta n t i nit ia l c on dit i ons. T h is pr oble m pla y s a n im por ta nt r ole in the B ig Ba n g T he or y of the c os molo gic a l e vol uti on in r e spe c t to ( a t le a st) the "f ir st thr e e min ute s ". 3 7

3. 323 T ime a s Bi olo gic a l a nd Ps yc holo g ic a l T ime Pe r iod ic or osc illa ti ng pr oc e sse s c a n be obse r ve d on a ll le ve ls of liv ing or ga nis ms. T he f r e que nc y spe c tr um e xte nds f r om mi lli se c onds to h our s, da ys, w e e ks, months a nd ye a r s. T he time r or "biolo gic a l c loc k" f or the se pe r iods or f r e que nc ie s is loc a lise d in the or ga ni s ms ( e ve n in pr ote i ns of ti ssue s a nd or ga ns) th ough c onne c te d or pa r tia ll y sync hr o nise d w it h pe r io ds f r o m e xte r na l f a c tor s; he r e li ght a n d te m pe r a tur e a r e the mos t i mpor ta n t e xte r na l time r s w . r . t. the un it of a ppr ox ima t e ly a da y ( c ir c a dia ne ) ; w he r e the de via tio ns in a r e a s f a r f r om e qua tor a r e a da pte d by the or ga nis ms. T he or ga nis ms ho w e ve r do not f oll ow pa ss i ve ly the se e nv ir on me nta l pe r io ds, but ha ve de ve lope d ( dur i ng e vol uti on) the ir ow n bior hyth m, w hic h is w ith h ighe r or ga nis ms ve r y of te n a c ir c a dia ne r hy th m. A n e xa mp le is t he da ily mo ve me nt of the le a ve s of pla nts. A no the r e xa mpl e f or suc h a bior hyth m or "bi olo gic a l c loc k" in ma mma l s is the pr od uc tio n of the hor mone me la toni ne in the pine a l gla nd dur ing the da r k pe r i od. M or e ove r the se " bio logic a l c loc ks " a r e no t only de pe nde nt on e nvir on me nta l f a c tor s bu t a lso on the spe c if ic D N A . 3 8 Fr om the se f a c ts it i s c le a r tha t like in th e physic a l w or ld a l so in the bio logic a l w or ld the r e is no a bso lute t i me ; a nd w ha t the T he or y of Spe c ia l Re la tiv ity te lls f or the phys ic a l w or ld – tha t e ve r y huge physic a l sy ste m ( sa y pla ne ta r y syste m or syste m of sta r s) ha s it s ow n time – ho lds he r e too, a na logo usly : e ve r y spe c ie s of or ga nis ms ha s i ts ow n time . A n d bo th th e un its of ti me a nd the unif or mit y of f low a r e r e la tiv ise d to in te r na l pe r iodic pr oc e sse s of the 3 7 Cf. Weinberg (1977, FTM). T hat we ca n not decide concer ning such initial conditions (like the question whether the universe has a certain age) was true until very recently indeed when such th ings as the cosmic background radiatio n have been discovered (by Penzias and Wilson in 1 965) w hich is a rather strong support for the finite age of the universe – even if we could not say it is an absolute proof in the sense of demonstration from laws. Since there are also consistent theories of cosmology without a Big Bang. 3 8 Cf. Baumgartner (19 94, ZBZ), especially chapter 2 and 3. For more information see Moore - Ede/Sulzmann (1981, ITO) and Treismann et al. (1990, ICl).

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or ga nis m a nd e xte r na l pe r iodic pr oc e sse s w ith a n a ppr oxi ma te sync hr oni sa tio n be tw e e n the m. A f ur the r s ign f or t he r e la ti vity i s t he d if f e r e nt lif e ti me of dif f e r e nt or ga nis ms. So me ba c te r ia live 2 0 m inu te s be f or e th e y spli t, f lie s live o ne da y, m ic e live 100 da ys, hu ma ns l ive up to a b out 1 00 ye a r s, a nd se quoia s live 40 00 ye a r s. D oe s time f low e qua b ly f or a ll the se dif f e r e nt living c r e a tur e s? H uma ns know tha t t he ir e xpe r ie nc e of how f a st t ime f l ow s is d if f e r e nt w he n w a iting a nd dif f e r e nt w he n e nga ge d i n a n in te r e sting a nd e xc i tin g a c tiv ity. O f a tw o - w e e k holi da y the f ir st w e e k is usua ll y e xpe r ie nc e d a s pa ssi ng m or e slow l y t ha n the se c ond. T he sa me se e m s to hol d f o r e a r lie r a nd la te r pe r iod s of lif e . T his is s o de spi te the f a c t tha t h uma ns u se c loc ks a nd w a tc he s w hic h show t he m ( l oc a lly) o bje c tive uni ts of t ime or t ime inte r va l s. T he suc c e ssi ve c ha r a c te r of psyc hologic a l ti me is e xpe r ie nc e d ve r y c le a r ly w he n we c ons ide r to mo bil ise me a ns i n or de r to r e a c h a goa l. T he ge ne r a l unde r lying s tr uc tur e of suc h a n e xpe r ie nc e d suc c e ssi on is the a xiom of pa r tia l or de r in g e ve n if the inte r va ls ma y be so me ti me s e xpe r ie nc e d a s str e tc he d or c ontr a c te d. T his sho w s tha t ti me in hu ma n e xpe r ie nc e ( psyc hologic a l ti me ) is suc h tha t both i ts un its a nd the unif or mi ty of it s f low is r e la ti vise d to the ki nd of e xpe r ie nc e , to the kind of a ge , to the kind of c ultur e e tc . Mor e ove r it is pla i n tha t, in c ontr a st t o biolo gic a l a nd psyc ho log ic a l ti me , physic a l t ime is c le a r ly mor e obje c tive , e ve n if it is a lso r e la tive w . r . t. units, to si multa ne ity a nd f low . Fr om thi s a na lys is of b iolo gic a l a nd p s yc holog ic a l ti me it w ill be c le a r tha t suc h a ti me c a nnot be a ttr ibute d to G o d or to G od 's kn ow le dge . T hi s c a n be se e n f r om the f ollow i ng r e a sons: ( i) A s the c o nsi de r a tions a bove s how bio lo gic a l a nd p syc ho log ic a l ti me a r e

stil l muc h mor e de pe nding on loc a l a nd spe c if ic dif f e r e nc e s – like c ha nge of the le ng th of the da y or D N A of the r e spe c tive spe c ie s – tha n ph ysic a l ti me of thi s w or ld. But phy sic a l ti me of thi s w or ld ( un ive r se ) c a nnot be a ttr ibute d to G od a s ha s be e n show n a b ove ( 3. 321) . T he r e f or e a ll the le ss bio logic a l or psyc h olog ic a l ti me c a n be a ttr ibute d to G od.

( i i ) Fr om a ll tha t w e know a bou t b iolo gic a l a nd psyc h olog ic a l t ime – a n d Chr ono bio logy a nd Psyc h olo gy know a lot mor e tha n w ha t ha s be e n touc he d a bove – it se e m s muc h mor e r e a sona ble to a ssu me tha t G o d ha s de signe d the t ime sc he du le a nd the "bio log ic a l a nd psyc hol ogic a l c loc ks" w he n c r e a tin g t he se or ga ni sm s tha n to thi nk tha t w e sh ould a pply t he se r e la tiv ise d k inds of t ime unit s a nd ti me f low s to G od him se lf or to his know le dge .

35

3. 4 A ns w e r to th e O b jec t io ns

3. 41 ( to obje c ti on 3. 11) T he se c ond pr e mise of th is a r gume n t is a f a lla c y. T he mis ta ke inv olve d in th is f a lla c y is a lr e a dy c la r if ie d in 3. 3 1. Fr o m kno w ing tha t some e ve nt p ha ppe ns a t so me tim e ( Kpt) , one ca nnot c onc lude tha t the a c tion of kn ow ing ha ppe ns a t so me ( the sa me or othe r ) ti me ( Kt p ) . T his is a c onf usion of tw o dif f e r e nt ti me indic e s, w he r e one be longs to the e ve nt a nd the othe r t o the a c ti on of know ing. N o w a lthou gh f or h uma n s it is f a c tua l ly tr ue tha t if t he y kn ow t ha t so me th ing, p, ha ppe ns a t so me t ime t, the n the y a lso know a t so me ti me t, tha t p( is the c a se ) – this doe s not ho ld in ge ne r a l. E spe c ia lly it doe s no t h old f or G o d: T h ough he kn ow s tha t a c e r ta in e ve n t p of thi s w or ld ha ppe ns a t ti me t of t hi s w or l d, pt ( i. e . so me spe c if ic t ime me a sur e d by so me k ind of c loc k) a n d a lso tha t pt1 ha ppe n s e a r lie r t ha n e ve nt qt 2 ( in th is w or ld) , it doe s n ot f o llow f r om tha t tha t his know le dge is a t a c e r ta in time . T he r e f or e the se c ond pr e mise is f a lse a nd the c onc lus ion i n 3. 11 is not pr ove d. 3. 42 ( to o bje c tio ns 3. 1 2 a nd 3. 1 3) I t i s c or r e c t to sa y t ha t to know a bout p a st ( pr e se nt) e ve nts i mpl ie s to know a t w ha t time the y ha ppe ne d ( ha p pe n) . But to know a t w ha t ti me e ve nt p ha ppe ns, d oe s not i mply to know thi s a t some ( this) t ime , a s ha s be e n c la r if ie d in 3. 31 a nd 3. 41 a bo ve . T hus if G od know s tha t t he pa st e ve nt ( pr e se n t e ve n t) ha p pe ns a t t ( of thi s w or ld) it doe s n ot f ollow t ha t he know s thi s a lso a t t ( of th i s w or ld) or a t so me othe r ti me of this w or ld.

36

37

4. Whet her God Kn ows Al l P ast and P r e sent

E vent s T his que st ion c a n a l so be e xpr e s se d in t he f ollow ing w a y: I s it c or r e c t t o sa y tha t if e ve nt e oc c ur r e d in the pa st or e ve nt e oc c ur s a t pr e se nt, the n G od know s tha t e oc c ur r e d in the pa st or a t pr e se nt? O r sy mb olic a ll y, w he r e pt ≤ 0 me a ns tha t e ve nt e oc c ur r e d a t t < 0 ( pa st) or t = 0 ( pr e se nt) : ∀p( pt ≤ 0 → gKpt ≤ 0 ) ? 4. 1 A rg u me nt s A g ai ns t

4. 11 T ha t G od know s a ll pa st a nd pr e se nt e ve nts me a ns tha t if a n e ve nt oc c ur r e d ( oc c ur s) in the pa st or a t pre se nt, the n G od know s it. T hu s the oc c ur r e nc e of the r e spe c tive e ve nt is the r e a son or c a use f or G od' s kn ow le dge of it. Bu t t his is i mpo ssi ble , si nc e G od h a s c r e a te d the w or ld in w hic h a ll pa st a nd pr e se nt e ve nts oc c ur . T he r e f or e it doe s not se e m to be r igh t to sa y tha t G o d kn ow s a l l pa s t a nd pr e se nt e ve nts. 4. 12 I f the know le dge of G od is t he c a use o f things ( e ve nts) a nd if G od kn ow s a ll pa st a nd pr e se nt e ve nts, t he n G od is the c a use of a ll pa st a nd pr e se nt e ve nts. N ow a c c or ding to T ho ma s A q uina s "t he know le dge of G od is t he c a use of th ing s". 3 9 T hus G od se e m s t o b e the c a use of a ll pa s t a nd pr e se nt e ve nts. Bu t t his is i mpos sib le si nc e unde r the pa st a nd pr e se n t e ve nt s the r e a r e f r e e immor a l a c tions ( sin s) of me n w hic h c a nnot be c a use d by G od. T he r e f or e it c a nnot be tr ue tha t G od know s a ll pa st a nd pr e se nt e ve nts. 4. 2 A rg u me nt s P ro

G od's kn ow le dge mu st be muc h m or e pe r f e c t a nd muc h mor e c omple te tha n ma n's know le dge . A nd on the a ss ump ti on tha t G od ha s c r e a te d t his uni ve r se , his kn ow le dge a bo ut i ts ( pa st a n d pr e s e nt) e ve nts m ust be mos t pe r f e c t a nd mos t c omp le te . N ow to know the pa st a nd pr e se nt e ve nts mi gh t be poss ible i n pr inc iple f or ma n e ve n if i t i s no t po ssi b le in fact be c a use of the hu ge nu mbe r of pa st a nd pr e se nt e ve n ts ( of th is un i ve r se ) a nd a lso be c a use of the ma ny hidde n pa r a me te r s not kn ow n so f a r . 3 9 Thomas Aquinas (STh) I, 14, 8.

38

So muc h t he mor e G od mus t know a ll p a st a nd pr e se nt e ve nts. 4. 3 P r opo se d A n sw e r

G od k now s a ll pa st a nd pr e se nt e ve nts. T h is c a n be s uppor te d by the f ollow ing tw o i ndir e c t a r gume nt s: ( 1) Supp ose the r e w oul d be a n e ve nt ( in th e pa st or a t pr e se nt) suc h tha t G od

doe s no t k now tha t it oc c ur r e d . Sinc e the e ve nts w i th w hic h w e a r e c onc e r ne d a r e e ve nts of this w or ld ( un iv e r se ) , the time a t w hic h the y oc c ur is a lso the ti me of this unive r se ( c f . c h. 3. 32) . T hus the e ve nts a nd the ir oc c ur r e nc e a t some ti me be l ong to th is w or ld ( u nive r se ) . T o be i gno r a nt of one of t he e ve nts of thi s un ive r se w o uld me a n t ha t G od ha s in suf f ic ie nt or inc omp le te know le dge of hi s ow n c r e a tion. A nd s inc e w e a ssume ( se e intr od uc tion) tha t G o d ha s r e a lly c r e a te d thi s w or ld – no t ou t of a nyt hing a nd he ha s not me r e ly give n a s tr uc tur e to some th ing a lr e a dy the r e – it is impo ssi ble tha t he is ig nor a nt of some p a r t of his c r e a tion. T he r e f or e G od know s a ll pa st a nd pr e se nt e ve nts ( of this w or l d, unive r se ) . O bse r ve tha t "r e a l c r e a tion n ot ou t of a nythin g" d oe s not ye t de te r m ine f ur the r pr ope r tie s. I t d oe s n ot pr e supp ose tha t c r e a tion is f in ishe d a t a c e r ta in time a nd is pe r f e c tly c ompa ti ble w ith a long e vo lut iona r y pr oc e ss in w hic h a ls o de gr e e s of f r e e dom a nd c ha nc e ha ve the ir pla c e . I t is only inc ompa tib le w ith a n e volu tio n ou t of not a ny thin g ( out of "n oth ing ") by c ha nc e . Be c a use in this c a se the c onc e pt of c ha nc e se e ms to be pr oble ma t ic , if not inc on sis te nt, si nc e a ny de f ini tion of c ha nc e pr e suppo se s thing s, ob je c ts or sta te s ( w h ic h a ga in pr e suppose thi ngs or ob je c ts) w hic h a r e a l r e a dy the r e . T his c a n be se e n by a n a na lysi s of the c onc e pt of c ha nc e . A w ide r de f in iti on of c ha nc e w . r . t. e v e nts i s th is: e ve nt e 2 ha p pe ns b y c ha nc e a f te r ( or w . r. t. ) e ve nt e 1 if f ther e is no dyna m ic a l ( de te r min ist ic ) la w suc h tha t w e c ould e xpla in a nd pr e dic t e 2 w ith the he lp of e 1 plus the r e spe c tive la w . A mor e na r r ow de f ini tio n is : e 2 ha ppe n s b y c ha nc e a f te r ( or w . r . t. ) e ve nts pr e c e ding e 2 if f the r e a re ne ithe r dyna mic a l nor sta ti stic a l la w s suc h tha t e 2 c oul d be e xp la ine d o r pr e dic te d w it h the he lp of suc h la w s a nd pr e c e ding e ve nt s. A dif f e r e nt de f in iti on i s t ha t of a c ha nc e se que nc e ( i. e . a se que nc e of e ve nts by c ha nc e ) due to Cha iti n: A c ha nc e se que nc e is a se que nc e of obje c t s ( n umbe r s, le t te r s, th ings, . . . in the sim ple st c a se a 0 - 1 - se que nc e ) f or w h ic h the r e is no de sc r ipt ion or c ode or c ompute r pr ogr a m w h ic h is shor te r tha n the se que nc e itse lf . A ll thr e e de f in itio ns of c ha nc e or mor e a c c ur a te ly of "e ve nt by c ha nc e " pr e suppose ob je c ts or e ve nts or s ta te s ( c ompose d of o bje c ts) w he r e the se obje c ts a r e r e a l o bje c ts, n ot me r e ly c o n c e ptua l ob je c ts like num be r s. T hu s

39

if the r e a r e no obje c ts of a ny sor t, the r e c a nnot be sta te s or e ve nts a nd c onse que ntl y c ha nc e c a nnot be de f ine d. A lso a n e ve nt or sta te c a nnot de ve lop by c ha nc e out of not hin g ( out o f not a ny th in g) si nc e the r e is o nly c ha nc e f or a n e ve nt w . r . t. ea r lie r e ve nts. Sinc e r e a l c r e a tion ( not out of a nythin g) doe s not pr e sup pose o bje c ts, e ve nts or sta te s w hic h a r e a lr e a dy the r e , r ea l c r ea tion c a nnot oc c ur by c ha nc e .

( 2) I f the r e is a n e ve nt ( in t he pa st or a t pr e se nt) of thi s w or ld of w hic h G od w ould no t know , the n G od w ou ld not k now his ow n po w e r . Be c a use G od c a n know h is ow n pow e r o nly if he kn o w s to w ha t h is p ow e r e xte nds. But his pow e r e xte nds f ir s t to a ll f a c ts of hi s c r e a tion ( of the w or ld) w . r . t. pa s t a nd pr e se nt a nd se c ond, mor e ove r to possib le f a c ts w hic h a r e c ompa tible w ith hi s E sse nc e a nd w ith G od's p la n a nd c omma nds c onc e r ning hi s c r e a tion. 4 0 T he r e f or e be ing ignor a nt of some e ve nt ( in the pa st or a t pr e se nt) of thi s w or ld w ould me a n to ha ve ins uf f ic ie nt ( a nd no t pe r f e c t a nd not c omp le te ) know le d ge of the e xte nsion of hi s pow e r c onc e r ning the w or ld. B ut t his is im poss ible f or G od a s a pe r f e c t be ing. S inc e a pe r f e c t be ing mu st know h is ow n po w e r .

T he r e f or e w e ha ve to a ssume tha t t he r e is no e ve nt of thi s w or ld ( i n the pa st or a t pr e se nt) of w hic h G od w ould no t ha ve know le dge . A nd c onse que nt ly: G od know s a l l pa st a nd pr e se nt e ve nts ( of his c r e a tion) . 4 1 4. 4 A ns w e r to th e O b jec t io ns

4. 41 ( to 4. 11) T he c or r e c t me a nin g of t he sta te me nt "G o d know s a ll pa s t a nd pr e se nt e ve nts " i s a n if - t he n sta te me nt ( impl ic a tion) in the se nse : I f e ve nt e oc c ur r e d in the pa st or if e ve nt e oc c ur s a t pr e se nt, the n G od kno w s tha t e oc c ur r e d in the pa s t or tha t e oc c ur s a t pr e se nt. Sy mbo lic a lly : ∀p( pt ≤ 0 → gKpt

≤ 0 ) . A nd w e m a y a dd: I f e ve nt e oc c ur r e d in the pa st or e ve nt e oc c ur s a t pr e se nt, the n G od a l so k now s how e oc c ur r e d in t he pa st a nd h ow e oc c ur s a t pr e se nt. But a n if - the n sta te me nt ( imp lic a ti on) d oe s not ne c e ssa r ily r e pr e se nt a c a usa l r e la tion. A lth ough s ome c a usa l r e la tion s a r e f or mula te d a s impl ic a tion s; bu t a lso in this c a se the me a ning of a n im plic a tio n ( give n b y tw o va lue d tr u th

4 0 Cf. Weingartner (2003, EDK), ch. 7. 451 and 7.452 and Appendix Def. 4, and this book ch. 11 a nd chs. 13. 22 and 13. 23. 4 1 If in addition to this world (universe) other par ts of creation (like that of immaterial spirits or angels) are included, the extensi on o f God' s power will al so include thi s part of creation.

40

ta ble s or by r ule s in C la ssic a l L og ic or by o the r ma tr ic e s or r u le s in W e a ke r L ogic s) i s no t suf f ic ie nt t o de sc r ibe a c a usa l r e la tion ; it c a n be a t be st a ne c e ssa r y c ondi tion f or suc h a r e la tio n. T hus the se c ond pr e mi se of the a r gume nt in 4. 11 is f a lse a nd the r e f or e the c onc lusion i s not pr ove d. 4. 42 ( to 4. 12) T he k now le d ge of G od is no t a suf f ic ie nt c a use of thin gs ( e ve nts) of his c r e a t ion but onl y a ne ce ssa r y one like the know le dge of the de signe r is a ne c e ssa r y c ondit ion f or t he thing s he de s igns. T h us T homa s A quina s sa ys i n the sa me a r tic le c ite d in 4. 12: "H is k now le dge m ust be the c a use of th ings, ins of a r a s hi s w ill is j o ine d t o i t. " 4 2 T he r e f or e G od c a n ha ve know le dge of f r e e immor a l a c tion s of me n w ithou t c a using the m. Sinc e c onc e r ning i mmor a l a c t ions he ne ithe r w ill s tha t the y oc c ur nor w ill s tha t the y do no t oc c ur b ut pe r mit s t he m to oc c ur . Be c a use if he w oul d w i ll tha t the y do not oc c ur , the y w ould not oc c ur , sinc e his w i ll is a lw a y s f ulf i lle d. T he r e f or e he ke e ps ba c k ( or ke e ps of f ) his w i ll w . r . t. f r e e a c tions of me n sinc e he is n ot a n a llw i lli ng a nd no t a n a l lc a usin g G o d be c a use he ha s gi ve n the a bil ity of c a using to hi s c r e a tur e s, a nd tha t of f re e ly c a using, to some of the m. 4 3

4 2 (STh) I, 14, 8. 4 3 For a detailed discussion of the wrong thesis of an allwilling and allcausing God – which is not a the sis of the great religions Jud aism, Christianity an d Islam anyway – and for its connection with religious fatalism see Weingartner (2003, EDK), ch. 6. 4.

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5. Whet her God' s Know l edge E xceed s Hi s

P ower G od's pow e r e x te nds to a ll tho se sta te s o f a f f a ir s w hic h he can br ing a bou t ( or can ma ke t o oc c ur ) but doe s not ne e d t o a c tua lly br ing a bout ( doe s n ot ne e d to m a ke oc c ur r ing) . T hus this que s tio n c a n a lso be f or mula te d in this w a y: D o the sta te s of a f f a ir s w hic h a r e know n by G od e xc e e d the sta te s of a f f a ir s w hic h he c a n br i ng a bo ut ( c a n ma ke ) in c luding tho se he a c tua ll y br i ngs a b out ( a c tua lly ma ke s oc c ur r ing) . 5. 1 A rg u me nt s A g ai ns t

5. 11 G od's po w e r ( or omnipo te nc e ) e xc e e ds the f a c ts; tha t is he can br ing a bout ( c a use ) sta te s of a f f a ir s w hic h a r e not r e a lise d f or insta nc e tha t a f ur the r spe c ie s of a ni ma ls oc c ur un de r the l ivi ng spe c ie s. But w ha t is not the c a se ( tha t this f ur t he r spe c ie s live s) c a nnot b e know n by him, ot he r w ise he w ould know so me th ing w h ic h is f a lse , w hic h is i mpos sib le ( unde r the sup posi tio n tha t he is omn isc ie nt) . T he r e f or e G od's pow e r e xc e e ds his know le dge . 5. 12 W ha te ve r G od kno w s is tr ue ( se e c h. 1. 3) ; a nd w ha te ve r is tr ue c or r e sponds to a f a c t. W ha te ve r c ome s unde r G od's pow e r ( i. e . w ha te ve r G od can c a use or can w il l) m ust be c onsi st e nt w it h G od 's e sse nc e . Bu t the r e a r e sta te s of a f f a ir s tha t a r e c ons iste n t w it h hi s e sse nc e a n d w h ic h c o me un de r G od's pow e r ( li ke c r e a ting a not he r w or l d) a lthou gh t he y a r e not r e a li se d f a c ts; a nd thus the y c a nnot be kno w n by hi m. T he r e f or e G od's pow e r e xc e e ds his know le dge . 5. 13 T he r e se e m to be sta te s of a f f a ir s ( e ve nts) w hic h G od can ( c ou ld ) w i ll to br ing a bout ( c a n c a use ) but w hic h he ( in f a c t) doe s not w ill t o br ing a bou t: "S o nothi ng pr e ve nts the r e be ing so me thing i n the divine pow e r w hic h he doe s not w il l. " 4 4 But unde r those e ve nts w hic h G od doe s not w il l to br ing a bout a r e th ose w h ic h no body e lse br i ngs a bo ut. A nd of t he se it c a nnot be know n tha t t he y a r e . T he r e f or e G od's know le dge doe s no t e xc e e d G od's pow e r .

4 4 Thomas Aquina s (STh) I, 25, 5 ad 1.

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5. 14 W ha te ve r G od know s he know s ne c e ssa r ily ( c h. 2) . A mong tho se sta te s of a f f a ir s w hic h c a n be w ille d by G od some a r e w ille d n e c e ssa r ily ( a ll tho se c onc e r ning hi s e sse nc e ) a nd so me oth e r s a r e e ithe r w ille d not ne c e ssa r ily ( those c onc e r ni ng the w or ld) or c a n be w il le d n ot ne c e ssa r ily ( those w hic h c ould be r e a lise d but a r e not) . T he r e f or e w ha t G od c a n w ill ( G od's po w e r ) e xc ee ds G od's know le dge . 5. 2 A rg u me nt s P ro

5. 21 W he ne ve r a n e ve nt ( hu ma n a c tion ) is a mor a l e v il, the n G od d oe s no t w ill i t a nd G od c a nn ot w i ll ( a nd c a nnot c a use ) it. T his is s o f or tw o r e a sons : f ir st be c a use e ve r yth ing tha t G od c a n w ill ( c a n c a use ) a nd e ve r y thin g tha t he w ill s ( or c a use s) is goo d. Se c on dly be c a use G od ha s c r e a te d ma n w ith f r e e w ill w h ic h a llow s hi m ( ma n) a lso t o c omm it m or a lly ba d a c tio ns. A nd t hus i t w ould be inc o nsi ste nt to c r e a te ma n w ith f r e e w ill a nd g ive hi m mor a l c omma nd s on the one ha nd a nd c a use mor a l e vil on the othe r . But t he e ve nts w hic h a r e mor a l e vi ls c omm it te d by me n a r e know n b y G od. T he r e f or e G od's know le dge e xc e e ds G od's pow e r . 5. 3 P r opo se d A n sw e r

G od's know le d ge e xc e e ds G od's pow e r . T ha t th is i s so c a n be su bsta n tia te d b y show i ng tha t the sta te s of a f f a ir s ( e ve nts ) w hic h a r e know n by G od e xc e e d the sta te s of a f f a ir s w hic h he c a n br in g a bout ( c a n c a use or c a n w i ll) . G od’ s know le dge e xte nds to f our gr e a t dom a ins: H is know le dge a bou t h im se lf ( a bout his e sse nc e ) , his kno w le dge a bout log ic a nd ma the ma t ic s, his know le dge a b out his c r e a tion a nd hi s know le dge a bou t a ll pos sib ili tie s c onsis te nt w ith h is e s se nc e a nd w ith lo gic a nd ma the ma tic s. N ow h is pow e r c onc e r ns only his c r e a tion a nd the po s sibi lit ie s c on sis te nt w ith his e sse nc e a nd w ith l ogic a nd ma t he ma t ic s; i t doe s ne ithe r c onc e r n himse lf ( hi s e sse nc e ) nor log ic a nd ma the ma t ic s. T he r e f or e G od’ s kn ow le dge e xc e e ds G o d’ s pow e r . Mor e ove r i t c a n be show n t ha t a l so c o nc e r ning t he do ma in of c r e a t ion ( a nd c r e a tur e s) a nd tha t of possibi li tie s G od’ s know le d ge e xc e e ds his pow e r . T his w ill be c ome e vide n t f r om a de f in it ion of omn ipo te nc e . W e sha ll the r e f or e f ir st g ive a de f ini tio n of o mn ipo te nc e a nd the n c onsi de r the pa r ts of i ts de f inie ns w . r . t. the qu e stion w he t he r G od's know le dge e xc e e ds his pow e r .

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5.31 Definition of Omnipotence (God's power) D e f . 1: G od is omnip ote nt if f

( 1) W ha te ve r G od w ills i s r e a lise d a nd ( 2) G od c a n c a use ( c a n w ill, c a n ma ke ) e ve r y sta te of a f f a ir s ( e ve nts)

w hic h ( a ) is se lf c onsiste nt a nd ( b) is c ompa tib le w ith G od 's e sse nc e a nd ( c ) is c onditiona l ly c ompa tib le w ith G od 's pr ovide nc e a nd ( d) is c ompa tib le w ith G od 's c om ma nds.

I n thi s de f in iti on c o ndit ion ( a ) f ollow s f r om c o n dit ion ( b) ; s uc h t ha t one c o uld dispe nse w i th ( a ) . H ow e ve r , f or a de ta il e d disc u ssi on it se e ms be tte r to li st a l l the f our c onditi ons. A shor t e la bor a ti on of the se c onditi ons is a s f ol low s : ( 1) sta te s tha t G od' s w il l is a lw a ys f ul f ille d, i. e . if G od w ills tha t a c e r ta in sta te of a f f a ir s ( a c e r ta in e ve nt) p oc c urs, the n p oc c ur s. O r in othe r w or ds : it is not t he c a se ( in f a c t: it c a nnot be the c a se ) tha t G od w ills so me th ing, sa y tha t e ve nt e oc c ur s, bu t e ve nt e doe s no t oc c ur . T his f r e que nt ly ha ppe n s w i th t he w ill of me n tha t the ir de sir e s a r e not r e a lise d, but it c a nnot ha ppe n to a n omni pote n t ( or a lmigh ty) G od. I t c ould be ob je c te d tha t G o d w il ls t ha t ma n doe s n ot si n, a lthou gh ma n sin s. But in th is c a se w e ha ve to a s su me tha t ma n 's a c t ion is a f r e e w il l de c i sion, othe r w ise it c ou ld n ot be a sin. A n d c o nc e r ning s ins tha t oc c ur , G od ne it he r w ill s tha t the y oc c ur nor w il ls tha t the y do not oc c ur ( othe r w ise the y w o uld not oc c ur ) ; be c a use he i s ne i the r a n a l l w ill ing nor a n a llc a usi ng G od a nd c a n ke e p of f hi s w il l f r o m s uc h f r e e a c ti ons. T he r e f or e w e ha ve to sa y tha t c onc e r ning m or a lly r e le va n t a c tio ns or c onc e r ning w ha t he w i ll s a c c or ding to his c o mma n ds ( tow a r ds ma n) G od w ill s tha t ma n should will a n d should act in a mor a lly good w a y. Bu t f r om "G od w ill s tha t ma n should w i ll ( a c t) mor a lly go od" i t doe s not f oll ow tha t "G od w il ls ( dir e c tly) tha t ma n w ill s ( a c ts) mor a lly goo d". A n d a lt houg h it f ollow s t ha t a n a c ti on w h ic h i s i n a c c or da nc e w ith w ha t G od w il ls t ha t ma n shou ld w ill a n d do is mor a l ly good, it doe s no t f ol low tha t the r e spe c tive a c tion is a c tua lly c o mm itte d b y ma n, sinc e it is st ill a f r e e w ill de c ision. 4 5 a d ( 2) : But G o d's o mn ipote nc e is not r e str ic te d to w ha t he w il ls or to w ha t he c a use s; i. e . it is not r e str ic te d to the e f f e cts of his w il l a nd c a use : "W he nc e it f oll ow s tha t H is e f f e c t is a lw a ys le ss tha n th is p ow e r . " 4 6 T he r e f or e in pa r t ( 2) of the de f inie ns f our ne c e ssa r y ( toge the r suf f ic ie nt) c ondi tio ns a r e 4 5 For further details see Weingartner (2 003, EDK), chs. 6. 4, 7. 45; Appendix, definitions D4, D7, D11, D12. Cf. below ch. 13, D13 and D15 and 13. 25. 4 6 Thomas Aquinas (STh) I, 25, 2 ad 2.

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liste d f or G o d's pow e r in the se n se of w ha t G od can c a use ( or can w il l or can ma ke or can br ing a bo ut) . A lth ough he doe s not ne e d t o, in f a c t, c a use it ( or w ill i t, or ma ke it, or br ing it a bout) . Be f or e I sha ll c omme nt on the f our c onditio ns it i s ne c e ssa r y to sa y some t hing a bou t the r e la ti on of c a usi ng a nd w i lli ng in G od. A c c or di ng to the de f init ion D 5 of c h. 13 be low “ G od c a use s tha t p” ( gCp) i s de f ine d a s “ p be longs to the the or e m s a bou t ( G od’ s) c r e a tion a nd G od w ill s t ha t p” ( gWp) . T hus it h old s tha t w ha te ve r G od c a use s he w i lls. But the o ppos ite d oe s no t hold s inc e G od ( ne c e ssa r ily or by h is ow n na tur e ) w ill s ( a nd c a n w il l) his o w n e xiste nc e a nd his goo dne ss but he doe s not ( a nd c a nnot) c a u se it. A lso a s a f ir st c a use he is only r e la te d to his c r e ation a nd c r e a tur e s but not to hi mse lf . T he soc a lle d “ c a usa su i” is a n i nve nt ion of M ode r n T i me s ( c f . Spin oz a , E thic s, D e f . 1) bu t in A r is tot le a nd in t he Mid dle A ge s the c a usa l r e la tio n i s a lw a ys ir r e f le xive . S im ila r ly i t ho lds : W ha te ve r G od c a n c a use he c a n w ill; or : w ha te ve r he c a nnot w i ll ( or doe s n ot w il l) he c a nnot c a use ( or doe s no t c a use ) . T he r e f or e c onc e r ning his c r e a ti on, w ha t he c a u se s a nd w ha t he w il ls c oinc ide a nd s inc e his pow e r i s a lso c o nc e r ne d w ith h is c r e a tion w ha t he c a n c a use a nd w ha t he ca n w ill c oinc ide too. T he f ir st c ond iti on sa ys tha t w ha t G od c a n c a use ( c a n w ill, c a n ma ke , c a n br ing a bout) mu st be se lf - c onsis te nt. I nc onsis te nt sta te s of a f f a ir s (e ve nts) c a nnot be c a use d a nd c a nnot be done by a pe r f e c t pe r son. I n othe r w or ds G od's pow e r is b oun d to c on sis te nc y. But ob se r ve tha t th is is on ly a sig n of pe r f e c tion si nc e only i mpe r f e c t be ings like h uma n s c a n ha ve i nc ons iste n t thoug hts. T he se c ond c ondit ion sa ys t h a t w ha t G od c a n c a use ( c a n w ill, c a n ma ke , c a n br ing a bout) ha s to be c ompa tible w it h G od's e sse nc e . W e ma y e xpr e ss th is a lso by sa yin g t ha t i t ha s to be c o mpa t ible w ith a ll w ha t G od ne c e ssa r ily kn ow s a n d ne c e ssa r ily w i l ls a bou t h im se lf . I n th is se nse i t i s impo ssi ble tha t G od c ould c a nc e l hi s o w n e xis te nc e or h is ow n goo dne ss. T he thir d c on dit ion sa y s tha t G od c a n c a use ( c a n w ill, c a n ma ke , c a n br ing a bou t) only sta te s of a f f a ir s ( e ve nts) w hic h a r e c onditiona l ly c ompa t ible w i th his pr ovide nc e . G od's pr ov ide nc e is his p la n c onc e r ning c r e a tion. I t doe s not c onc e r n himse lf ( h is e sse nc e ) a nd it d o e s not c onc e r n the la w s of log ic or of ma the ma t ic s. W e ma y give a de f inition of pr ovide nc e a s f ollow s: D e f . 2: A sta te of af f a ir s or a n e ve nt p belongs t o G od's pr o vide nc e if f

( 1) G od know s tha t p a n d ( 2) p be longs to the the or e m s a bout c r e a tio n ( 3) G od le a ds p tow a r ds i ts goa l or G od su bor dina te s p u nde r some goa l

or hig he r good or w ill s c on dit iona l ly tha t p in or de r to sa t isf y a highe r good.

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( 4) G od pe r mits tha t p . T hus w ha t G od c a n c a use ( c a n w ill, c a n ma ke , c a n br ing a bo ut) ha s to be c ompa ti ble w it h G od 's kn ow le dge ( D e f . 2 ( 1) ) . O bse r ve tha t a lso e ve nts w hic h p oss ibly oc c ur bu t d o n ot in f a c t oc c ur a r e inc lude d in G od 's pr ovide nc e via his kno w le dge : he know s tha t ( a nd how ) the y a r e possible . G od’ s pr o vi de nc e is c onc e r ne d w ith c r e a tion ( D e f . 2. ( 2) ) . T hus G od’ s pow e r or om nipo te nc e m ust be c o mpa ti ble w it h w ha t ha ppe ns thr ough hi s c r e a tion, i. e . w ith a ll t he pa st a nd pr e se nt e ve nts of c r e a tion ( c f . c h. 4) a nd ( c onditi ona ll y) w it h a ll the f u tur e e v e nts w h i c h c a n be i n h is p la n a nd know le dge ( c f . c hs. 10 a nd 11) . Cond it ion ( 3) sa ys tha t e ve r y sta te of a f fa ir s be longi ng to G od’ s pr ov ide nc e is one w hic h is le d by hi m to w a r ds its g o a l or is subor di na te d und e r so me goa l or highe r good or is w ille d c ond iti ona l ly to sa tisf y a highe r good. T hu s he le a ds ma n by h is c o mma n dme nt s a nd r e le va tion t ow a r ds h is g oa l ( w i thou t viola t ing ma n’ s f r e e w ill) a nd he le a ds liv ing c r e a tur e s w it hout in te lle c t to the ir goa ls by g iv i ng the m inst inc t a nd a bilit ie s to le a r n a nd impr o ve . T he sa me is tr ue f or those sta te s of a f f a ir s ( eve nts) w hic h G od w i lls c on dit iona l ly f or some goa l, viz . f or some highe r good. For e xa mp le he w ills j ust punis hme n t be c a use he w i lls the h ighe r good ( goa l) of ul ti ma te poe t ic ju stic e ; or he w ills tha t so me c r e a tur e s a re le ss pe r f e c t tha n othe r s be ca use he w ills the mul tip lic i ty a nd dif f e r e ntia te d s tr uc tur e of the unive r se ; or he w il ls tha t livi ng or ga nis ms le a r n by tr ia l a nd e r r or be c a use he w i lls tha t i mpe r f e c t c r e a tur e s c ontr ibute t o the ir ow n de ve lo pme nt a nd to t he de ve lop me nt of the w hole unive r se . A c c or ding to I n w a ge n 4 7 free will, natural indeterminism a nd the initial state of the c r e a te d uni ve r se do not be lon g t o G od’ s p la n or pr ovi de nc e . T he r e a son f or suc h a vie w c ould be tha t I nw a ge n ide ntif ie s G od’ s pla n ( G o d’ s pr ovide nc e ) w it h G od’ s w ill. But a l tho ugh it hol ds tha t w ha te ve r G od w ill s c onc e r ning his c r e a tion be long s a lso to his pr ovi de nc e , the opposite doe s not hold; i. e . the r e a r e some sta te s of a f f a ir s, like oc c ur r ing mor a l e vi ls, tha t be long to G od’ s k now le d ge a nd to G o d’ s pr ovi de nc e but not to his w i ll sinc e he doe s not w il l the m t o oc c ur nor doe s he w ill the m no t to oc c ur but he pe r mits the m to oc c ur . A nd c o nc e r ning his w i ll it h old s tha t his w il l is a lw a ys f ulf ille d viz . w ha te ve r he w i lls is the c a se . So i n th is r e spe c t the r e is n o pla c e f or f r e e dom, inde te r m ini sm or c ha nc e . N ow c onc e r ning ma n’ s a c t ions of f r e e w ill w e ha ve a lr e a dy sa id tha t G od ’ s c omma nd s w hic h be lon g to his pr ovide nc e me a n tha t G od w i lls tha t ma n should w i ll a nd a c t a c c or dingl y; bu t it doe s not me a n tha t G o d w ill s ( dir e c tly) tha t ma n w il ls a nd a c ts tha t w a y, 4 7 Inwagen (1995, GKM) p. 54

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othe r w ise ma n w o uld a lw a ys o be y G o d’ s w il l w i tho ut ha v ing f r e e do m ( c f . c h. 13, de f initio n 15 a bout G o d’ s w il l w . r . t. ma n) . Conc e r nin g in de te r min is m w e ma y sa y tha t G od mu st ha ve c r e a te d the w or ld in suc h a w a y tha t t he r e a r e de gr ee s of fr e e dom in r e a lity a lr e a dy a t t he le ve l of non - l ivin g c r e a tur e s in a l l the doma ins w he r e w e u se sta t is t ic a l la w s in physic s ( c f . c h. 7 be low ) . A nd on highe r le ve ls w . r . t. living c r e a tur e s the y a r e c r e a te d in suc h a w a y tha t t he y le a r n via tr ia l a nd e r r or w hic h a ga i n pr e suppose s de gr e e s of f r e e dom a nd th a t the y go t the a b ili ty of be ing c a use s a nd pa r tic ipa t ing in the de ve lo pme n t of the w or l d. Conc e r ni ng t he c ha nc e of the f ir st i nit ia l c on dit ion s t oda ys c os molo gy know s ve r y li ttle a bout the que sti ons w ha t kind of c ha nc e thi s r e a l ly w a s. W ha t i s r a the r c e r ta in is tha t the se f ir st in itia l c ond iti ons w hic h inc lu de a lso imp or ta nt c o nsta n ts of na tur e c a n ha r dly ha ve a lte r na tive va lue s if only a ve r y w e a k ver sion of the anthropic principle is c or r e c t. 4 8 T hus w hy c ould n ot so me th ing l ike the a nthr opic pr inc i ple be long t o G od’ s pla n or pr ovide nc e ! W ha t G od pe r m its, be l ong s to h is pr o vi de nc e but not ne c e ssa r ily to hi s pow e r ( D e f . 2 ( 4) ) . T hus he pe r m its tha t e ve n ts oc c ur w h ic h a r e mor a l e v ils. T ha t me a ns t ha t he doe s not w i ll tha t suc h e v e nts d o no t oc c ur . Be c a use ot he r w ise mor a l e vil w ou ld no t oc c ur sinc e his w i ll is a lw a ys f ulf ille d a s c ond itio n ( 1) of the de f ini tion of om nipo te nc e sa ys. A nd the n he w o u ld pr e ve nt w i th hi s w ill the f r e e a c tions of me n w hic h w ould be inc on sis te nt w i th his w ill c onc e r ning c r e a tion, sinc e he e ndow e d me n w ith f r e e w ill. Mor e ove r he doe s not w il l tha t mor a l e vil s oc c ur , a nd he c a nnot w ill tha t mor a l e vil s oc c ur , sinc e th is w ou ld be inc o nsi ste nt w i th hi s e sse nc e . Fr om th is toge t he r w it h h is pe r miss ion of m or a l e vil it f oll ow s tha t he ke e ps of f hi s w i ll f r o m mor a l e vi l: ne ithe r he w ills t ha t mor a l e vi ls oc c ur , nor he w ills tha t the y d o not oc c ur . W hic h a lso me a ns tha t he is ne i th e r a n allw i lli ng, nor a n a llc a using G od. 4 9 Co ming ba c k to the f our th c o ndi tion of t he de f ini tion of om nipo te nc e ( D e f . 1) w e obse r ve tha t it is c onc e r ne d w i th G od's e thic a nd m or a l r ule s w . r . t. his c r e a tion. I t sta te s tha t G od c a nnot w il l ( c a nnot c a use , ma ke or br ing a b out) sta te s of a f f a ir s ( e ve nts) w h ic h vio la te his e th ic a l or mor a l r u le s. A nd t his f ollow s f r om the f a c t tha t his w ill c a nnot be nor ma t ive ly inc o nsi ste nt. I t w ould be n or ma ti ve ly inc on sis te nt if he w ould w i ll tha t ma n sho uld a c t t ha t p is the c a se ( honour your pa r e nts) but w o uld pr e ve nt p or c a use non - p . 4 8 Cf. Barrow and Ti pler (1986, ACP) p. 16. Mittelstaedt, Weingartner (2005, LNt) ch. 8. 2. 2. 1 4 9 For a detailed discussion of the wrong thesis (or assumption) of an allwilling an d allcausing God (also in connection with religious fatalism) see Weingartner (2003, EDK), ch. 6. 4 and Appendix: Axiom 4 and theorems T68 and T89. Cf. ch. 13. 25 below.

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5.32 God's knowledge exceeds his power T his c a n be se e n f r om a n e xa mina tio n of this que s tio n in r e f e r e nc e to the pa r ts of the de f inie ns of G od's po w e r ( omnipo te nc e ) : Cond it ion ( 1) is r e str ic te d to th ose s ta t e s of a f f a ir s ( e ve nt s) of w hic h G od w ill s ( c a use s) tha t the y oc c ur . Si nc e thi s r a nge of s ta te s of a f f a ir s ( e ve n ts) i s inc lude d in tha t of c ondit ion ( 2) – i. e . in the sta te s of a f f a ir s ( e ve nts) w hic h G od can w i ll ( or c a use ) – w e ne e d not to be c onc e r ne d w ith ( 1) . Bu t inde pe nde nt ly of tha t G od' s know le d ge e xc e e ds G od's pow e r ( omnipote nc e ) w . r . t. c ondition ( 1) , be c a use he know s a lso tho se oc c ur r ing sta te s of a f f a ir s ( e ve nts) w hic h he doe s no t w il l ( w hic h h e doe s not c a use ) like mor a l e vil. Cond it ion ( 2a ) of D e f . 1 of omnipote nc e W e c a n dis ting uis h t hr e e c a se s: ( α ) W h a te ve r G od c a n c a use ( c a n w il l, ma ke , br ing a bou t) m ust be log ic a lly c o nsi ste nt or se lf - c on sis te nt. I n th is c a se G od know s t ha t it is lo gic a lly c on sis te nt. A n d inc ons iste n t sta te s of a f f a ir s c a nnot be c a use d ( w ille d, ma de , br ought a bout) a nd c a nnot be know n. ( β ) I f G od can c a use ( w ill, ma ke , br ing a bout) tha t the sta te of a f f a ir s (e v e nt) p oc c ur s, but doe s no t c a use i t, suc h tha t p d oe s no t o c c ur , the n p i s ( st ill) pos sib le . I n th is c a se G od know s tha t p is p oss ible . ( γ) I f G od can c a use ( w ill, ma ke , br ing a bout) t ha t p oc c ur s a n d c a use s ( w il ls, ma ke s, br ings a bou t) t ha t p oc c ur s, the n p obta in s. I n this c a se G od know s t ha t p obta ins. Conc e r nin g c ondi tion ( 2a ) , the n w e m a y sa y tha t G od' s know le dge ha s the sa me e xte nsio n a s G od's pow e r . Cond it ion ( 2b) of D e f . 1 of omnipote nc e W ha te ve r G od can c a use ( w il l, ma ke , b r ing a bou t) m ust be c o mpa ti ble w i th G od's e sse nc e , i. e . w ith e ve r ythi ng w ha t G od ne c e ssa r ily kn ow s a bou t hi mse lf a nd w it h e ve r yth ing w ha t G o d ne c e ss a r ily w i lls a bout hi mse lf . T h us f or e xa mple G od c a nno t w il l to c ha nge hi mse lf or he c a nno t di mi nis h his o w n goodne s s. I n this c a se it holds t ha t e ve r ythin g tha t G od kn ow s a bou t him se lf , he a lso w il ls a bou t hi mse lf a nd e ve r yt hing G o d w il ls ( a nd c a n w il l) a bout him se lf he a lso know s a bou t him se lf . T he r e f or e w .r . t. c onditio n ( 2b) G od's k now le dge ha s the sa me e xte nsio n a s G od's pow e r . Cond it ion ( 2c ) of D e f . 1 of omnipote nc e

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Conc e r nin g G od' s pr ov ide nc e w hic h i s c onc e r ne d w ith G o d's c r e a tio n it h old s tha t G o d's kno w le dge a bo ut his c r e a ti on ha s the sa me e xte n sio n a s G od' s pr ovide nc e . T his c a n be se e n a s f ollow s. A c c or ding to c ondit ion ( 1) of D e f . 2 ( pr ovide nc e ) it ho lds tha t w ha te ve r be lo ngs to G od' s pr ov ide nc e is kn ow n by G od. D oe s the op posi te ho ld a l so, doe s it a ls o ho ld tha t w ha te ve r G od know s a bout hi s c r e a tion a nd dir e c ts t o so me goa l ( D e f . 2 ( 3 ) ) be longs to h is pr ovide nc e ? T he a ns w e r to thi s que stio n is pos itive if pr o vide nc e i s de f ine d in the w ide se nse a s in D e f . 2. Pr o vide nc e ma y be de f ine d in a na r r ow e r se nse if one r e quir e s a ddit iona l ly tha t w ha t be lo ngs to G od's pr ovide nc e is w il le d by G od. I n thi s c a se im mor a l hu ma n a c tions c a nno t c ome un de r G od's pr ovide nc e . H ow e ve r , w e a ssu me he r e t he w ide r c onc e pt of pr ovi de nc e in t he se nse tha t no thi ng w h ic h oc c ur s, c a n e sc a pe G od's pr ov ide nc e ; th is v ie w of pr ovide nc e w a s a lso ta ke n b y A ug ust ine a nd T homa s A qu ina s, w ho de f e nde d the pr inc ip le : W ha te ve r oc c ur s, is e it he r w ille d or pe r m itte d by G o d. 5 0 T hus the w ide c onc e pt of pr ovide nc e e xc e e ds the c onc e pt of G od 's po w e r sinc e his pr ovide nc e inc lude s suc h f a c ts a s imm o r a l a c tions, but the s e c a nnot be w il le d or c a use d by G od. T ha t the oppos ite i mpl ic a tion, i. e . w ha te ve r G od know s c onc e r ning hi s c r e a tion ( c ond it ion ( 2) ) a nd dir e c ts to s ome g oa l ( c ondi tio n( 3) ) be longs to his pr ovi de nc e , is a ls o tr ue – pr ovide d one a c c e pts t he w ide se nse of pr o vide nc e of D e f . 2 – c a n be se e n a s f ollow s:

( i) W ha te ve r G od know s is the c a se , is tr ue ( c h. 1. 3 a bove ) ; i. e . ∀p ( gKp → p )

( ii) W ha te ve r is the c a se ( is tr ue ) i s ( a t le a s t) pe r mi tte d by G od. T hi s is the pr inc iple ∀p( p → gPp ) me nt ione d a bove .

( iii) Fr om ( i) a nd ( ii) i t f o llow s tha t: W ha te ve r G od kn ow s is pe r mi tte d by G od.

T he c onc lusi on c onc e r ning pr ovide nc e ( c onditi on 2c of D e f . 1) is the r e f or e tha t G o d's kno w le dge a bo ut his c r e a ti on ha s the sa me e xte n sio n a s G od' s pr ovide nc e . H ow e ve r , if w e ta ke G o d's kn ow le dge in ge ne r a l ( or in a n unr e str ic te d se nse ) , the n h is know le dge e xc e e ds his pr ovi de nc e be c a use his know le dge e xte nds to bo th, tr u ths a b o ut H i mse lf a nd tr uth s a bou t c r e a tion w he r e a s his pr ovide nc e e xte nds onl y to his c r e a tion. Conc e r nin g the r e la ti on be tw e e n G o d's pow e r , pr ovide nc e a nd kno w le dge w e ha ve to c onside r the f ollow ing c a se : I f w e a ssume G od c ould ha ve c r e a te d anothe r w or ld, the r e a r e some sta te s of a f f a ir s hold ing in the othe r w or ld w hic h a r e not in G o d's pr ov ide nc e ( pla n) 5 0 For a discuss ion of this princi ple see Weingar tner (2003, EDK) ch. 6. 45, principle WP and Append ix theorem T15: ∀p ( p → gPp ) (' p ' for ' permits' ). From t his theorem the above principle i s derivable.

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w hic h is c o nc e r ne d w it h t his e xis tin g w or ld, i. e . "c on dit iona l ly c o mpa t ible w ith G od 's pr ov ide nc e ” me a ns tha t u nde r the c onditi on tha t G od 's pla n ( pr ovide nc e ) f or the e xis ting un ive r se is not ma de , G od 's pow e r i s a ls o c ompa ti ble w ith a nothe r pla n ( p r o vide nc e ) . H ow e ve r , unde r the c ond it ion tha t the pla n is ma de , G od c a nnot w i ll so m e thing a ga in st hi s pla n w hic h w ou ld me a n to w ill so me th ing a ga ins t his f r e e de c ision of his w il l, i. e . in this c a se his w il l w o uld be inc ons iste n t. T h us a bstr a c ting f r om a g i ve n pr o vide nc e ( pla n) a bout thi s uni ve r se ( mor e ge ne r ally a bout c r e a tion) a nd c ons ide r ing a possi ble pla n G od' s pow e r e xc e e ds his p r ovide nc e ( pla n) . D oe s it f o llow f r o m this tha t G od 's po w e r e xc e e ds a lso his k now le dge ? T hi s is n ot t he c a se f or the f ollow i ng r e a son: G o d's k now le d ge is c o nc e r ne d w ith w ha t is tr ue or w ha t is a f a c t not on ly in the se nse that it is true or that it is , b ut a l so how it is true or how it is. N ow the sta te s of a f f a ir s c o nc e r ning w hic h G od' s p ow e r e xc e e ds h is pr ovide nc e a r e sta te s w hic h a r e possible a nd not sta te s w hic h a r e ac tua l. A nd a s suc h, a s possib le sta te s, the y a r e know n by G od. T hu s the r a nge of his know le dge is n ot s ma lle r t ha n the r a ng e of his po w e r , a lthoug h the r a nge of pr ovide nc e ma y be na r r ow e r if i t i s c onsi de r e d a s G o d's f r e e ly c hose n se le c tion. Cond it ion ( 2d) of D e f . 1 of omnipote nc e Fir s t w e w a n t to sh ow t ha t c on dit ion 2d ( of D e f . 1) doe s ne ithe r f o llow f r om c ondit ion 2b nor f r o m c on dit ion 2c ( of D e f . 1) . T his c a n be se e n a s f ol low s : A ssu me th a t p i s a sta te of a f f a ir s ( a n e ve nt) w hic h oc c ur s a nd w hic h i s a ( huma n) mor a l e v il. T he n p is c ons is te nt w i th a l l sta te s of a f f a ir s w hic h hol d of G od's e sse nc e . – T his is so si nc e a ll sta te s of a f f a ir s w hic h hold of the c r e a tion or of the w or ld a r e c ompa tible w ith e ve r yth ing tha t h olds a bo ut G od 's e sse nc e . T he ult ima te r e a son f or tha t i s tha t the c r e a tion is no t a ne c e ssa r y outc ome of G o d's e s se nc e , but the e f f e c t of his f r e e de c ision of hi s w il l. Si mila r l y unde r the a bove a ssu mpt ion p is c onsi ste nt ( c o mp a tib le ) w ith G o d's pr ovide nc e . – T his i s so be c a use e ve r yth ing w hic h i s the c a se , e ve r y oc c ur r ing e ve nt, of the w or ld w hic h is dir e c te d or subor d ina te d to so me goa l c o me s unde r G od's pr ovi de nc e ( a c c or ding to D e f . 2 a bove ) . But in the c a se of mor a l e vil p i s inc on sis te nt ( inc o mpa ti ble ) w ith G od's c om ma nds. Se c ond, it c a n be show n tha t w . r . t. c onditio n ( 2d) of D e f . 1 ( of omnipo te nc e ) G od's kno w le dge e xc e e ds G od' s p ow e r : A ss ume a ga in tha t p i s a sta te of a f f a ir s ( e ve nt) w hic h oc c ur s a nd w h ic h is a ( h uma n) mor a l e v il. T he n G od know s tha t p oc c ur s, but G od c a nn ot w ill ( a nd c a nnot c a use , ma ke , br ing a bout) tha t p oc c ur s.

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Su mm ing up now w e c a n sa y : H uma n mor a l e v il w hic h oc c ur s is a c o nsi ste nt sta te of a f f a ir s ( e ve nt) w hic h is k now n b y G od a nd i t is c o mpa ti ble w it h G od' s e sse nc e a nd is c ompa t ible w i th G od 's pr ovide nc e ; bu t it is no t c ompa t ible w ith G od's c om ma nds. Sinc e c om pa t ibil ity w ith G od' s c om ma nd s is a ne c e ssa r y c ondi tion of e ve r y sta te of a f f a ir s ( e ve nt) w h ic h c a n c o me un de r G od's pow e r ( or G o d's om nip ote nc e ) mor a l e vi l w h ic h oc c ur s c a nn ot c o me unde r G od 's pow e r ( o mnip ote nc e ) . Bu t oc c ur r ing mor a l e vil i s kn ow n by G od. T he r e f or e – a nd in this se nse – G o d's know le dge e xc e e ds G od's pow e r . 5. 4 A ns w e r to th e O b jec t io ns

5. 41 ( to 5. 11) T ho se sta te s of a f f a ir s ( e ve n ts) w hic h G od c a n ( c ould) c a use ( w ill, ma ke , br ing a bout) but a r e not c a use d by him a nd the r e f or e a r e not r e a lise d a r e know n by hi m jus t a s tho se w hic h a r e not r e a lise d but w h ic h c ould be r e a li se d b y hi m or a r e poss ibl e in a s pe c ia l se nse . T hus the se c on d pr e mise of the a r gume n t ( 5. 11) shou ld r e a d: But w ha t i s not the c a se c a nnot be know n by him as being the case , but is know n by h im a s poss ible or a s be ing in h is p ow e r othe r w ise he w o uld kno w so me thi ng f a lse … I f th is c or r e c tion is inse r te d, the f a lse c onc l usio n doe s not f oll ow a ny mor e . 5. 42 ( to 5. 12 a nd to 5. 13) I n or de r to g i ve a n a nsw e r to the o bje c ti on 5. 12 it ha s to be n otic e d tha t the e x pr e ssio n "n ot r e a lise d f a c t" in the f o ur th pr e mise of thi s a r gu me nt is a mb i guo us. I t c a n m e a n tha t a sta te of a f f a ir s ( e ve nt) p i s not r e a li se d u nti l n ow b ut w il l be r e a li s e d in the f u tur e . O r i t c a n me a n t ha t p is ( w i ll be ) ne ve r r e a lise d. I n b oth c a se s p i s a s ta te of a f f a ir s of the u nive r se ( or mor e ge ne r a lly of c r e a tion) . A c c or di ng to th is d ist inc ti on t he r e ply c a n be give n a s f ollow s: I f the r e spe c tive sta te of a f f a ir s p i s n ot r e a lise d un til now bu t w ill be r e a li se d in the f utur e , the n – pr ovide d tha t p is c onsis te nt w i th G od' s c om ma nds – p c ome s unde r G od' s pow e r ( or G od can c a use or w ill tha t p ) no t a s p in the pa st or a t pr e se nt ( i. e . not a s pt ≤ 0 ) but a s p in the f utur e ( a s pt >0 ) ; w he r e ‘ pa st’ , ‘ pr e se nt’ a nd ‘ f utur e ’ a lw a ys me a n ‘ pa st, pr e se nt or f u tur e r e la tive t o a r e f e r e nce syste m of thi s w or ld ( un ive r se ) ’ . O the r w ise pt≤ 0 w ould be inc ons iste n t w i th G o d's a lr e a dy de c ide d pr ovide nc e of w h ic h pt >0 is a the or e m a nd ¬pt≤ 0 i s a t he or e m. B ut the r e s pe c tive sta te of a f f a ir s i s i n G o d's know le dge a lso a s p in the f utur e ( a s pt >0 ) , i.e . G od know s tha t pt >0 ( gK pt >0 ) . T he a bove me nti one d pr o viso " pr ovid e d tha t p is c ons iste n t w i th G od' s c omma nd s" is ne c e ssa r y: p t >0 ( p in the f utur e ) c a n c ome un de r G od' s p ow e r only if p i s c o mpa tib le w ith G od' s c o m ma nds ( tow a r ds ma n) . T hus it c a nnot

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be in G od' s pow e r t o c a use a sin ( a n i mmor a l a c t ion) . G od c a nno t w il l a nd c a nnot c a use immor a l a c tion s. But su c h e ve nts c a n be of c our se in his pr ovide nc e if he f or e se e s tha t some ma n w ill c om mi t a sin. I f the r e spe c tive sta te of a f f a ir s ( e ve nt) p is ( w il l be ) ne ve r r e a lise d ( in the uni ve r se or in the c r e a tion) , the n p is not a the or e m ( r e pr e se nting a sta te of a f f a ir s) in G od's pr ovide nc e . H ow e v e r , sinc e G od's pr ov ide nc e is n ot de te r mine d by h is e sse nc e , but is hi s p la n f or the unive r se ( c r e a tion) f r e e ly de c ide d a nd se le c te d by hi s w il l, one c ould a sk w he t he r some sta te of a f f a ir s q w hic h is not i n hi s pr ov ide nc e c a n be in his pow e r ; f or e xa mple w he t he r G od c ould ha ve c r e a te d a not he r uni ve r se , one w hic h d if f e r s in ini tia l c o ndi tio ns, or a lso in la w s or c ons ta nts of na tu r e ; or m or e ge ne r a lly w he the r a dif f e r e nt pla n ( pr ovide nc e ) tha n the o ne c hose n c o me s unde r his p ow e r ( omn ipo te nc e ) . T his que sti on is a nsw e r e d posi tive l y by T ho ma s A qui na s: "Bu t w e show e d t ha t G od d oe s not a c t f r om na tur a l ne c e ssit y

( …) w he nc e in no w a y a t a ll i s t he p r e se nt c our se of e ve nt s pr oduc e d by G od f r o m a ny ne c e ssit y, s o tha t othe r t hing s c ou ld not ha ppe n ( …) . W he r e f or e w e must s i mply sa y tha t G od c a n do othe r thing s tha n tho se H e ha s done . " 5 1 "S o no thi ng pr e ve n ts the r e be ing so me t hing in the d ivi ne pow e r w hic h H e d oe s no t w i ll a n d w h ic h i s n ot inc lude d in t he or de r w hic h H e ha s pla c e d in things. " 5 2

I n the a r gu me nts 5. 12 a nd 5. 13 the r e is a f ur t he r e xpr e ssio n w h ic h i s a mbigu ous : " the y a r e not r e a lise d f a c ts ; a nd th us the y c a nn ot be k now n by him. " I f the sta te of a f f a ir s p is not r e a lise d, the n p c a nnot be kn ow n, i. e . "so me pe r son k now s tha t p " w ou ld be f a lse . But w ha t i s know n the n is n on - p , in the mod us of "ne c e ssa r ily not - p " or " c ontinge n tly not - p " or "f a c tua lly not -p". T hu s in the c a se w he r e the s ta te of a f f a ir s p c onc e r ni ng c r e a tio n i s n ot r e a lise d, G od k now s tha t c ont inge n tly n ot - p bu t p oss ibl y p. Sinc e in this c a se his pow e r e xte nds a l so to po ssi bly p , his pow e r doe s not e xc e e d his know le dge . 5. 43 ( to 5. 14) T he que st ion w he the r G od's k now le d ge e xc e e ds his pow e r is c onc e r ne d w ith a c om pa r ison of t he sc ope ( e xte nsi on) of tho se s ta te s of a f f a ir s tha t G od know s w i th the sc ope ( e xte nsion) of tho se sta te s of a f f a ir s tha t G o d w i lls ; bu t i t i s no t c onc e r ne d w ith the ki nd or moda lity of kn ow le dge or the kin d of moda l ity of w il l ( ne c e ss a r y or not ne c e ssa r y) . T hus a lth ough ( a c c or ding to c h. 2) w ha te ve r G od know s he ne c e ssa r ily know s – 5 1 Thomas Aquinas (STh) I, 25, 5. 5 2 Ibid. 25, 5 ad 1.

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symb olic a l ly: ( ∀p ) ( gKp → l gKp) – nothi ng h inde r s tha t he ne c e ssa r ily know s tha t so me th ing i s c ont inge nt o r tha t so me thin g i s n ot r e a li se d b ut possi ble ; a n d m or e ove r – if w e a b str a c t f r om hi s pr ov ide nc e – he mig ht know tha t he ha s the pow e r ( he ca n w ill, he c an c a use ) to br ing tha t a bout. Fr om thi s c onsi de r a tion i t is c le a r tha t G od's kn ow le dge c onc e r ns a ls o w ha t is possi ble a nd the r e f or e his w ill or his p o w e r doe s not e xc e e d his know le dge .

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6. Whet her God Caus es E ver yt hi ng What He

Knows T his q ue sti on ma y be e xpr e sse d a l so dif f e r e ntly: W he the r i t ho lds tha t if G od know s so me thi ng, the n he c a use s i t. O r : I s it tr ue tha t w ha te ve r G od kno w s he c a use s? Symb olic a ll y the que st ion c a n be e xpr e sse d thus: ∀p ( gKp → gCp ) ? Be f or e w e be gin w ith the a r gume n ts a nd the a nsw e r , some pr e limina r y r e ma r ks a r e ne e de d c onc e r ning the c on c e pt of cause a s use d i n th is r e spe c t. T he f ir st r e ma r k is tha t the c a usa l r e la ti on is a tw o pla c e r e la tion w he r e one me mbe r of the r e la tion is G o d a nd the othe r is t he w or ld ( the unive r se ) or e ve nts of t his w or ld. Both a r e no t ide n ti c a l a nd the e xis te nc e of the f ir s t ( G od) is ne c e ssa r y a nd tha t of the se c ond ( unive r se ) a nd its e ve nts is c onti nge nt ( a t le a st w . r . t. the kin d of ne c e ssi ty a p plie d t o G od 's e x iste nc e ) . Se c ond, c onc e r ning the pr ope r tie s of the c a usa l r e la tion w ha t is r e qu ir e d is tha t it i s ir r e f le xive a nd a sy mme tr ic ; t ha t me a ns i t is r ule d o ut tha t x c a use s x suc h tha t a lso Spi noz a 's c o nc e pt 5 3 of a causa sui i s r ule d out. A nd a s ym me tr y me a ns tha t if x c a use s y, the n it is not the c a se tha t y c a use s x. T he r e a r e se ve r a l f ur the r pr ope r tie s w hic h a c a usa l r e la tion ha s to ha ve if it is a pplie d a mong thing s or sta te s ( e ve nt s) of t he uni ve r se . T he se a r e f or e xa mple te mpor a l or de r ( the e f f e c t c a nnot be e a r lie r tha n t he c a use ) , c hr onolog y c ond itio n ( the r e a r e no c lose d time - l ike c ur ve s, i. e . the ti m e c oor dina te doe s n ot ma ke a loop) , lim it of c a usa l pr opa ga ti on ( ve loc i ty o f light) , ob je c tiv ity ( i nde pe nde nc e of r e f e r e nce syste m) . 5 4 N one of the m sho ul d be r e quir e d f or the c a usa l r e la tio n be tw e e n G od a nd the w or ld ( unive r se ) o r be tw e e n G od a nd sta te s or e ve nts of this w or l d. A ls o tr a nsit ivi ty is not a p plic a ble a s i t w i ll be s how n be lo w . I nde pe nde ntly of t ha t tr a nsi tiv ity i s n ot ge ne r a lly sa ti sf ie d f or the c a usa l r e la tion e x pr e sse d b y la w s of na tur e e it h e r : it is on ly sa t isf ie d w . r . t. dyna m ic a l la w s, but no t w . r . t. s ta tis tic a l la w s; th e sa me h olds f or c o ntin uit y a nd f or c ounte r f a c tua lity. O n t he othe r ha nd c o unte r f a c tua lity ma y be a ppl ie d to the c a usa l r e la tion be tw e e n G o d a n d c r e a tio n sinc e G od a s t he f ir st c a use m ust be a c a use in the se nse of a ne ce ssa r y c ondition.

5 3 Cf. his Ethics, Def. 1. 5 4 Cf. Weingartner (2005, PCC) and Mittelstaedt,Weingartner (2005, LNt), ch. 9.

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6. 1 A rg u me nt s P ro

6. 11 I f the know le dge of G od is t he c a use of thing s, the n G o d c a use s e ve r ything w ha t he kno w s. N ow a s T h o ma s A q uina s sa ys, the kn ow le dge of G od i t he c a use of th ings : "I a nsw e r t ha t the kn ow le dge of G od is the c a use of thing s. " 5 5 T he r e f or e G od c a use s e ver ything w ha t h e know s. 6. 12 Be c a use the c r e a tur e s e xist, ma n c an ha ve know le dge of the m. But f or G od the oppo site mu st ho ld, a s A ugust in e sa ys: "N ot be c a use the y a r e , doe s G od know a ll c r e a tur e s spir it ua l a nd te m por a l, but be c a use he know s the m, the r e f or e the y a r e. " 5 6 T he r e f or e G od c a use s e ver ything w ha t h e know s. 6. 13 1. I f G od i s om nisc ie nt a nd e x ist s a t t1 the n, u nde r the c ond it ion t ha t Jone s a c ts a t t2 tha t p ( is the c a se ) , G od be lie ve s a t t1 tha t J one s a c ts a t t2 t ha t p ( t1 < t2 , i. e. t1 is a ssume d to be e a r lie r tha n t2 ) . 2. I f G od be lie ve s tha t p, the n p ( is the c a se , is tr ue ) . 3. I f G od be lie ve s a t t1 tha t Jone s a c t s a t t2 tha t p, the n, u nde r the c ond iti on t ha t Jo ne s can a c t a t t2 tha t non - p, one of the f ol low i ng thr e e c onditio ns a r e sa tisf ie d: (i) Jone s can a c t a t t2 suc h tha t G od be lie ve d a t t1 tha t p, but p is f a lse . (ii) Jone s can a c t a t t2 suc h tha t G od did not be lie ve a s H e did a t t1 . (iii) Jone s can a c t a t t2 suc h tha t G od did not e xist a t t1 . 4. I f G od is omnisc ie n t, the n a ll thr e e ( i) , ( ii) a nd ( iii ) a r e fa lse . 5. T he r e f or e : I f G od is omn isc ie n t a nd e xists a t t1 , the n, u nde r the c ond it ion tha t Jo ne s a c ts a t t2 t ha t p, it is n ot t he c a se tha t Jone s can a c t a t t2 tha t n on -p. 5 7 T hus it se e ms tha t G od, be lie vin g tha t Jone s a c ts a t t2 tha t p c a use s John to a c t this w a y.

5 5 Thomas Aquinas (STh) I, 14, 8. 5 6 Agustine (Trin) XV. 5 7 This is an abbreviated v ersion of an argument by Nelson Pike in his (1970, DOV). Cf. also Craig (1991, DFH), p. 23. We express "it is in his power at t, to bring it about that p" by "he can act at t, that p " (in accordance w ith Pike, p. 84). This argument does not use possible wo rlds since P ike uses such a ve r sion only in his (1977, DFH). Althoug h according to chapter 3 the attribution of time indices to actions of God does not make sense, it is accepted here for the sake of the argument. The conclusion of the argument is interpre ted by Pike as saying that Jones' actio n at t2 cannot be free, but is det ermined by God' s foreknowledge, i. e . God causes by his foreknowledge.

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6. 2 A rg u me nt s C o nt ra

I f G od c a use s e ve r ythi ng he kn ow s, the n, sinc e G od k now s tha t H itle r br e a ks H is e thic a l r ule s ( c om ma nd me nts) , it f ollow s tha t G od h im se lf c a use s this br e a king of H is r ule s. T his i s a bsur d. T he r e f or e the the sis tha t G od c a use s e ve r ythin g w ha t he know s mu st be f a lse . 6. 3 P r opo se d A n sw e r

I t is n ot t he c a se tha t e ve r yth ing w ha t G od know s he c a use s. T h is c a n be se e n f r om the f ollow ing r e a sons :

6.31 The knowledge need not to be a sufficient condition for causing something T his c a n be jus tif ie d a s f ollo w s: I n hu m a ns it is a f a c t tha t kno w ing a n a c tion or a pr oc e ss is not a suf f ic ie nt c o ndi tion f or br ing ing it a bout or f or c a using i t. For e xa mple a ma s te r buil de r know s h o w to bui ld a hou se ; he ha d the ide a in his min d a nd de s igne d a n e xa c t pla n. But his know le dge is not suf f ic ie n t to e xe c ute the pla n. I n or de r t o e xe c ute h is pla n he ha s to e mplo y ( m obi lise ) h is w ill. T h is i s so a l so f or ot he r huma n a c ti ons: k now le d ge is ne ve r suf f ic ie n t f or c a using the m, i. e . f or the ir e xe c ution. H ow e ve r , know le dge a bout the a c tion or pr oc e ss ( a t le a st s ome kind of k no w le dge ) is a ne c e ssa r y c ond iti on f or ( c onsc ious ly) c a usi ng t he a c tion or pr oc e ss. T ha t i s, the oppo site im plic a ti on doe s ge ne r a lly ho ld: I f so me hu ma n pe r son ( c onsc io usl y) c a use s some a c ti on or pr oc e ss, the n he ha s some kind of kno w le dge of it. Fr om the f a c t t ha t f or h uma n p e r sons k now le dge is n ot a s uf f ic ie nt c o ndit ion f or c a using, it f o llow s tha t the sta te me n t " For a ll pe r so ns A, e ve r ythi ng w ha t A know s is c a use d b y A" is f a lse ; be c a use it doe s n ot ho ld f or hu ma n pe r so ns. T he r e f or e this sta te me n t doe s no t ne c e ssa r ily ho ld i n t he se nse tha t it is unive r sa ll y tr ue f or a ll pe r sons or be lon gs t o the na tur e of pe r sons. W e ma y the r e f or e c onc lude tha t i t ne e d not to hold f or G o d. T ha t it doe s n ot a nd c a nnot hold f or G od is s how n by the su b se que nt a r gume nt s in 6. 32 – 6. 35.

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6.32 The statement "God causes everything what he knows" leads to absurd consequences Sinc e w e ha ve to a s su me tha t G o d kno w s a ll t he im mor a l a c tio ns w h ic h ha ve be e n c omm itte d by me n, 5 8 it w ou ld f ol lo w tha t he c a use s ( c a use d) a ll t he se im mor a l a c tions. Fr o m th is, thr e e f ur the r a bsur d c onse que nc e s f ollow : (i) tha t s uc h a G od w ou ld be inc on sis te nt, sinc e im mor a l a c ti ons a r e

inc ons iste n t w i th his c om ma nd s ( spe c if i c a lly the T e n Co mma n dme n ts) give n to me n ( se e be low 6. 34) .

(ii) tha t s uc h a G od w ho c a use s i mm or a l a c tions c a nnot be a l l g ood or pe r f e c t.

(iii) tha t ma n c a nnot ha ve f r e e w ill. A nd if ma n c a nnot ha ve f r e e w ill, he c a nnot ha ve r e sponsi bil ity f or hi s a c tions. I f ma n c a nnot ha ve r e sponsi bil ity f or his a c tio ns, j ur id ic a l insti tut ion s like c our ts, punis hme n t la w , pr ison e tc . no t on ly ma ke no se nse , bu t a r e i n f a c t f r a ud a nd de c e ptio n. T hi s c on se que nc e is a bs ur d; a n d tha t i t i s a bsur d c a n be sho w n by e mpir ic a l e vide nc e . T he r e f or e , on the a ss um pti on tha t G od know s th e im mor a l a c tio ns c om mi t te d by hu ma ns, i t c a nnot be tr ue tha t G od c a use s e ve r ythin g w ha t he kno w s.

6.33 The thesis "God causes everything what he knows" excludes cooperation and learning processes in creatures T his c a n be se e n a s f ol low s. I f G o d c a u se s e ve r ythi ng w ha t he kn ow s, t he n it is imp oss ible tha t G o d w ill s the i mpe r f e c t c oope r a tion a nd impe r f e c t c ontr ibu tion of im pe r f e c t c r e a tur e s in t h e ha ppe ning s of the w or ld ( unive r se ) . Be c a use sinc e he know s the se impe r f e c t c ontr ibution s he c a use s the m him se lf . T his i s f ir st of a ll inc o nsi ste nt w ith h is pe r f e c tion. Se c on dly, the r e a r e a numbe r of go od r e a son s tha t G od w ill s t he c oope r a ti on a n d c on tr ibu tion of impe r f e c t c r e a tur e s ca use d by the m a nd not c a use d by G od: "I n a nothe r w a y one is sa i d to be he lp e d by a pe r son thr oug h

w hom he c a r r ie s out h is w or k, a s a ma s te r thr ough a se r va nt. I n this w a y G od is he l pe d by u s; ina s m uc h a s w e e xe c ute his or de r s, a c c or ding to 1 C or . I I I , 9: W e a r e G od's c oa d jut or s. N or is th is on a c c ount of a ny de f e c t in the po w e r of G od , but be c a use he e mploy s inte r me dia r y c a use s, in o r de r tha t the be a uty of or de r ma y be pr e se r ve d in the un ive r s e ; a nd a ls o tha t he ma y

5 8 That this holds follo ws from what has been de fended in chapter 4: tha t God know s all past and present events.

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c ommu nic a te to c r e a tur e s the dignit y of c a usa lity. 5 9 Fur the r : I f G od c a use s e ve r ythi ng w h a t he know s, the n the r e c a nnot be a ge nuine pr oc e ss of le a r ning in h ighe r or ga nis ms a nd in ma n. T his c a n be se e n a s f ollow s. E ve r y ge nu ine pr oc e ss o f le a r ning r e quir e s tha t the hi ghe r or ga nis m or the huma n pe r son h im se lf ha s a t le a st some de gr e e s of f r e e dom to ma ke tr ia ls a n d e r r or s a nd a f te r w a r ds to ma ke de c isio ns f or im pr ove me n t. Sinc e le a r nin g w i thou t tr ia l a nd e r r or se e ms to be i mpo ssib le . Bu t if G od, sinc e he know s a ll oc c ur r ing le a r ni ng pr oc e sse s, him se lf c a use s e ve r y tr ia l, e r r or a nd im pr ove me n t of the or ga nis m or hu ma n pe r so n, th e n w e c a nno t spe a k of a ge nui ne pr oc e ss of le a r nin g. W e c ould no t inte r pr e t a le a r ning pr oc e ss a s a n in sti nc t ( c a use d by G o d) e ithe r , be c a use a n ins tinc t le a ds dir e c tly a nd str a ig htf or w a r dly t o the o pti ma l a c tion w i thou t tr ia l a nd e r r or . Sinc e w e k now f r o m the bio logic a l sc i e nc e s tha t the r e a r e ge nui ne le a r ning pr oc e sse s in hi ghe r or ga ni sm s a nd in huma n pe r sons w he r e tr ia l a nd e r r or pla y a n e sse nt ia l r ole . T he r e f or e it c a nn ot be tr ue t ha t G od c a use s e ve r ythi ng w ha t he know s.

6.34 If God causes everything what he knows, then he is normative and volitive inconsistent W e sa y t ha t a pe r s on is nor ma t ive a nd voli tive inc on sis te nt if a nd on ly if the pe r son e ithe r w i lls or or de r s ( c o mma n d s) tha t p oc c ur s ( sh ould oc c ur ) but ( a t the sa me ti me ) c a use s or pe r mits t ha t n on - p oc c ur s. A n e xa mple w ou ld be a dic ta tor w ho or de r s tha t pe ople sh ou ld not be im pr iso ne d f or pol itic a l oppos iti on but a ll ow s ( or c omma nd s) his polic e to im pr iso n the m. Mor e a c c ur a te ly a nd a pplie d to G od w e ma y s a y tha t G od is nor ma ti ve a nd voli tive c onsis te nt. A nd thi s w e migh t de f ine a s f ollow s: D e f . 1 G od is nor ma tive a nd vol iti ve c onsis te nt if f , if p is a the or e m of

G od's w i ll w . r . t. ma n, the n G od pe r mits p. D e f . 2 p is a the or e m of G od's w il l w . r . t. ma n iff f or a ll huma ns h :

( a ) e ithe r G od w ill s tha t h w il ls tha t p or ( b) G od w ill s tha t h a c ts w ith t he inte nt ion t o br ing a bout p or ( c ) G od w ill s tha t h sho uld w i ll tha t p or ( d) G od w ill s tha t h sho uld a c t w ith t he inte ntion t o br ing a bou t p 6 0

5 9 Thomas Aquinas (STh) I, 23, 8 ad 2. 6 0 For a formal (axiom) system in which these definitions are used cf. Weingartner (2003, EDK) Appendix, Def. 12 and 13 and ch. 13, D6, D6. 1, D15 of this book.

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I n the c a se s ( a ) a nd ( b) ma n h w ills tha t p a nd a c ts w ith t he inte n tion to br in g a bout p a nd p i s s ome t hing go od if w e a ssume tha t bot h of the f o llow ing c ondit ions ho ld f or G od: (i) G od's w i ll is a lw a y s f ulf il le d, i. e . w ha te ve r G od w il ls is the c a se . (ii) W ha te ve r G od w ills i s good. Ca se s ( a ) a nd ( b) ho ld f or ins ta nc e if t he r e is a na tur a l i nc lina tion to some good in ma n l ike to sur v ive or to live in a c ommuni ty. O n the othe r ha nd in c a se s ( c ) a nd ( d) ma n h , sinc e his a c tions a r e f r e e , ma y n ot be w i llin g t ha t p ( or ma y e ve n w il l t ha t non - p ) , a ltho ugh G od w il ls tha t he should w i ll t ha t p . S im ila r ly c o nc e r ning his a c tio n w i th t he inte n tio n to br ing a bout tha t p : he m ight n ot a c t w it h su c h a n inte nti on or m ight a c t w i th a n oppos ite in te nti on, a l tho ugh G o d w il ls t ha t h should a c t w i th the i nte nt ion t o br ing a bout p. Co ming ba c k n ow to the t he sis tha t G o d c a use s e ve r yt hing w ha t he k now s, it f ollow s tha t if thi s t he sis is tr ue , the n G od c a use s im mor a l a c t ions suc h tha t he is nor ma tive inc ons iste n t w . r . t. c ondi tion s ( c ) a nd ( d) be c a use he ha s give n c omma nd s ( f or e xa mple the T e n Com m a ndme nts) t o ma n. Sinc e w e c a nno t a t tr ibu te to G od a vol i tive a nd nor ma tive inc ons iste nc y ( a n inc ons iste nc y of h is w ill) , the the sis "G od c a use s e ve r ythi ng w ha t he know s " mus t be f a lse .

6.35 If God causes everything what he knows, then he causes everything Sinc e G od d oe s not c a use i mmor a l a c ti ons, he doe s not c a use e ve r ythi ng a nd the r e f or e the the sis tha t G o d c a use s e ve r ythin g w ha t he know s mus t be f a ls e . T he a bove the si s, tha t if G od c a use s e ve r ything w ha t he know s, the n he c a use s e ve r ything, c a n be substa ntia te d a s f ollow s. I n c ha pte r 4 it w a s de f e nde d tha t G od know s a ll pa st a nd pr e se nt e ve nts. T hu s if p is a pa st or a pre se nt e ve nt ( of this unive r se ) , the n G od know s tha t p . Sy mbol ic a lly : ∀pt ≤ t0 ( p → gKp) . T oge t he r w ith the w r ong the s is: G o d c a use s e ve r ything w ha t he kn ow s ( sy mbo lic a lly : ∀p ( gKp → gCp ) ) it f oll ow s f r om i t tha t G od c a use s ( c a use d) e ve r y pa st a n pr e se nt e ve nt. S ym bol ic a lly: ∀pt ≤ t0 ( p → gCp ) . I t w il l be de f e nde d la te r tha t also the mor e ge ne r a l the sis ho lds f or G od's know le dge : G od know s a l l e ve nt s tha t oc c ur ; or G od know s e ve r yt hing w hic h i s the c a se . S ymb olic a l ly: ∀p ( F(p) → gKp) , w he r e ' F(p) ' sta n ds f or ' p is the c a se ' or ' p obta ins'. Fr om t his a ss ump tio n toge t he r w ith the ( f a lse ) the sis G od c a use s e ve r ything w ha t he kn ow s, i t f ol low s tha t G od is a l lc a using. T h is c a n be se e n a s f ol low s : f r om F(p) → gKp a nd gKp → gCp it f o llow s tha t F(p) → gCp, i. e . w ha te ve r

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is t he c a se is c a use d by G od. Fr om t his it f oll ow s ( b y c on tr a posi tio n, by subst itu tio n of ¬p f or p a nd by the a ss umpt ion tha t F(¬p) = ¬F(p) ) tha t f or e ve r y e ve nt p e ithe r G od c a use s t ha t p or G od c a use s tha t n on - p . Sy mbol ic a lly : ∀p ( gCp ∨ gC¬p) . T his the sis w e ma y c a ll the the sis of the a llc a using G od. I t w a s disc u sse d in de ta il a nd sho w n to be f a l se to ge the r w i th the a na logo us the si s of the a l lw il lin g G od in a not he r pub lic a tio n. 6 1 T he t he sis of the a llc a using G o d le a ds to t he sa me a bsur d c onse que nc e s w hic h ha ve be e n disc us se d a lr e a dy in c h. 6. 32 a bove . T hus t he y ne e d no t be r e pe a te d he r e . T he se c onse que nc e s show tha t – si nc e w e c a n de f e nd the the sis tha t G od know s e ve r ythi ng w hic h is t he c a se – the r e ma ining othe r pr e mise m ust be f a lse , i. e . the pr e mise : G od c a use s e ve r ything w ha t he know s, must be f a lse .

6.36 The thesis of the allcausing God and transitivity O bse r ve tha t the ( w r ong) the si s of t he a l lc a using G od w ould a lso f oll ow f r om a w r ong a pplic a tion of tr a n s iti vit y to t he c a usa l r e la tion be tw e e n G od a nd c r e a tion. Sinc e if G od i s the f ir st c a use in a c a usa l c ha in or in a c a usa l tr e e a nd if the c a usa l r e la tio n is tr a nsi tive , t he n the f ir st c a use c a use s e ve r yth ing w ha t the subse q ue nt me mbe r s c a use , i. e . the n th e f ir st c a use c a use s e ve r ything ( e ve r y me mbe r of the c ha in or tr e e ) in the se nse of a suf f ic ie nt c a use . I n suc h a ca se G od w ould be a llc a using. T hus w e a r e a sking the que sti on: D oe s it f oll ow f r o m be ing a f ir st c a use ( in a c ha in or ne t of c a usa l r e la tions ) tha t t he f ir st c a use c a use s e ve r y me mbe r ( i n the c ha in or ne t) ? I t is c e r ta inly ma nif e st tha t t he f ir st c a use a n d f ir st me mbe r of a c a usa l c ha in mu st c a use the se c ond me mbe r . A nd if the r e i s a br a nc hing ( a "tr e e ") , the n the r e a r e mor e ( tha n one ) se c on d m e mbe r s a nd a ll the se m ust be c a use d by the f ir st c a use ( me mbe r ) . But the se c ond me m be r s a r e c a usa lly r e la te d to the thir d me mbe r ( or me mbe r s) a nd c a use the m; t hose a ga in c a use the f our th. . . e tc . But the se c ond me mbe r s ne e d no t c a use the f our th me mbe r s a lth ough t he y a r e c a usa lly r e la te d ( c onne c te d) w it h the m via the th ir d me m be r s; a nd t hus a l so the f ir st me m be r ne e d not to c a use the t hir d or f our th me mbe r s a l tho ugh it i s c a usa lly c onne c te d w ith the m via t he s e c ond me m be r s. T his me a ns w e ha ve to dis ting uis h t he f ollow ing tw o thin gs: ( 1) be ing c a usa ll y c onne c te d ( r e la te d) to so me me m be r ( x is c a usa lly r e la te d to

y in some w a y) a nd ( 2) be ing c a use d by so me me mbe r ( x is c a use d by y) or y be ing c a usa lly

de p e nde nt on x.

6 1 See Weingartner (2003, EDK), ch. 6. 4.

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A n e xa mple ma y il lustr a te t he dif f e r e nc e : T he 4 gr a ndpa r e nts a r e the c a use of the pa r e nts a nd the se pa r e nt s a r e th e c a use of the ir c hi ldr e n. Bu t the gr a ndpa r e nts a r e not the c a use of th e ir gr a ndc hildr e n a lth ough the y a r e c a usa lly r e la te d ( c onn e c te d) w ith the m. A ssume tha t a gr a ndc hil d ( a s a n a dult) s olve s so me i mpor ta n t sc ie n tif i c pr oble m. W e c a nno t sa y tha t the pa r e nts or gr a ndpa r e nts c a use d thi s solu tion a l thou gh bo th a r e c a usa lly c onne c te d w it h tha t gr a ndc hil d; or a s su me tha t the gr a ndc hi ld ( a s a n a d ult) c omm itte d a c r ime . A ga i n, w e c a nnot sa y tha t the pa r e nts or gr a ndpa r e nts c a use d tha t c r ime ( pr e supposi ng tha t the c hild ha d a nor ma l e duc a tion) . T hus it is c le a r tha t the gr a ndpa r e nts are not a sufficient cause ( not a c a use a s a sufficient condition ) f or the gr a ndc hil dr e n, but the y a r e c e r ta inly a ne c e ssa r y c a use ( a c a use in the se nse of a necessary condition ) f or the m. Si mila r ly t he f ir st c a use ( G od) is a ne c e ssa r y c a use ( a c a use in the se nse of a ne c e ssa r y c ondit ion) f or a ll othe r c a use s a nd e ve nt s, but not a suf f ic ie nt o ne . Fr om th is it f ollow s tha t tr a ns iti vit y hold s f or the c a use s a s ne c e ssa r y c onditi ons, bu t not f or the c a use s a s suf f ic ie nt c onditio ns. A sim ila r c ounte r e xa m ple to tr a n sit ivi ty ( of c a use s a s suf f ic ie nt c ond iti on) is give n by Pe a r l; w he r e sta te X is c a pa ble of c ha nging the sta te Y a nd Y is c a pa ble of c ha nging the s ta te Z, ye t X i s inc a pa ble of c ha nging Z. "T ha t c a usa l de pe nde nc e is n ot tr a n sit ive i s c le a r . . . The que sti on na tur a lly a r i se s a s to w h y tr a n sit ivi ty i s s o of te n c onc e ive d a s a n i nhe r e nt pr o pe r ty of c a usa l de pe nde nc e . . . " 6 2 T he ma in point i s tha t X is not suf f ic ie nt in or de r to c ha nge Z. Bu t t he e a r lie r ( a nc e stor s) in t he c a us a l c ha in or ne t mi ght be ne c e ssa r y a nd the f ir st me m be r is c e r ta inly ne c e ssa r y f or a ll the othe r s, but no t suf f ic ie nt. I n this r e spe c t i t is inte r e st ing tha t T ho ma s A quina s in h is se c ond ( c a usa l) w a y to pr ove t he e xiste nc e of G od r e quir e d only ir r e f le xivit y ( e xpl ic ite ly in h is pr e mise s) of the c a usa l r e l a ti on w h ic h hold s be tw e e n th ings a nd a f ir s t e le me nt. I nte r e st ingl y e no ugh he d idn ’ t a ssu me tr a n sit ivi ty. Ce r ta inly he a ssume d a lso a sy mme tr y be tw e e n G od a s t he c a use a nd the w or ld a s the e f f e c t. Conc e r ning the c a usa l r e la tion w ithi n the w or ld w e kno w toda y : T he f unda me nta l la w s of Q ua n tum Me c ha nic s a nd Re la tiv ity T he or y a r e time -r e ve r sa l sym me tr ic suc h tha t t he y do not de s igna te a c a usa l or de r in one dir e c tion on ly. H ow e ve r the dir e c tio n of the a c tua l move me n t ( of sta r s, pla ne ts, a tom s … e tc . ) c a nnot be r e ve rse d; its just tha t the dyna mic a l la w s don’ t f or bid the oppo si te dir e c tion. A n d – to give a n e xa mp le f r om a nothe r a r e a – the ne ur ona l c onne c tions in the br a in a r e r e c ipr oc a l ( ne ur on A f ir e s to 6 2 Cf. Pearl (20 00, CMR), p. 237. The failure of transitivity is also illustrated by Pear l with the he lp of a figur e which represents a model as a c ounterexample. For further counterexamples against transitivity see Galles - Pearl (1997, ACR).

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ne ur on B a nd vic e ve r sa ) a nd do not s how a n a sym me tr y e ithe r ( e xc e pt the a sym me tr y i ntr od uc e d by the ti me of pr opa ga ti on of the ne ur ona l e f f e c t w hic h c a nnot e xe e d the ve loc ity of lig ht ) . 6 3 6. 4 A ns w e r to th e O b jec t io ns

6.41 God’s knowledge – a necessary cause (ad 6.11) T homa s A q uina s doe s no t c la im tha t t he know le dge of G od is a suf f ic ie nt "c a use of things ". T his i s pla in f r om t he e nd of a r tic le 8 w he r e he sa ys: "H is know le dge m ust be the c a use of things, i n so f a r a s H is w ill is joi ne d to it. " 6 4 A nd in a r t ic le 9, w hic h de a ls w i th t he que sti on w he t he r G od ha s know le dge of things tha t a r e not, he ma ke s tha t point e ve n mor e e xplic it : "T he know le dge of G o d, joine d t o H is w ill i s the c a use of thing s. H e nc e it is not ne c e ssa r y tha t w ha te ve r G od know s, is , or w a s, or w ill be ; b ut o nly is t his ne c e ssa r y a s r e ga r ds w ha t H e w ills to b e , or pe r mits to be . " 6 5 Mor e ove r , it is c le a r f r om the te xt of a r tic le 8 tha t the kind of c a u se w hic h is me a nt he r e is the causa formalis ( inte ll igi ble f or m) a nd not the causa efficiens . G od' s know le dge w . r . t. c r e a tur e s is c omp a r e d t o the know le dge of the a r tif ic e r w . r . t. his w or k s of a r t. But the causa formalis i s not suf f ic ie nt a s the f oll ow in g quota t ion s how s : ". . . the in te lli gib le f or m doe s not de n ote a pr inc i ple of a c tio n insof a r a s i t r e side s in the one w h o un de r sta nds u nl e ss the r e is a d de d to it the inc lina t ion to a n e f f e c t, w hic h inc lina ti o n is thr oug h the w ill. " 6 6

6.42 God’s knowledge – not a sufficient cause (ad 6.12) A lso the qu ota ti on of A ugu sti ne ne e d no t be in te r pr e te d in suc h a w a y tha t th e know le dge of G od w ould be a suf f ic ie nt c a use f or the e xi ste nc e of t he c r e a tur e s. But it c a n be inte r pr e te d a s sa ying tha t G od's know le dge w . r . t. c r e a tur e s in the se nse of his pla n of the c r e a tion must be pr i nc ipa ll y pr ior a nd mus t be a ne c e ssa r y c onditio n ( c a use ) for the ir e xiste nc e . W ha t is pointe d ou t by A ugu st ine is tha t w he r e a s in the c a se of ma n, th ings a r e f ir st a nd t he n ma n c a n ha ve know le dge of the m, i t i s t he o pposi te w i th G od w ho d oe s no t ne e d thing s in or de r to ha ve know le dge . 6 3 For neuronal interaction se e Popper - Eccles (1984, SfB), p. 228 and 241ff. For a discussion of the causality relation which is expressed by laws of nature, see Mittelstaedt/Weingartner (2005, LNt), ch. 9. 6 4 Thomas Aquinas (STh) I, 14, 8. 6 5 Ibid. 14, 9 ad 3. 6 6 Ibid. 14, 8.

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6.43 Omniscience and Freedom (ad 6.13) Be f or e w e give a c om me nt o n the a r gu me nt i n 6. 13 w e s ha ll tr a nsla te i t in to symb olic f or m. T he a r gu me nt ha s f our p r e mise s of w hic h the t hir d ha s a mor e c ompl ic a te d f or m. W e sta te the r e f or e the thir d pr e mise in a sim ple r f or m f ir st a nd give its de ta i ls onl y a f te r the a r gume nt. 1. ( OSg ∧ E!gt 1 ) → ( jAt2p → gBt 1 ( jAt 2 p) ) 2. gBp → p 3. gBt 1 ( jAt2p ) → [ jCAt 2 ¬p → ( ( i) ∨ ( ii) ∨ ( iii) ) ] 4. OSg → ¬( ( i) ∨ ( ii) ∨ ( iii) ) 5. T he r e f or e : ( OSg ∧ E!gt 1 ) → ( jAt2 p → ¬jCAt 2 ¬p ) T he thr e e a lt e r na tive s in pr e mise 3. a r e as f ollow s : (i) jCAt2 ( gBt 1 p ∧ ¬p) (ii) jCAt2 ( ¬gBt 2 p ∧ gBt 1 p) (iii) jCAt2 ( ¬E!gt 1 ) Sinc e w e ha ve tur ne d t he a r gume nt i nto pr e c ise f or m, w e sha l l f ir st a sk w he the r this a r gume n t is log ic a lly tr ue or va lid. T he a nsw e r to this que stion i s ye s. O ne c a n see this e a sily if one ma ke s the f ollow i ng a bbr e via ti ons in or de r to obta in a ve r y sim ple a r gume nt s tr uc tu r e : OSg . . . A . . . G od is omni sc ie nt jAt 2 p . . . B . . . Jone s a c ts a t t2 tha t p gBt 1 ( jAt2 p ) . . . C . . . G od be lie ve s a t t1 tha t Jone s a c ts a t t2 t ha t p jCAt2 ¬p . . . D . . . Jone s can a c t ( ha s the pow e r to a c t) a t t2 tha t non - p ( i) ∨ ( ii) ∨ ( iii ) . . . I E!gt1 . .. E . . . G od e xists a t t1 T he n the a r gume nt be c ome s the f ol low i ng sim ple f or m: 1'. ( A ∧ E ) → ( B → C) 2'. C → ( D → I ) 3'. A → ¬I T he r e f or e : ( A ∧ E ) → ( B → ¬D ) O ne c a n se e imme dia te ly tha t th is a r gu me nt is va lid. I t is a n a bbr e via t ion of the f or me r mor e de ta i le d a r gume nt w it hout pr e m ise 2. T o de r i ve the a bove c onc lusio n t he se c ond pr e m ise ( 2. ) i s not ne e de d. B ut w e ha ve no t ye t a na lyse d I a nd pr e mi s e 4. For the j ust i f ic a tion of pr e m ise 4. , pr e mise 2. is ne e de d . Be f or e w e ma ke a c omme nt to the pr e mise s w e sha ll f ir st e mpha s ise a ga in tha t a c c or ding to c ha p te r 3 the a ttr ib uti on of ti me indic e s to G od or t o G od' s a c tions d oe s no t ma ke se nse . A s it w a s sa id the r e , ti me i s unde r s tood he r e a s the ti me of th is unive r se w hic h is m e a sur e d dif f e r e ntly a n d r e la ti ve ly in

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subsy ste m s of thi s unive r se , i. e . f or insta nc e a t the e a r th ( not to spe a k of L ondon - ti me or L os A nge le s - ti me ) . T he r e is no u nive r sa l ( or a b sol u te ) ti me w hic h w ou ld be va lid f or the w h ole unive r se or f or a ll its s ubsy ste m s. A c c or dingly, a lth ough w e c a n sa y tha t G od, be ing omn isc ie nt, kno w s tha t some e ve nt A ( f or ins ta nc e a f r ee a c tion of a huma n pe r son) ha ppe ns a t a ti me t2 r e la tive to a t ime me a s ur e me nt use d o n e a r th a nd mor e ove r t ha t th is e ve n t A oc c ur r e d la te r tha n a nothe r one B a t t1 ( a c c or ding to t he sa me t ime me a sur e me nt) , t ime is only a ttr i bute d t o e ve nts of t his w or ld ( uni ve r se ) but not to G o d or his k now in g a nd w il lin g. I n this c onne c ti on it is in te r e sting to a sk w he the r dr opping a ll t he time ind i c e s a ttr ibute d to G od' s be lie f w ould ma ke a c ha nge w . r . t. the va l idi ty of t he a bove a r gu me nt. T he a nsw e r to thi s que sti on is: N o. T he va lid ity r e ma in s un touc he d in th is c a se . But the pr e mise s w ill r e c e ive a dif f e r e nt me a ning of c our se . W e a r e tur ning n ow to a disc u ssi o n of the f o ur pr e mi se s. T he m ost unc ontr ove r s ia l pr e m ise is pr e mi se 2: E ve r ything w ha t G o d be l ie ve s is tr ue . I f w e r e pla c e 'be lie ve s' by 'kno w s', the n the r e spe c tive pr e mise ha s be e n d e f e nde d a lr e a dy in c ha p te r 1: E ve r yt hing w ha t G o d k now s is tr ue . A nd a lthoug h it i s not ve r y r e a sona b le to a ttr ibute be l ie f s to G o d, this c a n be a c c e pte d f or the sa ke of the ar gume nt s inc e pr e mise 2 gua r a nte e s tha t a ll of G od's be lie f s a r e tr ue . I t m igh t b e w or th me n tio ning tha t Pi ke pr e supp ose s he r e tha t 'be lie f ' is unde r stoo d in suc h a w a y tha t “ pe r son a know s tha t p ” imp lie s “ pe r s on a be lie ve s t ha t p” ; i. e . w ha t one know s, one a l so be lie ve s 6 7 in the se nse of ho ldin g i t t o be tr ue . T he r e is how e ve r a not he r c onc e pt of be lie f w hic h ha s a dif f e r e nt, i. e. e xc lusive r e lation to k now le dge : w ha t one be lie ve s one doe s no t ( ye t) know a nd w ha t one know s o ne doe s no t ( ne e d to) be lie ve a ny mor e . T hi s k ind of be lie f is f a r m or e imp or ta nt tha n the f or me r o ne . Si nc e w ha t one mig ht c a l l sc ie n tif ic be lie f ( th e be lie f in sc ie nt if ic hy pothe se s) a nd a lso r e ligio us be lie f is of thi s se c ond kin d. 6 8 Pr e mi se 1. is c e r ta inly a c c e pta ble if w e dr op the time i nde x t1 a ttr i bute d t o G od's e xis te nc e a nd be lie ving. T he gist of it is the n ju st t ha t G od know s w ha t ha ppe ns a t t2 ( w he r e t2 is a point of tim e of this w or ld) . T he r e f or e it must be tr ue to sa y: if Jo ne s a c ts a t t2 tha t p, the n G od know s ( be lie ve s) tha t Jone s a c ts a t t2 tha t p . S inc e t his i s t he c onse q ue nt of pr e mi se 1. , the w ho le pr e m ise mus t be tr ue . I f w e a dd the time ind ic e s, the n w e f ir st ha ve to c onside r E!gt1 : G od e xists a t t1 . A lth ough th is se nte nc e w o ul d be f a lse if w e inte r pr e t it a s sa y ing tha t G od 's e xi ste nc e is b ound or de p e nde nt upo n ti me ( the t ime of t his 6 7 Pike (19 70, DOV) 6 8 For a detailed discussion see Weingartner (1994, SRB). Cf. section 1. 36 of this book.

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unive r se ) it c a n be a c c e pte d if i t j ust me a ns: G od c e r ta inly e xis ts a t a n y po int of time in w hic h th is uni ve r se e xists. I n the sa me se nse w e ma y inte r pr e t the c onse que nt. G od k now s a t t1 tha t Jo ne s a c ts a t t2 t ha t p . T his i s t o me a n tha t w ha t G od know s t ha t i t ha ppe n s a t s ome ti me ( of th is w or ld) he k now s a t a ny point of ti me of t his w or ld. I nte r pr e te d in th is se n se the f ir s t pr e mi se c a n be a c c e pte d to be tr ue . T he mo st c o mpl ic a te d a nd pr o ble ma t ic one is pr e mise 3. T he ma i n que s tio n is w he the r the a nte c e de nt is c ontr a di c t or y a nd the n the pr e mise w ou ld be tr ue , but logic a l ly tr ue or tr iv ia lly ( or e m pti l y) tr ue . T hi s c a n be se e n a s f oll ow s: Fr om G o d be lie ve s ( a t t1 ) tha t Jone s a c ts a t t2 tha t p, it f ollow s tha t: Jo ne s a c ts a t t2 tha t p ( by pr e mise 2) . But if the la tte r is tr ue , Jone s cannot a t the sa me time t2 a c t tha t no n - p. E ve n if he a c ts volunta r il y, i. e . f r ee ly. Sinc e it is ju st a n impo ssi bil ity to bo th a c t a t t2 tha t p a nd a c t a t t2 tha t n on - p. I t is a l so impo ssi ble to both a c t a t t2 tha t p a n d ha ve the pow e r ( or a bil i ty) a t t2 t o a c t a t t2 tha t non - p. Suc h a kind of " pow e r " no body c a n ha ve not e ve n G od, si nc e it w ould me a n a n inc ons iste nc y. T hi s inc onsis te nc y is s ym bol ic a lly e xpr e sse d thus : jAt 2 p ∧ jCAt2 ¬p. T he pow e r to a c t tha t ¬p J one s c ou ld ha ve e a r lie r tha n t2 but not e xa c tly a t t2 w he n he a c ts tha t p . T he r e f or e w ith t he he lp of pr e m ise 2 it f oll ow s f r o m pr e m ise 3 tha t the a b ove c ontr a dic t ion im plie s ( i) ∨ ( ii) ∨ ( iii) w hic h is a lso log ic a lly tr ue : ( jAt2 p ∧ jCAt2 ¬p ) → ( i) ∨ ( ii) ∨ ( iii) . T hus i t doe s not ma t te r tha t ( i) ∨ ( ii) ∨ ( iii) i s i ts e lf c ontr a dic tor y. A n d so pr e mise 4 is c or r e c t of c our se be c a use it is logic a lly t r ue . T he r e f or e w e ha ve to sa y: e ve n w it h f r e e ( volunta r y) a c tion s it hol ds tha t if the e ve nt ( a c tion) ta ke s pla c e ( a t t2 ) it c a nnot no t ta ke p la c e ( a t t2 ) . But f r om this one c a nnot c onc l ude tha t the a c tion ( a t t2 ) is ne c e ssa r y or not volunta r y, or not f r e e or not c ontinge nt : T ha t I a m sit ting no w a t t3 a nd w r iting thi s c ha pte r is both c on tin ge nt a nd vo lunta r y ( f r e e ), a lthough I a m not a b le ( I do not ha ve the pow e r , I c a nno t) no w ( a t t 3 ) to a c t in suc h a w a y tha t I a m not sitt ing or not w r i tin g; i. e . unde r the c ondit ion tha t I a m si tti ng I c a nnot do some t hing e lse w hic h w oul d i mpl y n ot - sitt ing. T h is w a s c a lle d "c on dit iona l ne c e ssity " i n the phi los ophic a l tr a di ti on. A s is c le a r f r o m the e xa mp le s, c ondit iona l ne c e ssit y is pe r f e c tly c o mpa tible w ith the a c t ion be ing c onti nge nt a nd volunta r y ( f r e e ) . T he re f or e , if the inte r pr e ta tion of "c ondi tio na l ne c e ssity " is a pplie d, the c onc lusi on of Pi ke 's a r gume nt is e ve n logic a l ly or tr ivia l ly tr ue be c a use the se c ond pa r t is logic a lly tr u e , na me ly: I f ( i.e . unde r the c ondition tha t) Jone s a c ts a t t2 tha t p, it is not t he c a se tha t Jone s c a n a c t a t t2 tha t non - p. Sy mbol ic a lly : jAt 2 pt 2 → ¬jCAt 2 ¬pt 2 . Fr om thi s c ons id e r a tion it f ol low s tha t J one s c a n a c t ( or ha s the pow e r to a c t) tha t no n - p onl y a t a po int of ti me e a r lie r tha n t2 ( a t w hic h he a c ts tha t p) . A t

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time t2 the a c tion is be in g c omm itte d a nd c a nnot be a lte r e d a ny mor e . A nd e a r lie r he c ould ha ve de c ide d othe r w i se ( on t he a ssu mp tion tha t i t w a s a f r e e volun ta r y a c tion) . A l thou gh o ne ha s t o obse r ve tha t pr e li mina r y pr e pa r ing a c tions c om mi tte d b y Jone s f or t he a c tion a t t2 tha t p, c a n ma ke it mor e a nd mor e im pr oba ble tha t J one s i s a ble t o a c t tha t non - p be f or e a c ti n g a t t2 tha t p. A nd if Jone s w o uld ha ve de c ide d ( a nd c omm it te d h imse lf ) to a c t tha t no n - p a t t2 ( inste a d of a c ting tha t p) , the n G o d w ould ha ve know n tha t he is a c ting tha t non - p a t t2 . A nothe r i nte r pr e ta tio n of P ike ’ s a r gu me nt w a s give n by Pla n tin ga . 6 9 H e tr ie s to show c onvi nc ing ly tha t ne it he r of ( i) or ( ii) or ( iii) f ollow s f r om “ John a c ts a t t2 t ha t p a nd Joh n c a n a c t a t t2 tha t ¬p” pr ovi de d t he la t te r is in te r pr e te d a s c onsis te nt. I nste a d the c ou nte r f a c tua l pr oposi tio ns ( 52’ ) , ( 53b) a nd ( 54’ ) f ollow . T he y a r e r a the r har mle ss a nd do not im ply t ha t G od is no t omn isc ie nt. For t he que s tion w he the r f or e kn ow le dg e c a n c ha nge the on tolo gic a l s ta tus of a n a c tion ( be it c ontinge nt a nd f r e e or nec e ssa r y) se e c hs. 10. a nd 11. be low .

6 9 Plantinga (1974, GFE) p. 68ff.

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7. Whet her God Kn ows S i ngu l ar T r ut hs? Conc e r nin g te r mino log y a sing ula r tr u t h is a tr ue sta te me nt a bou t a n obje c t w hic h is un de r stoo d a s ind ivid ua te d in s ome w a y or a bout a gr oup of ob je c ts w hic h a r e un ite d toge the r to a sin gle o bj e c t. For e xa mp le a n a to m, a l ivi ng be ing, a pe r son; but a lso a n ind ivid ua l s ta te or e ve nt or huma n a c tion, w he r e the la tte r a r e indivi dua te d by the pla c e or the point of ti me or by bot h. I nste a d of sa ying "tr ue sta te me nt a bo ut. . . " w e c ould a lso sa y "f a c t a bout. . . " or "obta i nin g sta te of a f f a ir s a bou t. . . ". I n this se nse w e c ould a l so s pe a k of "sin gula r f a c ts". I f the indivi dua ti on is e xpr e sse d mor e pr e c ise ly, one use s spa c e time c oor di na te s, like in the se nte nc e "the e xplo sion of the f ir st tow e r in Ma nha tta n on Se pt. 11, 200 1". I n ge ne r a l a se nte nc e p w ith spa c e ti me c oor dina te s ma y be e xpr e s se d a s " pl,t " w he r e l loc a te s po si tion ( pla c e ) a nd t time . I n disc uss ion s on omn ipo te nc e the so - c a lle d A- pr oposi tion s or A-se nte nc e s do not me n tio n t he pos iti on, but onl y t he poi nt of t ime ; suc h A-pr oposi tio ns c a n be f or m ula te d thu s: pt1 , qt2 , rt3 . . . pt2 , qt3 . . . e tc. I ntr oduc ing the ope r a tor s ' K', ' CK', ' TE', a nd ' TO' f or 'know s tha t ', 'c a n know tha t', 'tr uly e xpr e sse s tha t ' a nd ' tr uly to ke ns t ha t' r e s pe c tive ly w e c a n f or m se nte nc e s like aKpt , bCK pt, cTEpt . . . e tc . ( w he r e ' a ', ' b' a nd ' c ' sta nd f or pe r sons) . 7. 1 A rg u me nt s C o nt ra

7. 11 T he a im of the pe r f e c t sc ie nti st i s not to know a ll t he sing ula r tr ut hs a nd da ta , but t o kno w the a x iom s a nd la w s f r om w hic h the y f o llo w . I n a si mila r w a y A r ist otle c ha r a c te r ise s the w ise m a n: "W e supp ose f ir s t, the n tha t the w ise ma n kn ow s a l l t hin gs, a s f a r a s po ssib le , a lthou gh he ha s n o k now le d ge of e a c h of the m indi vidua l ly. " 7 0 N ow , sinc e G od is m ost pe r f e c t a nd m ost w ise , he know s r a the r the a xio ms tha n the inf i nite sing ula r tr u ths a nd da ta a nd the la tte r a s c o nse que nc e s of the f or me r . T he r e f or e G od doe s not se e m t o ha ve dir e c t know le dge of singu la r tr uths a nd of tr ut hs a bout s ingu la r thing s . 7. 12 T he r e a r e ma ny de spic a ble a nd ir r e le va nt tr ut hs un de r the sin gula r tr ut hs. But a s A ugu sti ne sa ys, the se a r e be tte r not to know t ha n to know : "T he si tua ti on is c o mp le te ly d if f e r e nt how e ve r if so me one

know s th is, a nd the othe r one tha t, th e one use f ul things, the othe r le ss u se f ul or e ve n de r oga t or y t hings. W h o w ou ld no t

7 0 Aristotle (Met), 982a7.

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pr e f e r – in the la t te r c a se – the one w h o doe s no t kno w ove r the one w ho know s? T he r e a r e e ve n things of w hic h it is be t te r not to know the m, tha n to know the m. " 7 1

But s inc e w e should a ttr ibu te to G od r a the r w ha t is be tte r , it s e e ms tha t he ne e d not to know a ll s ingu la r tr uths. 7. 13 E ve r y tr ue A- pr op osi tion is a s i ngula r tr u th. But a s G a le sa ys, G o d c a nnot kno w A- pr opo sit ion s. T he r e f or e G od doe s not know a l l s ingu la r tr uth s. T ha t G o d c a nnot kn ow A- pr o pos itio ns G a le tr ie s to pr ov e i n t he f oll ow in g w a y: 7 2 ( 1) A pe r son c a n know a pr opositi on onl y if she c a n tr uly e xpr e ss it. Fr om t his w e c a n ma ke the insta nt ia tio n: ( 1a ) A pe r son c a n know a n A- pr oposit ion on l y if she c a n tr uly e xpr e ss it. ( 2) A pe r son c a n tr u l y e xpr e ss a n A- pr opo s itio n on ly if she c a n tr ul y to ke n

a n A- se nte nc e ( w he r e a n A- se nte nc e i s a se nte nc e e xpr e ss ing a n A-pr oposi tio n) .

( 3) A pe r son c a n tr uly toke n a n A- se nte nc e only [ if she tr ul y toke ns i t] a t a time .

( 4) A pe r son tr uly toke n s a n A- se nte nc e a t a time only if she e xis ts in t ime . ( 5) A pe r son c a n know a n A- pr oposi tion o nly if she e xist s in t ime ( f r om

( 1a ) to ( 4) ) . ( 6) E nthy me m : A time le s s be ing doe s no t e xist i n time . ( 7) T he r e f or e : A time le ss be ing c a nno t kno w a n A- pr oposit ion. A nd c onse que n tly : Su ppo sing tha t G od i s a time le s s be ing he c a nno t know a n A- pr oposi tio n a nd the r e f or e he doe s not know a ll sin gula r tr ut hs. 7. 2 A rg u me nt s P ro

A c c or ding t o c ha pte r 4 G od kn ow s a l l p a st a nd pr e se nt e ve nt s. B ut ma ny tr ue de sc r iptio ns of pa s t a nd pr e se nt e ve nt s a r e singu la r tr ut hs. A n d s ome of t he m ha ve the f or m of A- pr op osi tion s. T he r e f or e G od know s sin gula r tr u ths a nd he know s a lso A- pr o pos iti ons.

7 1 Augustine (Ench), 17. 7 2 See Gale (1993, NEG), p. 65f. Thi s report o f t he argument is a reconstr uc tion, but one that tr ies to do j ustice to Gale' s i ntention though putting it i nto a more c oncise fo rm (for example avoi ding change s from "is expre ssible" to "a person can truly ex press" etc. ) and adding enthymemic premises.

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7. 3 P r opo se d A n sw e r

G od kno w s s ingu la r tr ut hs. O ne r e a son f or tha t i s a s f ol low s : A c c or din g to c h. 5 G od's k now le d ge e xc e e ds G od's po w e r . But G od's p ow e r e xte nds c e r ta inl y to sin gula r tr u ths or s ing ula r f a c ts. E xa mple s a r e hi s c r e a tur e s a nd his c r e a tion. T he r e f or e a lso his know le dg e must e xte nd to si ngula r tr ut hs or singu la r f a c ts. A se c ond r e a son c a n be give n by a compa r is on w it h ma n’ s kn ow le dge of singu la r tr ut hs. Ma n know s s ingu la r tr uths ( sing ula r f a c ts) via tw o dif f e r e nt w a ys: f ir s t thr oug h e xpe r ie nc e , se c ond w ith the he lp of la w s. I n t he f ir st se nse , by e xpe r ie nc e he know s o nly t ha t the y a r e , in t he se c ond se nse he know s w h y the y a r e so a nd n ot o the r w i se . T he se c ond w a y of know le d ge f or singu la r tr ut hs i s t he sc ie nt if ic w a y, a lt hough it a l so ha s to inc lu de the f ir st w a y ( e xpe r ie nc e ) in a r e f ine d a nd me thodo log ic a lly c ontr olle d w a y. I t i s r oughly a s f oll ow s: 7 3 I n or de r to e xp la in or pr e dic t ( r e tr odic t) s ingu la r tr uth s ( f a c ts) w e use w e ll c onf ir me d la w s ( of na tur e ) toge the r w ith i nit ia l c o ndi tion s w hic h a r e a lso sin gula r tr ut hs ( f a c ts) . For e xa mp le in or de r to e xp la in or pr e dic t a n e c lipse , the initia l c ondit ion is the c onste l la tio n of sun, e a r th a nd moon a t a c e r ta in ti me , w hic h to ge the r w ith N e w ton' s dyna mic a l la w s a llow to de r ive the de sc r i pti on of the e c li pse ( a s a sing ula r tr u th) f r o m t he se la w s. T hus i n ge ne r a l i t ho lds tha t s ing ula r t r uths c a n be k now n in t he se nse of be ing e xpla ine d a nd pr e dic te d ( r e tr odi c te d) w ith the he lp of othe r singula r tr uths ( u se d a s init ia l c ond iti ons) pl us d yna mic a l la w s. H ow e ve r , it ha s to be e mpha si se d tha t the la w s ha ve to be dynamical laws . Sta t ist ic a l la w s w oul d not be suf f ic ie nt. But s inc e la r ge a re a s of huma n know le dge a r e only a c c e ssible thr ou gh s ta tis tic a l la w s, ma n y sing ula r tr u ths in the se a r e a s c a nnot ( a t le a st not s o f a r ) be know n by ma n. T he se a r e a s a re : the r modyna mic s, r a dia tion, f r ic t ion, d if f usi on, e le c tr ic tr a nspor t, me a sur e me n t pr oc e ss in Q ua ntu m Me c ha nic s, pr oc e s se s of gr o w th, in ge ne r a l: pr oc e sse s of bio logy, psyc hol ogy a n d c os mol ogy. T he r e a son w hy s ta tis tic a l la w s a r e not sui ta ble f or e xp la in ing a nd pr e d ic ting s ingu la r tr uth s ( or sing ula r f a c ts) is the f ollow ing d if f e r e nc e be tw e e n tw o r e spe c tive c ha r a c te r istic s of dy na mic a l la w s ( D 1 a nd D 2) a nd sta tist ic a l la w s ( S 1 a nd S2) : D 1 T he sta te of the physic a l syste m S a t a ny give n time ti is a de f inite

f unc tion of it s sta te a t e a r lie r ti me ti- 1 . A uni que e a r lie r sta te ( c or r e sponding to a uni que sol uti on of the dif f e r e ntia l e qua t ion) le a ds

7 3 For a detailed analysis o f laws of nature, espe cially in the two forms of dynamica l and statistical laws cf. Mittelstaedt/Weingartner (2005, LNt), ch. 7.

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unde r the ti me e volu tio n to a un ique f in a l sta te ( a ga in c or r e spond ing to a unique solu tion of the e qua ti on) .

D 2 Cond it ion D 1 i s a ls o sa t isf ie d f or e ve r y pa r t of the p hys ic a l sy ste m, e spe c ia lly f or e ve r y ind ivi dua l bo dy ( ob je c t) a s pa r t of the sys te m e ve n if the ind ivi dua l o bje c ts ma y dif f e r in the c la ssic a l or in the q ua ntu m me c ha nic a l se nse . 7 4

S1 T he sta te of the physic a l syste m a t ti is not a de f inite f unc tion of a n e a r lie r sta te a t ti - 1 . T he sa me ini tia l s ta te ma y le a d to d if f e r e nt suc c e ssor sta te s ( br a nc hing) .

S2 Sta t ist ic a l la w s de sc r ibe a n d pr e dic t th e sta te s f or the w hole phy sic a l syste m, but the y do not de sc r ibe or pr e dic t the indiv idua l ( ob je c ts) of this sy ste m.

I t is e a sy to se e tha t t he r e is a n e sse n tia l dif f e r e nc e be tw e e n the c o ndit ion s D 1 a nd S 1. L ike D 1 is ne c e ssa r y f or d yna mic a l la w s, S1 is ne c e ssa r y f or sta tis tic a l la w s. T his pr e supp ose s ho w e ve r tha t w e inte r pr e t S1 ( a nd b y it sta tis tic a l la w s) r e a list ic a lly ( i. e . in a n ontic se nse ) . T ha t is w e a ssume the r e is r e a l br a nc hing in r e a li ty. A n e pis te mi c inte r pr e ta ti on a c c or din g t o w h ic h br a nc hing is o nly a sig n f or o ur la c k of know le dge w he r e a s in the un de r lyin g r e a lity e ve r yth ing is de te r m ine d ( by hid de n pa r a me te r s a n d dy na mic a l la w s of w hic h w e a r e ignor a nt) w e d o not f ind j ustif ie d. 7 5 T his c a n be s ubs ta ntia te d by the f a c t tha t t he a bove me n tione d type s of pr oc e sse s do not sa tisf y D 1 ( bu t sa tisf y S1) a s is e vide nt f r om a ll t he sophi stic a te d know le dge w e po sse ss toda y a bout t he se pr oc e sse s. Si mila r l y, D 2 a nd S 2 dif f e r in a n i mpor ta nt poi nt. S ta ti stic a l la w s a r e bound to hu ge e nse mb le s – the y de sc r ibe ph ysic a l sy ste ms c on sis ting of a hu ge numbe r of obje c ts. T he gr e a te r the numbe r of obje c ts, the mor e str ic t is the la w a bout t he w hole e nse m ble . T hou gh the r e is in de te r mi na c y f or e ve r y indiv idua l sys te m, the r e is a str ic t la w f or the w ho le sys te m if the e nse m ble i s la r ge e nough. T o s ome e x t e nt suc h la w s "e me r ge " f r o m t he " la w le ss " be ha viour of a la r ge numbe r of indi vi dua l sys te ms. I n thi s se nse W he e le r

7 4 It has to be observe d however that ' physical sy stem' can be understood in a twofol d way: classically and quantum mechanicall y. Classically D1 holds for example for every subsystem of a pl anetary system (for planets a nd parts of planets ) and thus for individual objects. Quantum mechani cally there is no de finite composition of subsys tems (they are not composable by Boolean operatio ns only) and objects as part s of physical systems have to have commensurable properties. 7 5 Cf. Weingartner (1998, SLG).

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spoke of "la w w i tho ut la w " 7 6 . T his pr oble m w a s c le a r ly unde r s tood a nd e mpha si se d a lr e a dy by Bo ltz ma nn a nd Poi nc a r é : H ow c a n the la w of e ntr opy e me r ge f r om r a ndo m be ha v iour of ind i vidua l sys te ms? Sc hr öd inge r ga ve t he f ollow ing a nsw e r in his i na ugur a l le c tur e of 1922 7 7 . "I n a ve r y la r ge nu mbe r of c a se s of tot a lly d if f e r e nt type s, w e

ha ve now suc c e e de d in e xpla ining the obse r ve d r e gula r ity a s c omple te l y due to the tr e me n dous ly la r ge num be r of m ole c ula r pr oc e sse s tha t a r e c oope r a tin g. T he ind ividua l pr oc e ss ma y, or ma y not, ha ve i ts ow n str ic t r e gu l a r ity . I n the obse r ve d r e gula r ity of the ma ss p he no me non the indiv idua l r e gula r it y ( if a ny) ne e d not be c ons ide r e d a s a f a c tor . O n the c ontr a r y, it i s c omple te l y e f f a c e d by a ve r a ging mi lli ons of s ingle pr oc e s se s, the a ve r a ge va lue s be in g the onl y th ing s tha t a r e ob se r va ble t o us. T he a ve r a ge va lue s ma nif e s t t he ir ow n p ur e ly statistical regularity … "

Su mm ing up w e ha ve to sa y tha t ma n 's know le dge of s ingu la r tr uths ( s ingu la r f a c ts) is r e s tr ic te d: F ir st it is po ssi ble to a tta in suc h know le dge to a high de gr e e of a cc ur a c y in those doma in s w he r e w e ha ve dyna mic a l la w s ( sa tisf yi ng D 1 a nd D 2, but a lso c ond itio n D 3, se e be low ) a nd a pr ec ise de sc r iptio n of init ia l c ondi tio ns. T he n a lso the indi vid ua l f utur e sta te s a nd the posi tion a n d othe r pr ope r t ie s of the in d ividua l obje c t s c a n be pr e dic te d w ith high a c c ur a c y. Se c ond, i t i s on ly pa r tia l ly po ssi ble t hr ough dir e c t e xpe r i me nt or obse r va tio n sinc e on ly a pa r t of the in divid ua l ob je c ts or sta te s on t he e a r th or in the c os mos a r e a c c e ssible in th i s se nse . T h ir d, ma n' s k now l e dge of singu la r tr ut hs is ve r y r e str ic te d c onc e r ning pr oc e sse s w h ic h c a n be only de sc r ibe d by sta t ist ic a l la w s. T his i s so be c a use if the r e ar e re a l de gr e e s of f r e e dom ( of dif f e r e nt type a nd pe r f e c tion) in r e a lit y – on the le ve l of the mole c ule s in a ga s , on the le ve l of liv in g or ga nis ms in le a r ning pr oc e sse s, on the le ve l of h uma n f r e e do m – t he n w e do not ha ve la w s to e xpla in or pr e dic t the se sin gula r pr oc e sse s ( w e c a n pr e dic t the m on ly w i th a ve r y lo w pr oba bil ity) . T h us w e d o no t ha ve ge nuine k now le d ge a bout the m or r e spe c tive ly a bo ut t he c or r e spond in g sin gula r tr u ths. W e ha ve o nly know le dge a bou t the a ve r a ge va lue s or a bout the de ve lopme nt of a huge e nse mble of s ingu la r obje c ts. T h is is e x pr e sse d in the thir d c on dit ion ( S3) of sta tis tic a l la w s be lo w . 7 6 Wheeler (1983, RLL). For more details on this question see chapter 13. 2 of Mittelstaedt/Weingartner (2005, LNt). 7 7 At the Universi ty of Zurich. This lecture was later published under the title "Was ist ein Naturgesetz?" . Cf. Schrödinger (1961, WNG), p. 11.

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But a lso c onc e r nin g dyna m ic a l la w s w e ha ve to a dd a n impor ta nt pr ov iso. Pr e dic ti on of si ngu la r f a c ts w i th the he l p of dy na mic a l la w s is onl y p oss ible if the syste m de sc r ibe d by the la w sa tisf ie s c onditi on D 3. O t he r w ise the sys te m be c ome s c ha otic a nd t he n the r e is a n e xpone ntia l inc r e a se of loss of inf or ma t ion a bou t the ind ivi dua l ob je c ts of the syste m. I n othe r w or ds t he r e is a n e xpone ntia l inc r e a se of ignor a nc e c onc e r ning singu la r tr uths. D 3 T he physic a l sy ste m S ha s a c e r ta in type of sta bili ty w hic h o be ys the

f ollow ing c ondi tio n: V e r y sma l l c ha nge s in the init ia l sta te s, sa y w it hin a ne ighb our hoo d d ista nc e of ε le a d to pr opor t iona l ly sma l l ( n o mor e tha n i n a c c or da nc e of a l ine a r ly inc r e a sing f unc ti on of ti me ) c ha nge s h ( ε ) in the f ina l sta te . T his k ind of sta bil ity w h ic h sur vi ve s sma l l pe r tur ba tion s a nd le a ds t o r e la xa ti on a f te r w a r ds is c a l le d perturbative stability a nd holds in ma ny li ne a r syste ms. 7 8

S3 T he loss of inf or ma tion ( a nd c onse q ue ntly the dif f ic u lty of pr e dic t ion) a bout the s ta te of a n in div idua l obje c t ( or a s ma ll pa r t) of the w hole syste m inc r e a se s e xpone n tia ll y w i th the c omple x ity of the sys te m. O n the othe r ha n d: ( a c c ur a c y of the ) i nf or ma tio n a bou t the a ve r a ge va l ue s of ma gnitu de s ( pa r a me te r s) of the sta te of a huge numbe r of individ ua l obje c ts ( or pa r tic le s) inc r e a se s a lso w ith the c omple x ity of the sys te m.

N one of the se r e str ic ti ons w hic h pe r ta in to the spe c if ic h uma n i nte lle c t c a n be a ttr ibute d t o G od. Fir s t be c a use the r e is no r e str ic tion in G od l ike tha t of our se nse s ( pl us t he te c hnic a l ins tr ume n ts to e xte n d the m) w . r . t. obse r va tio n; sinc e G od kn ow s w ith hi s i nte l le c t. Se c ondly, the r e is no r e str ic ti on in G od, like the one w e ha ve c onc e r ning pr oc e sse s a nd e ve nts de sc r iba b le only by sta tis tic a l l a w s ; sinc e unde r the a ssump ti on of G od a s c r e a tor he know s w hic h de gr e e s of f r e e dom he ha s give n to the dif f e r e nt type s of i ndiv idua l s a nd he him se lf ha s or de r e d tha t c r e a tur e s c ontr ibute to the ir ow n de ve lop me nt b y a le a r ning pr oc e s s via tr ia l a nd e r r or , pr ov iding f or t he m de gr e e s of f r e e dom on dif f e r e nt onto log ic a l le ve ls. T h ir dly, t he r e is no r e str ic t ion in G o d, like t ha t of our ignor a nc e w . r . t. c ha otic mo tio n; s inc e unde r the a ssu mpt ion of G od a s the c r e a tor he himse lf ha s c r ea te d a w or ld in w hic h c ha ot ic mo tion c a n de ve lop be c a use of se ns iti ve de pe nde nc e o n i nitia l c ond iti ons suc h tha t w e mus t

7 8 For chaotic motion in the sense of Dynamical Chaos cf. Schuster (1989, DCh) for a discussion of propert ies of dynami cal chaos c f. Weingartner (1996, UWT) and C hirikov (1996, NLH). For other kinds of chaos like Quantum Chaos cf. Casati, Chririkov (1994, QCh). For the restriction concerning pr edictability if D3 is not satisfied cf. Mittelstaedt/Weingartner (2005, LNt), ch. 9. 4.

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a ssume tha t he kn ow s w ha t Pr igo gine c a lle d the "L a w s of Cha os " 7 9 a nd in f a c t muc h mor e tha n tha t. 7. 4 A ns w e r to th e O b jec t io ns

7.41 Discursive Knowledge (to 7.11) A s it w a s de sc r i be d i n the a n sw e r , ma n 's kn ow le dge is suc h t ha t i t pr oc e e ds f r om the know le dge of ini tia l c ondi ti ons ( sing ula r tr uths) a nd f r om the know le dge of a xio ms or la w s, ta ke n t og e the r to t he kno w le dge of pr e dic ti ons ( othe r si ngula r tr uth s) . T hi s pr oc e dur e i s di sc ur sive a nd s te p b y s te p a s it is a ppr opr ia te to the r e str ic te d a nd i mp e r f e c t a bilitie s of the huma n min d. H ow e ve r , the r e is no ne e d to a s su me suc h i mpe r f e c t r e str ic ti ons f or the know le dge of G od; i. e . nothing h i nde r s tha t he e nc o mpa sse s ini tia l c ondit ions, la w s ( a xio ms) a nd pr e dic t io ns in o ne a c tion of k now le d ge . T hus w e do not ne e d to a s sume f or G od 's k now le dge a pr oc e dur e in ti me goi ng f r om one tr ut h to t he othe r , nor do w e ne e d to a ssu me f or his kn ow le dge a k ind of c a usa l c o nne c tio n in the se nse t ha t he w o uld know one tr uth be c a use of a nothe r like w e know the c onc lusio n be c a use of know ing the pr e mise s. 8 0

7.42 Irrelevant truths (to 7.12) A s A ug ust ine sa y s, the r e a r e ma ny ( in f a c t i nf in i te ly ma ny) tr iv ia l a nd ir r e le va nt tr uth s in ge ne r a l a nd c onse qu e ntly a lso a mong the sin gula r tr ut hs. A s e xa mple s ta ke the su bst itu tio n ins ta n c e s of the ge ne r a l la w of ide ntity x = x ( w he r e ' x' is a n individua l va r ia ble ) or of the la w of e quiva le nc e p ↔ p ( w he r e ' p' is a pr oposi tiona l va r ia b le f or singu la r pr oposi tio ns) . Mor e ove r , the r e a r e a lot of r e dunda nt a nd ir r e le v a nt f a c tua l tr uth s in the c onse que nc e c la ss of a ny f a c tua l pr oposit ion : For i nst a nc e , if p is a singula r tr uth, the n p ∨ q, ¬p → q , q → p , p ∨ p, p ∧ p, ( p ∧ q) ∨ ( p ∧ ¬q) … e tc . a r e non - ta uto logic a l ( f a c tua l) c onse que nc e s of p w h ic h a r e r e dunda nt a nd ir r e le va nt. T he r e dunda nc y a nd ir r e le va nc e c a n be se e n by the f a c t tha t in t he a bove c onse que nc e s the va r ia ble ' q' c a n be r e pla c e d on one or on bot h oc c ur r e nc e s by a n a r bitr a r y ( othe r ) va r ia ble ( a ls o by the ne ga tio n ¬q of q) sa lva va lid ita te

7 9 Prigogine (1995, GCh). 8 0 Cf. Thomas Aquinas (STh) I, 14, 7.

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of the inf e r e nc e ( c onse que nc e re la tion) ; sim ila r ly the se c ond oc c ur r e nc e of ' p ' in p ∨ p a nd p ∧ p c a n be dr oppe d. 8 1 I t is a l so r i ght to p oin t ou t tha t ma n a nd e spe c ia lly p hilo sop he r s a nd sc ie n tis ts c a n be distr a c te d a nd misle d b y suc h ir r e le va nt tr uth s. T his i s e vide nt f r o m the ma ny pa r a doxe s in dif f e r e nt do ma in s w hic h ha ve the ir r oot in r e dunda n t a nd ir r e le va nt e le me n ts of t he c onse q ue nc e c la ss a s it i s de f i ne d b y Cla ss ic a l L ogic a nd w hic h ha ve be e n di sc usse d i n the sc ie ntif ic lite r a tur e f or de c a de s. Suc h d oma i ns of pa r a doxe s a r e : T he or y of e xpla na t ion, of c onf ir ma ti on, of la w sta te me nt s, of dispo sit ion pr e dic a te s , of ve r simili tude , of Q ua ntu m L ogic , of E piste m ic L ogic of D e ontic L og ic . 8 2 A ltho ugh A ug ust ine 's c onc e r n w a s not a bout the se ki nds of m ode r n pa r a doxe s his poi nt w a s ne ve r the le ss not le ss i mpor ta n t: ma n ma y be se d uc e d or distr a c te d by de spic a ble a nd ir r e le va nt tr uths in a si mi la r w a y a s he ma y be se duc e d by know ing i mm or a l a c tio ns. A nd in thi s se n se f or ma n, bo th, ir r e le va nt a nd de spic a ble tr uths a nd i mmor a l a c tio ns a r e be tte r not know n tha n know n. H ow e ve r , in c ontr a d ist inc ti on t o ma n, w e c a nnot a ss ume tha t a mos t pe r f e c t be ing is mis le d or distr a c te d by kno w in g the e r r or s of ma n or a s he c a nnot be se duc e d or distr a c te d by ir r e le va nt a nd r e dunda nt tr uth s. L ike G od c a nnot be mis le d by kn ow in g the im mor a l a c tion s of ma n, s o he c a nno t be dis tr a c te d by ir r e le va nt a nd r e dunda n t tr u ths, e ve n if the y a r e inf ini te in nu mbe r . W e ha ve to a ssu me the r e f or e tha t he know s the ir r e le va nt a nd r e dunda nt tr uth s imp lic it ly w it hou t be ing di str a c te d by th e m.

7.43 God knows A-propositions? (to 7.13) L ike in pr e vio us a n sw e r s to a r g ume n t s w e sha l l a sk tw o que s tio ns: I s t he a r gume nt va lid? a nd : A r e the pr e mise s t r ue ? I n or de r to de c ide thi s in a mor e pr e c ise w a y w e sha ll put the a r gume nt in to a symbo lic f or m: ( 1) Pr e mi se aCKp → aTEp 8 3 CK… c a n know ( 1a ) aCK( A) → aTE ( A) TE… c a n tr uly e xpr e ss ( 2) Pr e mi se aTE ( A) → aCTOs ( A) ' a '… va r ia ble f or pe r sons 8 1 For a precise treatme nt of relevance and irrele vance in this sense see Weingartne r (2000, RFC) and (2000, BQT) ch. 9. 8 2 For a solutio n see W eingartner/Schurz (198 6, PSS), Schurz/Weingartner ( 1987, VDR) and Weingartner (2000, RFC) and (2004, RSL). 8 3 We do not u se quantifiers for prop ositional variables here, since all occurrence s can be universalised anyway. Also ' a ' can be u niversally quantified. The quantificat ion for time variables however is necessary.

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( 3) Pr e mi se aCTOs ( A) → ( ∃t) aTOt s( A) A… A- pr opos iti on ( 3a ) E nthy me m 1: ( ∀t) ( aTOts( A) → a e xist s a t ( in) t) s ( A) … A- se nte nc e

CTO. . . c a n tr uly toke n TO… tr u ly toke n s ( 4) ( ∃t) ( aTOt s( A) ) → ( ∃t) ( a e xis ts a t ( in) t) f r om E nth. 1 ( 5) aCK( A) → ( ∃t) a e xists a t ( in) t f r om ( 1a ) , ( 2), ( 3) a nd ( 4) ( 6) E nthy me m 2: ( ∀x) ( x is a time le ss be ing → ¬( ∃t) x e xists a t ( in) t) ( 7) T he r e f or e : ( ∀x) ( x is a time le ss be ing → ¬xCK( A) ) Conc e r nin g the f ir st q ue sti on, one c a n e a sily se e tha t t he a r gume nt – i n th is ve r sion – is va li d. G a le c la ims f or his ve r sion tha t i t is va li d too; a l thoug h thi s c a nnot be so e a si ly c he c ke d, be c a use h is ve r s ion is not in sy mbo li se d f or m a nd pr e supp ose s the r e f or e so me ti me s int uit ive u nde r sta nd ing of d if f e r e nt f or mula t ions li ke "i s e xpr e ss ible " a nd " c a n tr uly e xpr e ss " ( 4e , 4f ) or "by the toke nin g of " a nd "c a n tr uly to ke n". Mo r e ove r , he se e ms to pr e suppose w ha t w e c a lle d E nthyme m 1 a nd E nt hyme m 2. T he r e la tion of im p lic a tio n w hic h i s use d by G a le : p only if q i s inte r pr e te d a s usua l ( in te xt book s of logic ) a s p → q. T his is in a c c or da nc e w ith G a le 's u nd e r sta nding w hic h be c ome s c le a r f r om his c o mme n ta r y to the ste p s of the a r gume nt, i. e . q i s a ne c e ssa r y c ondi tio n f or p. Fur t he r w e unde r s ta nd b y a n A- pr oposi tio n a c on tinge n t s ta te me nt w i th a n inde x of time . F or e xa mple : Soc r a te s is si tti ng a t ti me t, symb olic a l ly: pt. A f te r the se pr e limina r ie s w e tur n now to the disc ussi on of the pr e mise s : ( 1) T he f ir st que s tio n is he r e w h a t it me a n s to " tr ul y e xpr e ss a pr op osi tion ".

G a le e nsur e s us tha t no t ove r t e xpr e s sion i n so me publ ic la ngua ge is ne c e ssa r y a nd the possibi lit y of pr iva t e la ngua ge is pe r mitte d. I f this is a ssume d, w e ma y sa y thr e e th ings to this pr e mise : ( i) I t ma y be r i ght f or a l l huma n a c ti ons of know ing t ha t the y oc c ur toge the r w i th a ki nd of i nte r na l or me nta l "spe a ki ng" ( a the or y w hic h go e s ba c k to A ugusti n) 8 4 . ( ii) A ltho ugh th is ma ke s se nse f or hum a ns, it is c omple te ly uni nte ll igi ble w hy th is s houl d hol d f or G od. W h y sho uld G od ha ve , be side s h is a c tio n of know in g, a n a c tion of "e xpr e ssi ng" a nd "toke n ing " ( se c ond pr e mi se ) ? I n a "pr iva te D e ite se la n gua ge " w i th D e ite s e le tte r s? T his w ou ld be a r a the r biz a r r e , if not c o mple te l y a bsur d a ssu mpt ion, w h ic h s how s tha t the f ir s t pr e mise , if a pplie d to G od, mu st be f a lse .

8 4 We leave that question open; here research in psychology has to find out whether this is generally true.

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( iii) A f ur the r w r ong a ssump tio n in pr e mise s ( 1) a nd ( 2) c onne c te d w ith tha t of ( ii) is tha t e ve r y pe r son ( the r e f or e a lso G od) c ould know onl y by f or ming pr o posi tio ns. But G od ne e d not to kno w b y f or mi ng pr o p osi tio ns or by e xpr e ss ing pr oposi tio ns; a ltho ugh G od ma y kno w a ll the tr ue pr opos iti ons w hic h a r e know n by ma n he ne e d not to know t he m by f or ming pr o posi tio ns, but ma y kno w the m by so me sor t of dir e c t ins ight. T hus T ho ma s A qu ina s sa ys: "G od know s a ll e n un c ia ti ons t ha t c a n be f or me d. . . H e know s e nunc ia ble thi ngs no t a f te r the ma nne r of e nunc ia ble things, a s in h is inte lle c t the r e w e r e c om posi tio n or div i sion of e nunc ia tio ns; f or he k now s e a c h thing by si mple inte lli ge nc e . " 8 5

( 2) A sim ila r c omme n t c a n be ma de to the se c ond pr e mise ( it c or r e spo nds t o G a le 's 4d) . I t might be r ight f or huma n a c tions of know i ng. But a pp lie d to G od, bo th a n te c e de nt a nd c onse que n t w i ll be f a lse a nd the r e f or e the w ho le pr e mise ( 2) w ill be tr ue , but tr ivia l ly or e mpt ily tr ue .

( 3) Pr e mi se ( 3) ( c or r e sponding to G a le 's 4g) is i mpor ta n t sinc e it h ide s a dif f e r e nc e be tw e e n tw o time - ind ic e s. T his c a n be show n a s f ollow s: A-se nte nc e s c a n be r e pr e se nte d by pr op osit iona l va r ia ble s to w h ic h t ime indic e s a r e a tta c he d: ' pt ' r e pr e se nts th e A- pr opos itio n pt. T he in de x ' t' indic a te s the ti me w he n the e ve nt de sc r i be d by the pr o pos iti on oc c ur s, f or e xa mple : S oc r a te s sits a t t ime t. O n the othe r ha nd the a c tion of know in g this A- pr opo sit ion ( or of toke ni ng the r e spe c tive A- se n te nc e ) oc c ur s a lso a t a c e r ta in ti me , sa y t1 , if h uma n s a r e kno w ing or toke n ing. T hus it hold s f or a ll huma n s tha t if a huma n pe r so n a kno w s tha t pt ( a n e ve nt oc c ur s a t time t) symb olic a l ly: aKpt – the n the a c tio n of know in g a lso oc c ur s a t a c e r ta in time , sa y t1 . Sy mbo lic a ll y: ∀a∈H , ∀t ( aKpt → ( ∃t1 ) aKt 1 pt ) w he r e t1 is usua ll y not ide n tic a l w ith t. 8 6 But tha t this pr inc ip le w hic h hol ds f or huma ns, shou ld a l so h old f or G od is r a the r inc onc e iva b le a nd c o mple te ly unjus tif ie d ; i. e . the sta te me n t tha t G od k now s t ha t p oc c ur s a t t ime t ( w he r e t is a poin t of t ime r e la te d to a ti me me a sur e me nt of thi s w or l d) is pe r f e c tly

8 5 Thomas Aquinas (STh) I, 14, 14. This was also pointed out by Leftow (1990, TAO), p. 309. 8 6 This is certainly so if the event, the o ccurren ce of which we know is external, s o that we need our senses a s mediator s, since e very causal propagation needs ti me (as we know from the Theory of Special Relativ ity) such that t1 must be later than t. The same holds if brain processes are needed as mediators. The only case when t1 could be simultaneous with t is one of a kind of knowin g as purely mental intr ospection of the ow n mental actions or processe s. But since this is also hardly possible (for hum ans) witho ut any brain processes there will be no factual case where t and t1 are strictly simultaneous (even if the time interval between t and t1 can be very short).

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a c c e pta ble ; but f r om thi s it doe s n ot f ol low tha t his know le dge is ( or ha s to be ) a t a ce r ta in time . T his ne e d not b e r e pe a te d he re be ca use it ha s be e n di sc us se d in de ta il a lr e a dy in c ha pte r 3. Spe c if ic a lly w . r . t. pr e mise 3 the f a lla c ious sw i tc h, w hic h tr a nsf e r s the ti me in de x f r o m t he e ve nt ( de sc r ibe d by a n A- pr opos it ion) to the a c ti on ( of to ke ning) , c a n be se e n be c omb ini ng pr e mise s 1a , 2 a nd 3, w hic h imp ly: aCK(A) → (∃t)aTOts(A). T hi s pr oposi tio n i s of c our se not ge ne r a lly tr u e , sinc e a c a n be a ny pe r son a nd it is spe c if ic a lly f a lse f or G od.

( 4) E nthy me m 1 c a n be c e r ta inl y a c c e pte d f or hu ma ns. A n d t he n s te ps ( 4) a nd ( 5) ( c f . 7. 43) ar e only c onse que nc ie s. A ppl ie d to G od, t he a nte c e de nt of e nthyme m 1 i s f a lse a nd the r e f or e e nthy me m 1 ( a pp lie d to G od) is ( tr ivia ll y) tr ue .

( 5) E nthy me m 2 c a n be a c ce pte d w ith a cla r if ic a tion. I f e nthyme m 2, or its insta nc e : "if G od is a ti me le ss be ing, th e n the r e is no ti me suc h tha t G od e xists a t ( or i n) tha t t ime " is i nte r pr e te d in suc h a w a y tha t ' ti me ' me a ns the time of thi s w or ld ( u nive r se , r e c a ll c h. 3) a nd 'G od e x ist s' me a ns the r e spe c tive obje c t ive pr op osi tio n w i thou t r e f e r e nc e of ma n's be lie f in G o d's e xiste nc e , the n e nthy me m 2 c a n be a c c e pte d. N ow be l ie ve r s in G o d's e xiste nc e ha ve the ir be lie f s a t a c e r ta in time of thi s w or l d. O ne m ight sa y the r e f or e tha t a be lie ve r a be lie ve s a t time t tha t G o d e xis ts now ( a t the time w he n the y be lie ve it) . But this is a n odd w a y of s pe a king. A l tho ugh i t is pe r f e c tly c or r e c t to sa y " a be lie ve s a t time t tha t G od e xis ts" a nd tha t i n this c a se bo th th is s ta te me n t a nd i ts c onte nt ( t ha t G od e x ist s) is tr ue , i t w ould be inc or r e c t or a t le a s t m isle a d ing to a dd the w or d ' now ' ( a f te r 'e xist s') e spe c ia lly if w e a ssume tha t G o d is time le ss or "out side " the time of this w or ld.

Co ming ba c k to t he w hole a r gume nt n ow , w e ha ve show n tha t pr e mise s ( 1) a nd ( 3) mus t be f a lse i n a pp lic a ti on t o G od. A nd si nc e onl y G o d c a n be ( unde r stoo d a s) a ti me le ss be in g, the c onc lusio n ( 7) is no t pr o ve d by t ha t a r gume nt.

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8. Whet her God' s Know l edge of S i ngul ar ,

Cont i ngent T r ut hs I m pl i es t he Mut abi l i t y of

God 8. 1 A rg u me nt s P ro

8. 11 I f G od know s singu la r tr uths, the n he a lw a ys know s w ha t ti me it is. But a s K r e tz ma nn sa ys : "A b e ing tha t a lw a ys k now s w ha t ti me it is, is sub je c t to c ha nge . " 8 7 , i. e . is muta ble . Bu t a s ha s be e n show n in c h. 7 G od know s sing ula r tr uths. T he r e f or e G od is muta ble . 8. 12 S ingu la r c onti nge nt tr uth s de sc r ib e f a c ts tha t c ha nge . Bu t to know the c ha nging of a nyth ing i s to kno w f ir st tha t p ( is the c a se ) a nd the n tha t not - p ( is the c a se , f or so me c on tin ge nt p ) . N ow a know ing pe r son w ho kn ow s f ir st one pr oposi tio n ( tha t p ) a nd t he n a nothe r o ne ( tha t not - p) is a kn ow in g pe r son w ho c ha nge s. 8 8 T hus s inc e G od kno w s the c ha ng ing of e ve r ything, he c ha nge s hi mse lf a nd is the r e f or e muta ble . 8. 2 A rg u me nt s C o nt ra

I f a te c hnic ia n c onstr uc t s a te c hnic a l o bje c t ( a ppa r a tus) , the n he kn ow s t ha t this ob je c t ha s a c e r ta in lif e ti me . T hu s he know s t ha t the ob je c t w ill la s t, sa y tw o ye a r s on the a ve r a ge, a nd w ill be out of or de r af te r w a r ds; w hic h is a sta tis tic a l k ind of k now le d ge c onc e r ning s ingu la r c onti nge nt f a c ts ( i. e . know le dge of the pr oba b ili ty of some s ingula r c on tin ge nt e ve nt, l ike tha t of ge tti n g ou t of or de r ) . N ow a l thou gh thi s te c hn ic a l ob je c t c ha nge s f r om f unc tion ing to ge ttin g ou t of or de r , it w ou ld be w r o ng t o sa y tha t the know le dge of the te c hnic ia n c ha nge s. O n the c ontr a r y the te c hnic ia n know s ( a nd c a n pr e dic t) b oth the a ve r a ge t ime of f u nc t ion ing a n d t he a ve r a ge poi nt of time of ge tti ng o ut of or de r w i tho ut c ha nging h is min d or kno w le dge w i th r e spe c t to tha t a ppa r a tus he c ons tr uc te d. Bu t w ha t ho lds f or the te c hn ic ia n, 8 7 Kretzmann (1966, OSI), p. 410. 8 8 Cf. ibid. p. 411.

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w ill ho ld a ll the m or e f or G od. I f G od know s the c ha nge s of the obje c ts of hi s ow n c r e a tion, it doe s not f ol low f r om t h is tha t hi s know le dge c ha nge s or tha t he his muta b le . 8. 3 P r opo se d A n sw e r

G od's kn ow le dge of sing ula r c ontin ge nt tr uth s doe s not i mpl y tha t he is muta b le . T his c a n be se e n a s f ollow s: Fir s t, by show i ng tha t t he unde r lyin g pr inc iple f or thi s c la im is no t e ve n unive r sa lly tr ue f or ma n' s know le d ge . Se c ond, by show ing tha t i t is no t tr ue f or G od's know le dge .

8.31 The underlying principle T he unde r lyin g pr inc ip le f or the c la im tha t G od's kn ow le dge of sin gula r ( a n d c ontinge n t) tr uth s imp lie s hi s mu ta bil ity is the f ollow ing one : KCH I f a per son x know s c ha nging f a c ts, the n the know le dge of x c ha nge s. T his or a si mila r f or m of th is pr i nc iple i s a lso use d i n the a r gume nt s 8. 11 a nd 8. 12. Mor e ove r this pr inc i ple is a l so de f e nde d by Stu mp a nd K r e tz ma nn 8 9 .

8.32 Principle KCH is not generally valid H ow e ve r , it c a n be show n t ha t the pr i n c iple KCH i s not ge ne r a ll y va li d f or ma n's k now le d ge . A ll the mor e w e ma y be suspic ious to a ppl y the pr inc iple to G od's k now le d ge . T he pr inc iple KCH is not va li d in a ll c a se s w he r e w e ha ve know le dge of s ingu la r ( c ontinge n t) tr uth s w ith t he he lp of dyna mic a l la w s; in the se nse de sc r ibe d a lr e a dy in c h. 7. 3 b y c ondi tion D1 a nd D2 . I n the se c a se s pr e dic ta bil ity in a str on g se n se is a lso p ossib le . T o se e tha t the pr inc iple KCH is no t va li d he r e , w e ha ve to look a t the sta tus of know le dge of a sc ie nt ist w ho e xpla ins a n d pr e dic ts sin gula r ( c ont ing e nt) f a c ts w ith the he lp of dyna mic a l la w s. I f he k now s f or e xa m ple the i nit i a l c ondi tio ns o f t he p la ne ta r y sy ste m ( sun plus so me pla ne ts) , i. e . its sta te S1 a t t1 . T he n he a lso know s a ll the suc c e ssor sta te s Sn a t tn ( by c a lc ula ti ng the m w ith the he lp of the dif f e r e ntia l e qua tion) . T he se suc c e ssor s ta te s a r e dif f e r e nt a t dif f e r e nt time s a nd the y a r e 8 9 Cf. Stump - Kretzmann (1 981, ETE), p. 455: "T hus a being th at always knows wha t time it is, knows first that it is now t1 (and not t2 ), then that it is now t2 (and not t1 ) and so on; and in that way such a being' s knowledg e is constantly changing. And if a being' s knowledge is cha nging in such a way that it no longer knows what it on ce knew, the n that being itself is also changing. "

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de sc r iba ble by dif f e r e nt sing ula r c ontin g e nt tr uths. N ow a lth ough t he sta te s of the sys te m c ha n ge w it h t he ti me de ve lo pme nt, t he know le dge of the sc ie n tis t doe s not c ha n ge . H e c a n know a ll t he c ha nge s of the suc c e ssor sta te s b y know in g the la w ( dif f e r e ntia l e qua ti on) plus t he init ia l sta te to ge the r w ith the c a lc ula tion pr oc e dur e . But he d oe s not c ha nge his know le dge , ne it he r c onc e r ning t he la w , nor c o nc e r ning the init ia l c on dit ions, nor c onc e r nin g the c a lc ula tion pr oc e dur e . A nd a lt houg h he ma y de r ive ( c a lc ula te ) the dif f e r e nt suc c e ssor sta te s a f te r one a nothe r , he know s the m i mp lic i tly a lr e a dy by know in g the la w a nd the initia l c ond iti o ns. T o put it mor e ge ne r a lly: T o know the c onse que nc e s b y ( or a f te r ) know in g the pr e mi se s a nd t he de r iva ti on r ule s doe s no t me a n t o c ha nge know le d ge . O the r w ise e ve r y log ic ia n a nd ma the ma t ic ia n ( w ho doe s n ot e ve n de a l w ith c o nti nge nt tr uth s) w ou ld pe r ma ne ntly c ha nge hi s kno w le dge j ust b y ma k ing pr oof s f or dif f e r e nt the or e ms. T he only th ing w hic h c a n be c a lle d a c ha nge he r e is tha t the sc ie ntis t or l ogic ia n ( ma the ma tic ia n) h a s to pr oc e e d suc c e ss ive ly sinc e he c a nnot e xplic i tly c om pr e he nd a ll the c onse que nc e s ( the or e ms) in one a c tion of know le dge . Bu t this doe s no t me a n to c ha nge h is know le dge c onc e r nin g the r e spe c tive do ma in, but only tha t he c ome s to a m or e c omple te k now le d ge of tha t doma in p ie c e by pie c e .

8.33 God does not need to change his knowledge T ha t the pr inc ip le KCH i s no t va l id if a p plie d t o G od 's know le d ge c a n be se e n a s f ollow s : ( i) Fir s t G od 's k now le dge is c e r ta inl y m or e pe r f e c t tha n ma n's know le dge

a nd the r e f or e tr iv ia lly, a t le a st a s pe r f e c t a s ma n 's know le dge . Bu t s inc e the pr inc i ple KCH is not va li d f or ma n' s know le dge , i t is c e r ta inly not va lid f or G od's kn ow le dge , too.

( ii) I t is ge ne r a lly a s su me d t ha t G o d's k now le dge is not disc ur sive or suc c e ssive ; if thi s a ss ump tio n is c or r e c t, the n G od know s in one a c tio n of know le dge t ha t a s yste m ( sa y a pla ne ta r y sys te m) is in a n ( ini ti a l) sta te S1 a t t1 a nd tha t it w i ll be ( b y i ts r e spe c tive la w s) in sta te s S2 , S3 , S4 . . . Sn a t t2 , t3 , t4 . .. tn in the f utur e ( w he r e the time i ndic e s t1 . . . tn r e f e r to a r e f e r e nc e syste m of thi s w or ld, he r e to the p la ne ta r y s yste m) . H e the r e f or e doe s not c h a nge his know le dge a lthough he know s a ll the dif f e r e nt suc c e ssor sta te s oc c ur r ing a t s uc c e ssive ti me s of t he pla ne ta r y syste m ( a s a r ef e r e nce syste m of this w o r ld) .

( iii) Conc e r nin g pr inc i ple KCH o ne ha s to ke e p in mi nd the d ist inc t ion a lr e a dy intr oduc e d in c h. 3: ( a ) A c tin g ( know in g) in suc h a w a y tha t the

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a c tion of know ing oc c ur s a t a c e r ta in time ( s ym bol ic a lly: aKt p ) . ( b) A c ting ( k now i ng) i n suc h a w a y tha t w ha t is know n oc c ur s a t a c e r ta in time ( sy mbol ic a lly : aKpt ) . Conc e r ni n g ma n's know le dge both, his a c tio n of kno w ing a n d tha t w ha t is k no w n ( if the la tte r i s a f a c t of this w or ld) oc c ur s a t a c e r ta in ( not ne c e ssa r ily the sa me ) t ime . Conc e r nin g G od's k now le dge a bou t the w or l d ( his c r e a tion) only ( b) is t he c a se , i. e . he know s tha t c e r ta in e ve nts of th is w or l d ha ppe n a t a c e r ta in ti me of ( a r e f e r e nce syste m of ) this w or ld.

( iv) I f the distinc t ion a bove ( iii) is ke p t in mind, the n the dif f ic u ltie s w hic h some pe o ple ha ve w i th some spe c ia l f or ms of sing ula r ( c onti nge nt) tr uths w il l disa p pe a r : So me se e a dif f ic u lty w i th t he sta te me nt " x k now s w ha t t ime it is ". T he y th ink tha t e ithe r G od c a nno t k now w ha t ti me i t i s or if G od w ould know i t, he must be mu t a ble . 9 0

T he big c onf usi on in suc h a c la im is tha t the phr a se "w ha t ti me it is" i s c omple te l y a mb iguo us. T o r e solve this c onf usion w e ha ve to po int o ut tha t 'ti me ' c a n only be unde r st ood a s ti me of this w or ld or a s c hr o nolo gic a l or de r or a s bio log ic a l ( psyc h olo gic a l) t ime ( r e c a ll c h. 3. 32) . I n the f ir s t c a se what time it is, de pe nd s on a r e f e r e nc e syste m. E ve r y sc hoo lboy tod a y know s tha t N e w Y or k ti me is dif f e r e nt f r om Mo sc o w ti me . A nd on a la r ge r sc a le the ti me in the sola r sy ste m i s dif f e r e nt f r om one in a syste m of s ta r s w hic h m ove w ith dif f e r e nt ve loc ity c o mpa r e d to the sola r syste m. . . e tc . But w hy sh ould G od not know w ha t ti me it is i n N e w Y or k ( a t a c e r ta in mo me nt) , i. e . w ha t ti me w ould be show n the r e by a c c ur a te c loc ks. T his is e ve n e a sy f or ma n to f ind ou t, w hy shoul d thi s be dif f ic ult f or G od. I n the se c ond c a se what time it is de pe n ds on a 'pla c e ' i n a c hr ono logic a l or de r or time sc a le . S inc e the r e is no e m pir ic a l me a sur ing uni t r e quir e d by t he a xiom s of c hr o nolo gy, po int s of ti me r e f e r to r e a l nu mbe r s ( if 't ime ' is unde r stoo d a s c on tin uous) . But a ltho ugh c hr ono log ic a l ti me c a nnot be str e tc he d or c ontr a c te d ( a s it is the c a se w ith ti me of thi s w or ld, i. e . w ith physic a l ti me ) , the r e c a n only be the dist inc ti on be tw e e n e a r lie r a nd la te r , w he n w e a s sume tha t the c hr ono logy c o ndit ion is sa ti sf ie d, i. e . w he n the r e a r e no c lo se d t ime like c ur ve s, tha t is no l oops. But w hy sh ould G od no t k now tha t one e ve nt is e a r lie r t ha n a nothe r o n e a c c or ding to c hr on olog ic a l or de r ? I t w ould be r a the r r idic ul ou s to a ssu me suc h ignor a nc e f or a pe rf e c t be ing. I n the thir d c a se , w ha t time it is, de pe nd s on some bi olog ic a l or psyc hol ogic a l c loc k of a n or ga nism. Suc h c loc ks a r e a djuste d to e ithe r inne r bio log ic a l pr oc e sse s or to e xte r na l one s, like the pe r iod of da y a nd night ( w he r e the pe r iod of da y a nd nig ht d oe s c e r ta inly h a ve a c a usa l inf lue nc e on t hose i nne r 9 0 Cf. Kretzmann (1966, OSI).

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biolo gic a l pr oc e sse s) . A c c or din gly a n or ga nis m c a n know s ome p oin t of ti me r e la tive to suc h a c loc k, sa y w he n i t i s a w a king in the mor n ing. But, a ga in, w hy s houl d G od not know w he n a c e r ta in a ni ma l or pe r so n i s a w a ki ng in the ( a t some ) mor ni ng ( r e la ti ve to some pla c e on the e a r th) a nd tha t the a ni ma l or pe r son is a w a r e ( or know s) a t this time t ha t it is a w a ke ning. O n the a s su mpt ion tha t G od is the c r e a tor o f the uni ve r se , the c la i m t ha t G o d c a nnot kn ow w ha t t ime it is ( in the se nse of the t hr e e c a se s a bove ) se e m s pa r tic ula r ly s tr a nge . Sinc e the n he ha s c r e a te d time by c r e a ting a c ha ngin g w or ld suc h tha t t ime is de pe nde n t on a nd r e la tive to the ki nd of c ha nge ha ppe ning in a c e r ta in pa r t of t he uni ve r se . A nd th is h old s a lso f or the ti me on dif f e r e nt pa r ts a n d in dif f e r e nt indi vid u a ls ( inc lu din g hu ma n pe r sons) on the e a r th. Su mm ing up: I n a l l t he se c a se s of know ing what time it is, G od know s tha t a n e ve nt of th i s w or ld oc c ur s a t a c e r ta in t ime r e la t ive t o a r e f e r e nc e syste m of thi s w or ld. I f he is o mni sc ie nt, he know s a ll t he se r e f e r e nc e syste ms a nd the r e spe c ti ve po ints of t ime f or oc c ur r ing e ve nts. Bu t s inc e he doe s not know suc c e ss ive ly f ir s t one e ve nt a n d the n a se c ond one , but c o mpr e he nd s the time de ve lop me nt of ph ysic a l a nd b iolog ic a l sys te ms in a non - d isc ur si ve ( non - suc c e ssive ) a c tion, he ne e d not a nd doe s not c ha nge his know le dge . 9 1 8. 4 A ns w e r to th e O b jec t io ns

8. 41 ( to 8. 11) A s it w a s sa id in the a n s w e r ( 8. 33) the phr a se "w ha t ti me i t is" is hi ghly a mb iguo us. A lt houg h G od k now s "w ha t t ime it i s" r e la t ive to a c e r ta in r e f e r e nc e syste m o n e a r th or in the un ive r se by kno w ing w ha t e ve nts oc c ur a t s uc h a r e la t ive ti me i t d oe s no t f ollow f r om thi s t ha t G o d's a c t ion of know in g w ould oc c ur a t a c e r ta in ti me . But on ly if h is a c t ivi ty of kn ow in g w ould oc c ur a t a c e r ta in time ( or w ould ha ve a time de ve lop me nt) , his know le dge w o uld be c ha ngi ng a nd he w ould be m uta ble . S inc e his kn ow in g a c tivity doe s not oc c ur a t a c e r ta in ti m e , a nd sinc e i t doe s no t ha ve a ti me de ve lopme n t, his k now le d ge ne e d not to c ha nge a nd G od ne e d no t to be muta b le . T he r e f or e the c onc lusion in a r g ume nt 8. 11 is n ot pr ove d. 8. 42 ( 8. 12) A lthou gh G od kno w s the c ha nging of f a c ts a nd a lthough he know s tha t p oc c ur s a t t1 a nd not - p oc c ur s a t t2 , he doe s n ot k now first t ha t p a nd later t ha t no t - p . Sinc e he know s the ti me de ve lo pme nt of a sys te m or the suc c e ssion of the d if f e r e nt e ve nts not a t t he ti me s the y oc c ur , but no t a t a ti me 9 1 See also t he discus sion in Castaneda (1967, OIR) and Kutschera (1990, VGI) p. 56f. and p. 337.

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a t a ll. T he r e f or e his know le dge ne e d not to c ha nge . I f a n a str onome r know s the or bit of a pla ne t a nd c o nse que nt ly k now s tha t it i s a t pos iti on P 1 a t t1 a nd a t pos iti on P 2 ( P 1 ≠ P 2 ) a t t2 , w e do not sa y t ha t t he a str o nom e r c ha nge s h is know le dge ( he w ou ld ha ve t o c ha nge hi s kno w le dge w ith e ve r y ne w po sit ion of the pla ne t) . O n the c ontr a r y, he c om pr e he nds the w h ole t ime de ve l opme n t of the pla ne t k now i ng h is or b it a nd the r e f or e a lso the suc c e ssi ve posi tio ns. S o muc h the m or e G od e nc ompa s se s w ith his kno w le dge a l l t he t ime de ve lopme n ts ( r e la tive to dif f e r e nt r e f er e nc e syste ms) of his c r e a tur e s sma ll or la r ge on the e a r th or in the unive r se w itho ut pa r tic ipa ting h im se lf in some time de ve lop me nt. T he r e f or e his e nc ompa ss ing kn ow l e dge ne e d no t to c ha nge .

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9. Whet her God Kn ows What Is Not. 9. 1 A rg u me nt s A g ai ns t

9. 11 I nste a d of sa ying "s ome th ing i s not ( the c a se ) " w e c a n sa y tha t it is f a lse . T hus A r ist otle sa ys: "A ga in, ' be ing' a nd 'is ' me a n tha t a s ta te me nt is tr ue , 'n ot be ing' tha t i t is no t tr ue but f a lse . " 9 2 But w ha t is f a lse c a nnot be know n. T he r e f or e G od c a nnot know what is not. 9. 12 W ha t is k now n is tr ue . W ha t is tr u e is sa t isf ie d by a mode l. What is not c a nnot be sa tisf ie d by a mode l. T he r e f or e what is not c a nnot be know n. T he r e f or e G od c a nnot know what is not. 9. 13 I t is not the c a se tha t G od c a n f a il. Bu t if G od c a nnot f a il, the n – a s L e f tow sa y s – G od c a nnot kno w " tha t b e ing a f a il ur e one se lf f e e ls l ike this ": "F or if G o d c a n not f a i l, G od c a nn ot ha ve the ki nd of e xpe r ie nc e ' thi s' p ic ks out, a nd s o i n a se nse c a nno t e ve n u n de r sta nd t he pr opo sit ion tha t 'be ing a f a ilur e one se lf f e e ls like this'. " 9 3 T he r e f or e G od c a nnot kn ow some thin g w hic h is not ( the c a se ) of hi mse lf a nd c onse qu e ntl y G od doe s no t know e ve r yt hing what is not. 9. 14 W ha t is know n is tr ue a nd w ha t i s t r ue c or r e sponds to a f a c t. Bu t w ha t is e xpr e sse d by a c ounte r f a c tua l doe s no t c or r e spond to a f a c t. Sinc e if p a nd q a r e f ac ts the r e spe c tive c ounte r f a c tua l r e a ds “ if p w e r e to oc c ur ( pr e supposin g tha t i t doe s not oc c ur ) the n q w oul d oc c ur ( pr e suppos ing tha t i t doe s not oc c ur ) ” ; but on t he a ssum pti on, bot h p a nd q oc c ur . T he r e f or e w ha t is e xpr e sse d by a c ounte r f a c tua l c a nnot be know n. A nd c onse que ntly t he r e a r e some t hi n gs that are not , i. e . those e xp r e sse d by c oun te r f a c tua ls, w hic h a r e not know n by G od. 9. 2 A rg u me nt s P ro

E ve r ythin g w ha t is the c a se is e ithe r w il le d by G od or pe r mit te d by G od tha t it is the c a se . A nd e ve r ythin g what is not ( the c a se ) is e ithe r w i lle d b y G od tha t it is no t or pe r mi tte d b y G od t ha t it is not. But e ve r yt hing w ha t is e i the r

9 2 Aristotle (Met) 1017a22. 9 3 Leftow (1990, TAO), p. 313.

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w ille d by G o d or pe r mit te d by G od is know n by G o d. T he r e f or e e ver ything what is not i s know n by G o d. 9. 3 P r opo se d A n sw e r

9.31 God's knowledge extends also to that what is not in the sense of what is either impossible or incompatible with laws of nature or accidentally not, but possible. Sinc e , w ha t i s not, i s i mpos sib le by la w s of logic or i nc ompa t ible w ith la w s of na tur e or not oc c ur r ing a c c ide nta lly be c a use of c e r ta in initia l c ondi tio ns. N ow G od kn ow s c e r ta in ly w ha t i s i mp oss ib le by la w s of log ic . A nd unde r t he a ssump tio n t ha t he is the c r e a to r of th e unive r se , he r ule d i ts e vo lut ion by la w s a nd i nit ia l c ond iti ons, kn ow in g w h a t w ill oc c ur a nd w ha t w ill not oc c ur a c c or ding to the m. T he r e f or e G od know s w ha t is not. A mor e de ta ile d a nsw e r is a s f ollow s : Conc e r nin g what is not it i s ne c e ssa r y t o d ist ing uish dif f e r e nt me a nin gs. F ir st it c a n r e f e r to s ome sta te of a f f a ir s w h ic h doe s not obta in. Se c on dly it c a n r e f e r to a thi ng w hic h d oe s n ot e x ist. Co nc e r ning both c a se s w e ha ve to dist ingu ish tha t w ha t i s l ogic a ll y i mpo ssib le f r om tha t w ha t is – a l th ou gh logic a ll y poss ible – f a c tua lly no t the c a se . ( 1) Sta te s of a f f a ir s w hic h a r e logic a lly i m possi ble , c a nnot obta i n a nd thin gs

w hic h a r e logic a lly im poss ible , c a nnot e xist ; i. e . tha t a n ea r thqua ke oc c ur s in Ja nua r y 2004 in Pe r sia a nd doe s not oc c ur in Ja nua r y 2004 in Pe r sia is impo ssi ble to obta in a nd a r ou nd sq ua r e c a nnot e xis t. I mpo ssi ble s ta te s of a f f a ir s a nd impo ssi ble th ings vio la te t he pr inc iple of n on - c ontr a dic tion. T his pr inc ip le c a n be e x pr e sse d i n dif f e r e nt ve r sion s w ith dif f e r e nt str e ngth. 9 4 T he w e a ke st pr inc iple of non - c ontr a dic t ion is va li d in a ll c la ssic a l a nd ma ny va lue d s yste ms of lo gic , e xc e pt pa r a c onsis te nt l ogic s 9 5 a nd qua si - tr ut h - f unc tio na l log ic s. I t is th is pr inc ip le :

NW A t mo st o ne me m be r of the pa ir p , ¬p c a n be tr ue ( or c a n ha ve a de signa te d va lue ) . T his mos t tole r a nt p r inc iple of no n - c ontr a dic t ion w a s a lso a lr e a dy de f e nde d by A r i stot le . 9 6 O bse r ve tha t it doe s no t e xc l ude ma ny va lue d l ogic sinc e if bo th p a nd ¬p w o uld r e c e ive the va l ue

9 4 Cf. Rescher ( 1969, MVL), p. 144ff. Re scher d istinguishes there six versions of th e principle. 9 5 For Paraconsistent Logics see Batens et al. (2000, FLP). 9 6 Aristotle (Met) 1011b14 and 1062a22.

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inde f ini te or u nde f ine d ( a s f or e xa mple in K le e ne 's sy ste m of thr e e va l ue d logic ) , it is st ill sa t isf ie d.

A s a r e a lis t I do no t t hink tha t on the l e ve l of unc o nsc iou s na t ur e or r e a lity the r e c a n be a viola tion of NW. V iola ti ons of NW c a n only ha ppe n in hu ma n think ing a nd i n or ga nis ms w hic h ha ve a l e a r ning pr oc e ss w it h tr ia l a nd e r r or . T he r e f or e pa r a c onsiste nt log ic s, w hic h a llow vi ola ti ons of NW, c a n be unde r stoo d a s mode l s of some pr oc e sse s of huma n thi nkin g or of some pr oc e sse s of tr ia l a nd e r r or of some or ga nism s ha ving c onsc i ousne s s, but not of the str uc tur e of unc onsc iou s r e a lity. T o su m up, w e ma y sa y tha t what is not i n the se nse of be i ng l ogic a ll y impo ssi ble is tha t w ha t doe s not sa t isf y t he pr inc ipl e NW of non - c on tr a diti on. ( 2) Sta te s of a f f a ir s w hic h a r e log ic a lly p ossib le a lth ough f a c tua l ly n ot t he

c a se , c a n be of a tw of old kind: T hose w hic h a r e not the c a se a t pr e se nt, bu t w e r e the c a se some ti me s in t he pa st or w ill be the c a se a t s ome t ime in t he f u tur e ( 2a ) ; a nd those w hic h ne ve r o bta in a lt houg h the y a r e log ic a lly possi ble ( 2b) . A n a na logous di sti nc tio n c a n be ma de c onc e r ning thing s ( indiv idua l s) ; t hose w hic h do not e xis t a t pr e se nt but di d i n t he pa st ( f or e xa mple spe c ie s w ho be c a me e xti nc t) or w il l e xis t in t he f utur e f r om tho se w hic h ne ve r e xist.

( 2a ) Conc e r ning th ose s ta te s of a f f a ir s w hic h do n ot obta i n a t pr e se n t b ut obta in e i the r in the pa s t or in the f ut ur e 9 7 , a pa r t of the m c a n be pr e dic te d

9 7 According to Aristotle it holds for all genuine possibilities (potencies ) in the sens e of contingencies: First tha t they are actualised at some point of time (in the past, present or future). In other words this opinion is expressed as follows: If the state of affairs p is possible, then there is some time t in t he pas t or fut ure suc h that p obtains at t ( mp → ( ∃t) pt ). Cf. Aristotle (Met) 1047b2, 1047b35 – 1048a1. Secondly it holds according to Aristotle that genuine possibilities (in the sense of contingencies; they would be expressed more completely by: mp ∧ m¬p ) are not actu a lized at some (other) time. In o ther words, this opinion is expressed as follo ws: If the sta te of affairs p is possible (in the sense of a contingent potency), then there is some time t such that p does not obtain at t ( mp → ( ∃t) ¬pt ), (Met) 1050b10 - 16. Fo r the first pa rt of the interpretation see also Hintikka (1973, TaN), p. 94 and 189. States of affairs which obtain for all times seem not to be possible, in the sen se of bei ng contingen t, for Aristotle. There are h owever such examples in modern cosmology : The numerical amount of mass (energy) of the whole un iverse is not determined by laws as we understand them; the law of the conservation of energy says only that this magnitude is constant, but not that it has a certain numerical value. Now this numerical value is (according to the law) the same for all times. But it is still a contingent fact relative to t he laws of nature. For a discu ssion see Mittelst aedt, Weingartner (2 005, LNt) chs. 8. 2. 2. 3 and 8. 2. 3. 2. Cf. 10. 31(17) below.

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or r e tr odic te d ( e ve n by ma n, viz . sc ie n tist s) if the r e a r e dyna mic a l la w s obe ying c o ndi tion s D 1 - D 3 ( r e c a ll c h. 7. 3) , w hic h de sc r ibe the m. A nothe r pa r t ma y be suc h tha t the si ngle e ve nt s ( or single sys te ms or pa r tic le s) obta in r a ndo mly a n d ma y be the r e f or e c a lc ula te d w ith a c e r ta in pr oba bil ity, w hi le only a huge e nse mbl e of single e ve nts ( sing le syste ms or pa r tic le s) be ha ve la w - l ike , suc h tha t the r e spe c t ive ma c r osta te c a n be pr e dic te d a c c or ding to sta ti stic a l la w s ( c f . S1 - S3 of c h. 7. 3) .

( 2b) T hose s ta te s of a f f a ir s w hic h do n ot o bta in a t a ny t ime a r e t hr e e f old: ( 2bi) the y ma y be r ule d ou t or ma y be i nc ompa t ible w ith dyna mic a l la w s, ( 2bii) the y ma y be r ule d ou t or ma y be inc ompa tib le w ith s ta ti stic a l la w s, a nd ( 2bi ii) t he y ma y no t oc c ur a c c id e nta lly be c a use of c e r ta in i nit ia l c ondit ions. A n e xa mp le f or ( 2bi) w ould be a stone w hic h is not a ttr a c te d by the e a r th, s uc h tha t it w ou ld v iola t e the la w of gr a v ita ti on, one f or ( 2bii) a pe r pe tuum mobi le of the se c ond kind, w hic h w o uld vi ol a te the la w of e ntr opy. A n e xa mp le f or ( 2bii i) w ou ld be a mic r os ta te of the un ive r se w hic h w ould ne ve r o bta in. T he la tte r c a n be e xp la ine d a s f o llow s: A litr e of a ir a t te m pe r a tur e 0° C ( 273K ) a nd a tmos phe r ic pr e ss ur e ( se a - le ve l) c onta ins a bout 2, 7 ⋅10 2 2 mol e c ule s. T hi s sys te m of m ole c ule s c a n be i n a huge nu mbe r of d if f e r e nt pos sib le m ic r osta te s. T he n um be r is a bo ut 10 5 ⋅1 0 2 2 . E ve r y suc h sta te c a n r e a lise the ma c r osta te " litr e of a ir unde r the c ondit ions me nt ione d ". A lr e a dy he r e w e c a n a sk the que s tion w he the r a l l the se poss ible m ic r osta te s w ill e ve r be r e a lise d ( a nd in w ha t ti me ) . But le t us e xtr a pola te n ow the e xa mple t o the w hole uni ve r se . W ha t is t he num be r of possib le mic r osta te s of a ll the mole c ule s in the w hole uni ve r se ( inc ludi ng da r k ma tte r ) . Ca n a ll the se p o ssib le m ic r osta te s e ve r be r e a li se d in t he l if e time of the un ive r se , if thi s l if e time is f ini te ? T he a nsw e r to thi s que sti on is ve r y pr oba bly : N o. T hus t he r e a re some mic r osta te s of the unive r se w hic h w il l ne ve r be r ea lise d. 9 8 T his c onsi de r a tion a ls o sh ow s tha t the la w s of na tur e , a s w e unde r sta n d the m, a r e va lid not only in our unive r se , but a lso in a ll th ose othe r s w h ic h dif f e r f r om our s only in so me mic r osta te s w hic h a r e not r e a lise d in our s but in othe r s. 9 9

Su mm ing u p, w e ma y sa y tha t sta te s o f a f f a ir s w hic h a r e logic a ll y po ssib le but do no t oc c ur , a r e r ule d out by dyna mic a l or sta t ist ic a l la w s e ithe r f or not oc c ur r ing a t a c er ta in point of ti me or ne ve r ; or the y do not oc c ur a c c ide nta lly, e ithe r not a t a c e r ta in ti me or ne ve r be c a use of c e r ta in i nit ia l c ond iti ons l ike 9 8 For a detailed discussion cf. Mittelstae dt/Weingartner (2005, LNt), ch. 7. 2. 3. 4. 3(2b). 9 9 For a more detailed argument with additional r easons see Mittelstaed t/Weingartne r (2005, LNt), ch. 8. 1. 6. and Weingartner (1996, UWT) ch. 7.

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the lim ite d lif e ti me of the unive r se . A simi la r c onside r a tion c a n be ma de f or thing s ( indi vid ua ls) w hic h do no t e xist. Co ming ba c k now to the q ue sti on w he th e r G od kno w s w ha t i s no t, the a ns w e r is a s f ollow s : Conc e r nin g ( 1) it w oul d be r a the r a bsu r d to c la im of a pe r f e c t be ing tha t he w ould not know w ha t is im poss ible a c c or ding to the la w s of logic , i n pa r tic ula r w ha t i s r ule d out b y a mo st t ole r a nt pr inc i ple of no n - c ontr a dic t ion ; or in ot he r w or ds, w hy shou ld a m ost p e r f e c t be ing not k now w ha t sta te s of a f f a ir s c a nnot o bta in be c a use the y a r e l ogic a lly i mpos sib le ? T hu s w e ha ve to sa y tha t G o d know s w ha t is no t in the se nse of be ing logic a l ly i mpo ssi ble . T his c a n be su bsta n tia te d f ur the r by tw o r e a sons: ( i) Ma n ha s the a b ili ty to know t he mos t ba sic la w s of log ic lik e the pr inc iple NW or si mi la r sim ple one s. A nd suc h a kno w le dge se e ms t o be r a the r c o mm on suc h tha t it is a va ila ble w it hout r e se a r c h, a t one 's d i sposa l w he ne ve r ne e de d a nd ( unde r nor ma l c ondi tio ns) 1 0 0 w ithout e r r or . ( ii) A c c or d ing to T ho ma s A qui na s a nge ls a r e inf a llib le w . r . t. to l ogic a l r e a soning. 1 0 1 Si nc e a lr e a dy ma n a nd in a mor e pe r f e c t w a y a nge ls ha ve this kind of k now le dge , a ll the mor e G od a s the ir c r e a tor must ha ve it. 1 0 2 Conc e r nin g ( 2a ) a sim ila r a r gume n t a s a bove is suita b le : A lr e a dy ma n kn ow s, a t le a st to a c ons ide r a ble e xte n d, w ha t i s inc o mpa t ible w it h la w s of na tur e in f or m of dyna mic a l a nd sta t ist ic a l la w s. T he r e f or e a ll the mor e G od w ill know w ha t is not the c a se ( a t w ha t ti me of so me r e f e r e nc e syste m of the un ive r se ) a c c or ding to la w s of na tur e a nd c e r ta in ini tia l c on dit ions. A n a na l ogou s a r gume nt hold s f or ( 2 b) w h ic h d if f e r s f r om ( 2a ) on ly in tha t the inc ompa tib ili ty w it h the la w s or ini tia l c onditio ns is n ot r e str ic te d to s ome pe r iod of time . Su mm ing up w e c a n sa y t ha t G od know s a lso what is not, be it in the se nse of what is not a c c or di ng to la w s of log i c or a c c or ding to la w s of na t ur e or a c c or ding to c e r ta in init ia l c ondit ion s.

9.32 God’s knowledge extends to things that are not actual T he r e is a n a r gume nt of T ho ma s A q uin a s in supp or t of the the sis t ha t G od 's know le dge e x te nds to what is not. T h i s a r gume n t c om ple me n ts our s a nd is 1 0 0 Abnormal conditions would be brain defects or si milar diseases. 1 0 1 Thomas Aquinas (STh) I, 58, 3. 1 0 2 For further supporting arguments recall chs. 1.32 - 1. 34.

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ba se d on the i de a tha t th ing s ( or sta te s of a f f a ir s) w hic h a r e not a c tua l, a r e in the pow e r e i the r of G o d or of a c r e a tur e . But G od k now s his pow e r a nd the pow e r of his c r e a tur e s. T he r e f or e he ha s know le dge a ls o of thi ngs t ha t a r e not. T h oma s A qu ina s pr e suppo se s tha t a ll the se " thi ngs " ( s ta te s of a f f a ir s) a r e not log ic a lly i mpo ssib le : "N ow it i s pos sib le tha t thi ngs tha t are not a bsol ute ly, sh ould b e

in a c e r ta in se nse . For thi ngs a bs olu te l y a r e w hic h a r e a c tua l; w he r e a s thin gs w hic h a r e no t a c tua l a r e in t he pow e r e i the r o f G od H i mse lf or of a c r e a tur e , w he th e r in a c tive pow e r , or pa ssive ; w he the r in pow e r of thou ght or of ima g ina ti on, or o f a ny othe r ma n ne r of me a nin g w ha ts oe ve r . W ha te ve r the r e f or e c a n be ma de , or thoug ht, or sa i d b y the c r e a tur e , a s a lso w ha te ve r H e H imse lf c a n do, a l l a r e know n to G od, a lth oug h the y a r e no t a c tua l. A nd in s o f a r i t c a n be sa id tha t H e ha s know le dge e ve n of thin gs tha t a r e not. " 1 0 3

9. 4 A ns w e r to th e O b jec t io ns

9.41 W ha t is not can be interpreted in two ways (to 9.11) Fir s t, a s tha t sta te of a f f a ir s w hic h is ( tr uly) ne ga te d a nd se c ond, a s the ne ga te d sta te of a f f a ir s. A cc or ding to the f ir st inte r pr e ta ti on, tha t w hic h i s ( tr uly) ne ga te d c a n be r e pla c e d – a s A r i stot le sa ys – by tha t w hic h is f a lse . 1 0 4 T hus the se n te nc e "it i s not t he c a se tha t the unive r se is spa tia ll y inf in ite " c a n a lso be e xpr e sse d by sa ying : " it i s f a lse tha t the un ive r se is spa tia l ly inf ini te ". A nd in thi s c a se what is not ( the c a se ) is tha t the unive r se is spa tia l ly inf i nite . T his, be c a use it is f a lse , c a nnot be know n. T he r e f or e what is not a c c or ding to the f ir st in te r pr e ta tion, i. e . tha t sta te of a f f a ir s w hic h i s tr uly ne ga te d, c a nnot be know n a nd a l so G od c a nno t k now it; but jus t be c a use some thin g w h ic h i s f a lse , c a nnot be know n, b e c a use w ha t i s know n ha s to be tr ue ( r e c a ll c h. 1. 31 a nd the pr inc iple KT) . H ow e ve r , a c c or ding to the se c ond in te r pr e ta tion what is not me a ns the ne ga te d sta te of a f f a ir s a nd this c a n be know n. I n our e xa mple the ne ga te d sta te of a f f a ir s is w ha t i s e xpr e ss e d b y t he tr ue se nte nc e "it is no t the c a se tha t the un ive r se is spa t ia lly inf ini te " a nd th is f a c t c a n be know n a nd it is know n

1 0 3 (STh) I, 14, 9. 1 0 4 The underlying principle here is Tarski' s Trut h Condition: T he sentence ‘ p’ is true if, and only if, p . Or: The sentence ‘ p ’ is f alse if, and only if, ¬p . For a detailed discussion of Tarski' s Truth Condition, see Weingartner (2000, BQT), ch. 7.

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by G od. Sinc e what is not ha s to be inte r pr e te d a c c or ding to the se c ond inte r pr e ta tio n in que s tion 9. a nd i n t h e a r gume nt 9. 11 i t f oll ow s tha t the c onc lusio n in a r gume n t 9. 11 is not pr o ve d.

9.42 Truly negated (to 9.12) T he se c ond a nd the t hir d pr e mise of a r g ume nt 9. 12 a r e only tr ue if what is not is inte r pr e te d a c c or ding to the f ir s t i nte r pr e ta tion ( a s tha t w h ic h is tr uly ne ga te d) . But if it is inte r pr e te d a c c or din g to the se c ond inte r pr e ta tio n – i. e . in the se nse of a "ne ga tive f a c t" 1 0 5 – it c a n be know n.

9.43 Does “God cannot know something false” imply that he is not omniscient? (to 9.13) I t is c or r e c t to sa y tha t G od c a nno t kno w some t hing w hic h i s f a lse ( to sa y) of him. A nd th is be c a use in ge ne r a l w ha t is f a lse c a nnot be know n ( r e c a ll c h. 1. 31) . A nd s inc e i t w o uld be f a lse to sa y of G od tha t he ha s hu ma n f e e li ngs a s be ing a f a ilur e , this – tha t he ha s suc h fe e lings – c a nnot be know n ( be c a use it is f a lse ) . O n the othe r ha nd G od kn ow s tha t he c a nnot ha ve suc h i mpe r f e c t f e e lings. T hu s the e xpr e ss ion what is not in t he c onc lus ion is o nly c or r e c t if i t is i nte r pr e te d i n the f ir st se nse a s tha t w ha t is f a lse . T hi s i n f a c t c a nnot be know n. But G od k now s what is not i n th e se nse tha t he know s a ll the ne ga t ive f a c ts, i. e . he know s what is not a c c or ding to the se c ond inte r pr e ta ti on, a s ha s be e n e xpla ine d in t he a nsw e r to the ot he r tw o ob je c tion s a bove . T he r e f or e , inte r pr e te d in the se c ond se nse , the c onc lusi on of 9. 13 is not c or r e c t. I nde pe nde ntly of w ha t ha s be e n sa id a s a c omme nta r y to the a r gume nt 9. 13, w e w a nt to ma ke a c omme n t to a f ur t h e r c la im of L e f tow i n the a r tic le c i te d a bove : A f te r the quota t ion in 9. 1 3 L e f to w c ontinue s : " So it se e ms tha t G od's ve r y pe r f e c tion, by e nta ilin g t ha t he c a nnot f a il, e n ta ils tha t he c a nnot be pr oposi tio na lly o mn isc ie nt – tha t the r e a r e know a ble tr uths G o d c a nnot know . " 1 0 6 Fr om the f a c t tha t G od c a nno t ha ve f e e lings like he h im se lf be in g a f a ilur e a nd f r om its tr ue c on se que nc e tha t G od c a nnot kn ow t ha t he ha s f e e ling s l ike he himse lf be ing a f a ilur e , L e f tow c onc l ude s tha t G o d is not o mni sc ie nt. T he str uc tur e of thi s f a lla c y is a s f ol low s: F ir st o ne look s f or some f a lse pr oposi ti o n ( f or e xa mple tha t G od f e e ls he h im se lf w ould be a f a i lur e , or 1 0 5 Concerning negative f acts like that there is no perpetuum mob ile or that t he diagonal in the square is not rational cf. Weingartner (200 0, BQT), ch. 8. 1 0 6 Leftow (1990, TAO), p. 313f.

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some o the r ) . T he n one c onc lude s c or r e c tly f r om thi s tha t G od c a nno t know this f a lse pr o pos iti on. 1 0 7 Fr om th is one c o nc lude s f a l la c ious ly tha t G od is no t omni sc ie nt. W e ma y a sk w ha t c a n be th e r e a son f or suc h a fa lla c y. I n or de r to f ind tha t out w e put t he a r gume nt in to sy mbol ic f or m: ( 1) Fa lse ( p ) A ssu mpt ion: p i s f a lse ( 2) Fa lse ( p ) → ( ¬∃x) xKp ( 3) ( ¬∃x) xKp T he r e is no pe r son x ( x r uns ove r pe r sons) suc h tha t x know s

tha t p. For m ( 1) a nd ( 2) w it h M. P. ( 4) ¬gKp G od doe s not kn ow tha t p. For m ( 3) by insta nt ia tio n. ( 5) ( ∃p ) ¬gKp T he r e is some pr opos iti on p suc h tha t G od doe s not kno w

tha t p. Pr opo sit ion ( 5) is of c our se tr ue a nd the de r iva tion of ( 5) is r a the r tr ivia l. ( 5) is of c our se tr ue , si nc e in a l l c a se s w he r e p is f a l se , G od d oe s no t kn ow t ha t p ( ta ke ' p' to sta nd f or '2 + 2 = 5' or f or 'the r e is a per pe tuum mob ile ') . N ow L e f tow se e ms to c onc lu de f r om ( 5) tha t G od is not o mn isc ie nt. S uc h a f a lla c ious c onc lu sion c ou ld a r ise f r om s ome str a nge ( or be tte r : c ontr a dic tor y) ide a of omnisc ie nc e w hic h i s thi s: x is omn isc ie nt me a ns tha t f or a ny pr oposi tio n p , G od know s tha t p . T his de f initio n is of c our se c ontr a dic t or y sinc e w e ma y i nsta n tia te f or p: ( q ∧ ¬q) . T he solut ion he r e is ju st t ha t G od c a n kno w onl y pr opo sit ion s tha t a r e t r ue , w hic h is c om ple me n te d by t he a nsw e r in c ha pte r one t ha t w ha te ve r G od kno w s i s tr ue . A nd unde r the a ssum tion t ha t p is f a lse G od c a nnot k no w tha t p. T hus it i s c or r e c t to sa y tha t the r e a r e some pr opo sit ions w hic h a r e not kn ow n ( a s tr ue ) by G o d, na me ly the f a lse one s; but G od of c our se know s tha t the y a r e f a lse 1 0 8

9.44 Does God know counterfactuals (9.14)? W e a sk tw o que stion s f ir st: I s the a r gu me nt va li d a nd a r e the pr e mise s tr ue ? Conc e r nin g the f ir st, w e se e im me dia t e ly tha t the a nsw e r i s Y e s; w he n w e c onside r the f ir s t a nd se c on d pr e mi se a nd the c onc lu sio n ( f or ge tti ng no w the just if ic a tio n of the se c ond pr e mise be gi nning w i th: "S inc e . . . ") . T he a r gume nt

1 0 7 Observe that this has nothing to do with G od, because any strong concept of knowledge implies that what is known, is true (recall ch. 1. 31). 1 0 8 There might be some further wrong i deas un derlying Leftow' s f allacy, but we do not want to speculate about them.

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ha s t he n the f ol low i ng si mple ( va lid) str uc tur e : K → T a nd T → F ; C → ¬F ; T he r e f or e : C → ¬K. Conc e r nin g the tr uth of t he pr e mise s, the r e is no pr oble m w ith the f ir s t pr e mise , sinc e bot h of it s pa r ts c a n be a c c e pte d a s tr ue . 1 0 9 T he se c ond pr e mise how e ve r is mis ta k e n. T hi s c a n be se e n a s f oll ow s: A ss umi ng tw o s ta te me n ts p a nd q, the r e ar e tw o r e la te d c ounte r f a c tua ls: C1 I f p w e r e to oc c ur , the n q w ould oc c ur . C2 I f p w e r e not to oc c ur , the n q w ould not oc c ur . E xa mple s : A c c or ding to Boyle - Ma r i otte 's la w , it holds f or a n isola te d sy ste m ( ke e ping te mpe r a tur e c onsta n t) of a n ide a l ga s : 1 1 0 I f the pr e ssur e w e r e inc r e a se d ( p) , the volume w oul d de c r e ase ( q ) . A nd: I f the pr e ssur e w e re not inc r e a se d ( ¬p) , the vol ume w o uld not ha ve de c r e a se d ( ¬q) . A c c or ding to K e ple r 's a nd N e w ton 's la w s it h olds : I f t he c onste lla t ion a m ong s un, e a r th a nd moon w e r e suc h a nd suc h a t t1 ( p) the r e w oul d be a n e c l ipse a t t2 ( q ) . A nd : I f the c onste l la tio n … w e r e not suc h a n d s uc h a t t1 ( ¬p) , the r e w ou ld n ot be a n e c lipse a t t2 ( ¬q ) . A ssuming n ow tha t b o th, p a nd q, a re tr ue , it is e a sy to se e tha t a lso the r e spe c ti ve f ir st c ounte r f a c t ua ls ( of the f or m C1) a r e tr ue . I n a ny c a se the a bove insta nc e s a r e we ll c onf ir me d phys ic a l la w s. But th is is e qua l ly so if bo th p a nd q a r e f a lse . T he sa me ho lds f or t he r e spe c tive se c ond c ounte r f a c tua ls ( of the f or m C2) . T he y a r e a lso tr ue in both c a se s, i. e . if p a nd q a r e tr ue a nd if p a nd q a r e f a lse . 1 1 1 T h is c onside r a tio n s how s tha t the se c on d pr e mise c la i min g tha t "w ha t i s e xpr e sse d by a c ou nte r f a c tua l doe s not 1 0 9 That true sentences or statements correspon d to facts has bee n explained an d formulated in different way s. It seems that the re are more than one consisten t ways to do that. A more complicated problem i n this respect are the so - called "negative facts" (for example, facts like that the diagonal of the square is not rational or that there is no perpetuum mobile). For one solution of this p roblem and for the related o ne of "negative properties" see Weingart ner (2000, BQT), ch. 8. 1 1 0 In fact it holds only for restricted domains and is replaced for the general case by state equations of thermodynamics. But this does not hinder to use Boyle - Mariotte’s law as an example in the above context. 1 1 1 For the case that the antecedent ( p ) (or bo th p and q ) is (are) tr ue, there are axiom s in Lewis' theory of counterfactuals stating that, if p is true, the counterfactual p l → q reduces to p→ q a nd that p∧q implies: p l → q . Cf. Lewis (1975, CCP), p. 24. Although Lewis' theory of counte rfactuals c an be applie d to the above examples, we do not adher e, in general, to Lewis' theory as an i nterpretat ion of the causal relatio n. Since it can be shown that this theory has only restricted domains of application for a part of the causal relations expressed by dynamical deter ministic laws and no or on ly wrong appli cation for causal relations expressed by statistical laws. See Hausman (1998, CAs), ch. 6 and Mittelstaedt/Weingartner (2005, LNt), ch. 9. 2.

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c or r e spon d to a f a c t" i s w r ong : T he a b ove c ounte r f a c tua ls of t he e xa mple s e xpr e ss w e ll c onf ir me d a nd tr ue phys ic a l la w s w hic h c or r e spond to f a c ts. A f te r ha ving show n tha t the se c ond pr e mise of the a r gume nt ( in 9. 14) is f a lse a nd the r e f or e the c onc lusion is no t p r ov e d, w e ma y r e tur n to the ma in que sti on of thi s a r gume nt : w he the r G od know s c oun te r f a c tua ls. T his que s tion ha s to be divi de d int o thr e e pa r ts: T he f i r st pa r t ( 1) de a ls w ith c oun te r f a c tua ls w hic h e xpr e ss a la w - l ike c onne c ti on; the se c ond ( 2) w i th c oun te r f a c t ua ls c onc e r ning sin gle e ve nts in w hic h pe r so ns w ith f r e e w ill a r e invo lve d; ( 3) the thir d w it h a histor ic a l r e ma r k. T he que st ion w he the r G od k now s c ount e r f a c tua ls is in f a c t a sub - que s tio n of que sti on 9: w he the r G od know s w ha t is not. A nd tha t G o d kno w s what is not w a s a lr e a dy substa n tia te d i n the a nsw e r to que stio n 9. T ha t the q ue sti on w he the r G od know s c oun te r f a c tua ls i s a sub - que s tion to que st ion 9 ( w he t he r G od know s what is not) c a n be se e n as f ollow s : I n a c ounte r f a c tua l of the f or m C2 it i s pr e suppo se d tha t p a nd q both oc c ur . A nd the que stion a nsw e r e d by C2 is w ha t w o uld ha ppe n if p w e r e not to oc c ur . ( 1) I n or de r to kn ow t ha t in the se n se of 9. 3 1 ( 1) a bove , it is ne c e ssa r y f ir s t t o

know w he the r t he non - oc c ur r e nc e of p i s c om pa tib le w i th the la w s of log ic or w ith the la w s of na tur e . But this kin d of know le dge is a va ila ble , a t le a st in ma ny c a se s, a lr e a dy f or ma n. Se c o ndly it is ne c e ssa r y t o k now the logic a l a nd e mpir ic a l ( a c c or ding to la w s of na tur e ) c onse que nc e s of the non - oc c ur r e nc e of p . But a l so th is k ind of know le d ge is a va i la ble to a gr e a t e xte nd a lr e a dy f or ma n by know ing la w s of l ogic a nd la w s of na tur e pl us init ia l a nd bou nda r y c ond iti ons ( w he r e by 'la w s of na tur e ' bo th, dy na mic a l a nd sta t ist ic a l la w s, a r e me a nt, c f . c h. 7 ) . A n a na logou s c on side r a t io n c a n be ma de c onc e r ni ng c ou nte r f a c tua ls o f the f or m of C1 in w h ic h i t is pr e suppose d t ha t both p a nd q do no t obt a in.

N ow if a lr e a dy ma n ha s a cc e ss to c ounte r f a c tua l know le dge ba se d on la w s – e ve n if not c o mp le te ly – w e ha ve to sa y tha t a l l the mor e G od , a s a pe r f e c t be ing a nd a s a c r e a tor of the unive r se a nd its la w s ( inc l udi ng ma n) , ha s a know le dge of c ounte r f a c tua ls. 1 1 2 A lthoug h f r om this it doe s no t f ollow t ha t hi s know le dge me a ns know ing by f or min g c ounte r f a c tua ls, a s he ne e d not to know by f or mi ng pr opo sit ion s. ( 2) I f p a nd q in C1 a nd C2 r e f e r to single e ve nts in w hic h pe r sons w i th f r e e

w ill a r e invo lve d, the n e ve n unde r ly ing la w s a r e not suf f ic ie nt to e x pla in the c hose n e ve nt. T he r e f or e ma n c a nno t pr e dic t suc h e ve n ts ( e xc e pt w i th ve r y low pr oba bil ity) .

1 1 2 For a reference in the Bible that God knows counterfactuals see Matthew 11, 20 -24.

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H ow e ve r , w e ha ve to sa y tha t G od c a n know suc h e ve n ts in a mu lt iple se n se : tha t a nd how the y a r e pos sib le ; t ha t, if the y w ou ld oc c ur , the n c e r ta in o the r e ve nts w ould oc c ur a nd if the y w ould not oc c ur , ce r ta in othe r s w ould not oc c ur . Justif yin g r e a sons f o r tha t a r e a s follow s: ( a ) A ssu ming G od a s the c r e a tor , he know s w ha t is i n me n 's ( a lso in a

pa r tic ula r ma n's) pow e r to br in g a bout. ( b) A ssu ming G od a s the c r e a tor , he know s t he log ic a l a nd e mp ir ic a l

c onse que nc e s of a ma n's pa r tic ula r de c ision a nd a c tion. ( c ) A ssu min g G od a s the c r e a tor , he know s t he log ic a l a nd e mp ir ic a l

c onse que nc e s of the omis sio n ( non - o c c ur r e nc e ) of a ma n's pa r tic ula r de c ision or a c tion.

Fr om the se c o nside r a ti ons it is pla in th a t G od k now s the f a c ts e xpr e sse d in tr ue c ount e r f a c tua ls. ( 3) H ist or ic a lly, G o d's know le dge of c o unte r f a c tua ls w a s a lr e a dy disc u sse d in the Mid dle A ge s. A c c or ding to Mo l ina ( 1535 - 16 00) , know i ng a ll tr ue c ounte r f a c tua ls is one of thr e e spe c ia l type s of know le dge p os se sse d by G od, w hic h he c a ll s middle knowledge: ( i) G od kno w s a l l po ssi ble sta te s of a f f a ir s a nd a ll its c o mbi na tio ns a nd c om ple xi ti e s; thi s is w ha t Mol ina c a lls natural knowledge. ( i i) Fur the r G od know s a ll c ontin ge nt f a c ts ( pa st a nd pr e se nt) ; thi s is h is free knowledge. ( ii i) G od know s c ounte r f a c tua ls; th is is w ha t M oli na c a lls middle knowledge. T his me a ns f or Mo lina t ha t G o d kn ow s a l so e spe c ia lly w ha t e a c h pa r tic ula r hu ma n pe r son w it h f r e e w ill w ou ld do w e r e this pe r son t o be pla c e d in thi s or tha t or . . . inf inite ly ma ny s itua t ion s a nd c ir c umsta nc e s. 1 1 3

1 1 3 For an ext ensive his torical ela boration se e Cra ig (1988, PDF), p. 169ff. and (1991, DFH), ch. XIII. The claim that Molina was th e first to point that out it is hardly tenable. At least at the time of Th om as Aquinas s uc h questions were frequent ly discussed and similar views have been defended. Cf. Thomas Aquinas (STh) I, qu. 14, articles 9, 12 and 13.

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10. Whet her Knowl edge or T r ut h Can Change

t he S t at us of a S t at e of Af f ai r s 10. 1 A r gu m en ts P ro

10. 11 I f the pr opositi on " A w in s the e le c tion " tur ns f r om f a lse a t t1 into tr ue a t t2 , the n the sta tus of the c or r e spondin g sta te of a f f a ir s c ha nge s f r om non -f a c tua l to f a c tua l. T he r e f or e tr uth c a n c ha nge the sta tus of a sta te of a f fa ir s. 10. 12 I f the pr opo sit ion p, to w hic h a st a te of a f f a ir s c or r e spond s e ve n if thi s sta te of a f f a ir s is c ont inge n t, is tr ue ( or ha s be e n tr ue f or some t ime or f or e ve r ) , the n this sta te of a f f a ir s tur ns int o a ne c e ssa r y sta te of a f f a ir s, be c a use it the n c a nn ot not ob ta in. I n th is se n se A r i sto tle sa y s: "H e nc e , if in the w hole of ti me the s ta te of t hing s w a s suc h tha t one or t he othe r w a s tr ue , it w a s ne c e ssa r y f or thi s to ha ppe n, a nd f o r the sta te of thin gs a lw a y s to be suc h tha t e ve r ythi ng tha t ha ppe ns ha p pe ns of ne c e ssity. F or w ha t a nyone ha s tr uly sa id w oul d be the c a se ca n not not ha ppe n. " 1 1 4 T he r e f or e tr uth c a n c ha nge the sta tus of a sta te of a f fa ir s. 1 1 5 10. 13 For ge n uine kn ow le dge w e a ssu me tha t w ha t i s know n mu st be tr ue suc h t ha t t he pr inc i ple aKp → p is a ne c e ssa r y c ond itio n f or ge nuine know le dge . N o w if it is k now n a t t1 < t0 ( t0 = pr e se nt) tha t it w il l be t he c a se tha t pt2 >t0 , the n pt2 >t0 ( the sta te of a f f a ir s p a t t2 > t0 ) must obta in a nd c a nnot not ob ta in ; othe r w i se it w oul d no t be c or r e c t to sa y it w a s kn ow n s o to ha ppe n. T hus a ll c on tin ge nt sta te s of a f f a ir s, tr uly kn ow n be f or e the y obta i n, mus t obta in ne c e ssa r il y. T he r e f or e know le dge c a n c ha nge the status of a sta te of a f f a ir s. 10. 14 A c c or ding to t he a nsw e r of que s tion 1, w ha te ve r G od kno w s is tr ue . N ow supp ose tha t G od kn ow s so me s ingula r f ut ur e c ontinge n t e ve nt l ik e : Soc r a te s is s itt ing a t t ime t > t0 ( t0 = pr e se nt) . T he n e ithe r it is po ssi ble tha t Soc r a te s i s no t s itt ing a t t > t0 or it is no t pos sib le . I f it i s no t p oss ible , the n it 1 1 4 Aristotle (Int), ch. 9, 19a1 - 5. 1 1 5 Instead of "status of a st ate of affairs" on e co uld say also "ontologic al status of a state of affairs" in order to keep it off from a more epistemological status.

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is i mpos sib le f or Soc r a te s no t to sit a t t > t0 . H e nc e f or Soc r a te s to s it i s ne c e ssa r y. O n the othe r ha nd, if it is pos sible tha t Soc r a te s is no t sit tin g a t t > t0 , the n G od's kno w le dge w ou ld be e r r one ous. 1 1 6 T hus on t he a ssump tio n tha t G od's kn ow le dge c a nnot be e r r one ous, the f a c t tha t Soc r a te s is sitt ing a t t > t0 mus t be ne c e ssa r y, a l th ough w e ha ve a ssume d it to be a c on tin ge nt e ve nt ( sta te of a f f a ir s) . T he r e f or e know le dge c a n c ha nge the status of a sta te of a f f a ir s. 10. 2 A r gu m en ts C on tr a

10. 21 E ve r y pr o pos iti on w h ic h r e pr e se n ts a sta te of a f f a ir s is e ithe r lo gic a lly tr ue or f a lse , or n ot logic a l ly tr ue or f a lse . I f it i s l ogic a ll y tr ue or f a lse , it r e pr e se nts a sta te of a f f a ir s w h ic h i s l ogic a lly de te r mi ne d. I n t his c a se the sta tus of t he sta te of a f f a ir s is it s l ogic a l de te r mina tion. I f it is not log ic a ll y tr ue or f a lse , it r e pr e se nts a sta te of a f f air s w hic h i s not l ogic a ll y de te r mi ne d. But tr ut h or f a l sit y doe s no t c ha nge the l ogic a l de te r mina t ion of the r e s pe c tive sta te of a f f a ir s. A nd thus tr ut h or f a lsit y doe s not c ha nge the sta tus of th is sta te of a f f a ir s. Si mila r l y tr ut h or f a lsity doe s n ot c ha nge t he log ic a l inde te r mi na tio n of a sta te of a f fa ir s. Si mila r l y t he f a c t t ha t s ome one kno w s a pr opo sit ion c a nnot c ha nge t he sta tus of logic a l de te r mina tion or lo gic a l in de te r mina t ion of its r e spe c tive s ta te o f a f f a ir s. T he r e f or e tr uth or f a lsit y or know le dge doe s not c ha n ge the sta t us of a sta te of a f f a ir s. 10. 22 I f the pr oposi tion p i s a la w of na tur e , the n it r e pr e se nts a sta te of a f f a ir s w ith the s ta tus of na tur a l ne c e ssit y. B ut the f a c t tha t p i s kn ow n b y so me physic ist s c a nnot c ha n ge the s ta tus of n a tur a l ne c e ssity of the r e spe c t ive sta te of a f f a ir s. T he r e f or e know le dge c a nnot c ha nge the sta te s of a f f a ir s w hic h c or r e spond to la w s of na tur e . B ut a s im ila r a r gume nt c a n be c onstr uc te d f or o the r c a se s of the sta te of a f f a ir s. T he r e f or e know le dge c a nnot c ha nge the sta tus of a sta te of a f f a ir s. 10. 3 P rop os ed A nsw er

N e ithe r tr uth nor know le dge c a n c ha nge the sta tus of a sta te of a f fa ir s w hic h is e xpr e sse d by a sta te me nt or pr opo sit io n. 1 1 6 Cf. the similar argument in Thomas Aquinas (Ver) 2, 12, objection 2.

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I n or de r to se e tha t, w e h a ve t o sh ow f i r st ( 10. 31) tha t the s ta tus of a sta te of a f f a ir s w hic h i s e xpr e sse d by a sta te me nt or a pr opo sit ion c a n be of dif f e r e nt kind. Se c ondly ( 1 0. 32) , it w i ll be show n tha t in the c a se w he r e the sta tu s of a sta te of a f f a ir s i s a ne c e ssa r y one or a c ondit iona l ly ne c e ssa r y o ne , tr uth or know le dge c a nnot c ha nge this s ta tu s. I n t his c a se the c or r e spond ing pr oposi tio ns a r e ne c e ssa r y or c ondit io na lly ne c e ssa r y. A spe c ia l c a se a r e sta te s of a f f a ir s w hic h o bta ine d in the p a st ( up to the pr e se nt) w hic h a r e l a te r unpr e ve nta ble a nd i n thi s spe c ia l se n se "ne c e ssa r y". T hir d ly ( 10. 33) , the que sti on w he the r tr u th or kno w le dge c a n c ha nge t he sta tus of a s ta te of a f f a ir s w ill be a na lyse d c onc e r ning c on tinge n t f utur e sta te s of a f f a ir s.

10.31 Different Kinds of States of Affairs T he sta tus of a sta te of a f f a ir s c a n be of dif f e r e nt kind. T he f ollow ing li st ma y not be c omple te , but i t is suf f ic ie n tly e x ha usti ve f or our pr oble m. ( 1) p is log ic a lly ne c e ssa r y in t he se nse of a la w or of a the or e m of logic 1 1 7 : p

= pL g Cor r e spond ing sta tus: Logical Necessity ( 2) p is ma the ma t ic a ll y ne c e ssa r y i n the se nse of a la w or a the or e m of

ma the ma t ic s: p = pM C or r e spond ing sta t us: Mathematical Necessity ( 3) p is na t ur a lly ( or e m pir ic a ll y) ne c e ssa r y in the se n se of dyna mic a l la w s of

na tur e : p = p N Cor r e spo ndin g sta tu s: Natural Necessity ( dyna m ic a l) ( 4) p is na t ur a lly ( or e mpir ic a l ly) ne c e ssa r y in the se n se of sta tis tic a l la w s of

na tur e : p = p S Cor r e spond ing sta tus: Natural Necessity ( sta ti stic a l) 1 1 8 ( 5) p is c ond iti ona ll y na tur a ll y ne c e ssa r y in the se n se tha t i t f oll ow s f r o m

dyna mic a l la w s + i nit ia l c ondi tion s: p = pNI Cor r e spon ding s ta tus : Conditional Natural Necessity ( dyna mic a l) ( 6) p is c ond iti ona ll y na tur a ll y ne c e ssa r y in the se n se tha t i t f oll ow s f r o m

sta tis tic a l la w s + in itia l c on dit ions : p = p S I Cor r e spon ding s ta tus : Conditional Natural Necessity ( sta t ist ic a l) O bse r ve how e ve r tha t si nc e sta ti stic a l la w s do not a p ply to t he si ngle s ta te

of a f f a ir s ( insta ntia t ion) in t he sa me se nse a s to the w ho le e nse mble ( f or e xa mple a the r mo dyna mic a l ma c r os ta te ) only t he ma c r osta te c a n be

1 1 7 Usually what is meant here are the theore ms of First Order Predicate Logic with Identity. 1 1 8 Examples for dynamical laws are Newton' s se cond law of motion, Maxwell' s equations or the Schrödinger equation. Examples for stat istical laws are the law of radioactive decay or the law of entropy. For details on dynamical and statistical laws, their pro perties and their differences see Mittelstaedt/Weingartner (2005, LNt), ch. 7.

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pr e dic te d or r e tr odic te d w it h c e r ta inty i. e . w ith na tur a l ne c e ssity ( c f . ( 7) be low ) .

( 7) p is pr oba b ili stic a l ly c o nti nge nt in the s e nse tha t it i s a s ing le s ta te w h ic h obe ys s ta tis tic a l la w s + ini tia l c on dit io ns. p = pP C . S inc e sta t ist ic a l la w s a llow de gr e e s of f r e e dom f or t he sin gle s ta te ( f or e xa mple a the r mody na mic a l mic r os ta te ) the y c a n be pr e dic te d or r e tr odic te d onl y w ith a c e r ta in pr o ba bil ity w he r e a s a ma c r osta te c a n be pr e dic te d or r e tr o dic te d w ith na tur a l ne c e ssit y ( c f . ( 6) a bove ) . Cor r e sp ondi ng sta tu s: Probabilistic contingency.

( 8) p is unpr e ve nta bly ne c e ssa r y in the s e nse tha t p r e pr e se nts a pa st or pr e se nt sta te of a f f a ir s: p = pt ≤ t 0 Cor r e spon ding s ta tus : Unpreventable or Past Nec essity

( 9) p is c onti nge nt i n the se nse tha t i t is n ot r ule d a nd not r ule d o ut by a ny ( know n) la w s. T ha t me a ns a l so tha t p is c ompa ti ble w i th a ll ( k now n) la w s: p = p C

Cor r e spon ding s ta tus : Contingency P os sib le Com bina t ion s: I t is pla in t ha t e a c h of p L g , p M , pN a nd p S c a nnot be c ombine d w i th a ny

othe r pr opos it ion r e pr e se nti ng ( a nothe r ) sta tus. T he r e a son is tha t t he ir c or r e sponding sta t us i s ti me le ss. Mor e a c c ur a te ly: T he la w s of lo gic a nd of ma the ma tic s ha ve no thin g t o do w ith ti me , the y ma y be c a l le d a te mpor a l. W he r e a s a ll la w s of na tur e d e sc r ibe pr oc e sse s of na tur e w hic h c ha nge in spa c e a nd ti me bu t a r e the mse l ve s unde r s tood a s ti me ( tr a nsla tio n) inva r ia nt ; i. e . a s not c ha nging thr ou gh ti me . 1 1 9 O n the ot he r ha nd the c or r e spondin g sta te s of a f f a ir s of pNI , pNS , pt ≤ t0 a nd pt > t0 a r e obta in ing a t a c e r ta in poi nt of t ime . pC ma y be c onjo ine d to the la tte r tw o, but ha s to be tr e a te d a l so se pa r a te ly sin c e the r e ma y be c onti nge nt sta te s of a f f a ir s w hic h ne ve r ha p pe n. T he r e f or e the r e ma ini ng c o mbi na tion s a r e those w it h pa st ( or pr e se nt) sta te s of a f fa ir s a nd those w ith f utur e sta te s of a f f a ir s a nd f ina lly p C se pa r a te ly:

1 1 9 There is the difficult question whether the laws of nature are strictly time translation invariant, because of the q uestio n whether fundamental con stants entering these laws are really con stant in time. But the most exact measurement s did not establ ish a convincing deviation from constan cy for co nstants like α , G, h or c so f ar. For details and further references cf. Mittelstadt/Weingartner (2005, LNt), ch. 8. The expression ' time translation invaria nt' should protect against co nfusion with ' time revers al invariant' , wh ich holds only for dynamical laws, but not for statistical ones.

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( 10) pt ≤ t 0 ∧ p NI r e pr e se nt sta te s of a f f a ir s w hic h a r e c onditio na lly ne c e ssa r y ( de r iva ble f r om d yna m ic a l la w s + in iti a l sta te s of a f f a ir s) a nd obta i n a t pr e se nt or in the pa st.

( 11) pt ≤ t 0 ∧ p NS r e pr e se nt s ta te s of a f f a ir s w hic h a r e c ondit iona ll y ne c e ssa r y ( de r iva ble f r om sta t ist ic a l la w s + ini ti a l sta te s of a f f a ir s) a nd obta i n a t pr e se nt or i n the pa st.

( 12) pt ≤ t 0 ∧ p C r e pr e se nt sta te s of a f f a ir s w h ic h a r e c ontin ge nt ( n ot r u le d b y la w s) a nd obta in a t pr e se nt or in the pa st .

O bse r ve tha t ( 10) , ( 11) a nd ( 12) ha ve in c ommo n tha t the ir s ta te s of a f f a ir s obta in a t pr e se n t or in the pa s t a nd a r e i n this se nse unpr e ve nta b ly ne c e ssa r y ( 8) . But t he y a r e st ill dif f e r e nt c o nc e r ning the ir sta t us: ( 10) , be c a use of the c ompone n t pNI , is c on dit iona l ly ne c e ssa r y in a str onge r se nse tha n ( 11) , sinc e pNS is w e a ke r be c a use of the sta ti st ic a l la w . A nd ( 1 2) r e pr e s e nts the w e a ke st ne c e ssity c o min g on ly f r om the f a c t tha t it is a pr e se nt or pa st e ve n t ( sta te of a f f a ir s) . T he r e f ore the sta tus of ( 12) , pt ≤ t0 ∧ p C , c ould a lso be c a lle d Past Contingency. ( 13) pt>t0 ∧ p NI r e pr e se nt sta te s of a f f a ir s c or r e c tly pr e dic ta ble w ith the he lp of

dyna mic a l la w s + e a r lie r sta te s of a f f a ir s. I ts sta tus c a n be c a lle d ( Conditional ) Future Necessity ( Dynamical) .

( 14) pt>t0 ∧ p S I r e pr e se nt s ta te s of a f f a ir s s ta tis tic a lly pr e dic ta ble w i th t he he l p of sta ti st ic a l la w s + e a r lie r in itia l c ond itio ns. Suc h s ta te s of a f f a ir s c a n only be pr e dic te d w ith c e r ta inty if the y a r e like the r modyna mic a l ma c r osta te s.

Cor r e spon ding s ta tus : ( Conditional ) Future Necessity ( Statistical ) . ( 15) pt >t 0 ∧ pP C r e pr e se nt sin gle sta te s of a f f a ir s sta ti stic a l ly pr e dic ta ble w i th

the he lp of sta t ist ic a l la w s a nd in itia l c o ndit ions. Suc h s ta te s of a f f a ir s c a n only be pr e dic te d w it h a c e r ta in de gr e e of pr oba bilit y.

Cor r e spon ding s ta tus : Future Probabilistic Contingency . ( 16) p is f utur e c ont inge nt in the se n se tha t p is c onti nge nt ( no t r ule d a nd no t

r ule d out by a ny la w s, c f . ( 9)) a nd re pre se nts a sta te of a f fa ir s w hic h w ill obta in in the f utur e : p = ( p C

∧ pt>t 0 ) or f or shor t : p = pCt>t 0 . O b se r ve tha t

pCt>t 0 i s no t pr e dic ta b le sinc e i t is n ot r ule d b y e ithe r d yna m ic a l or

sta tis tic a l la w s. A n e xa mple is a hu ma n f r e e w ill de c isio n. I ts sta t us c a n be c a lle d Future Contingency.

( 17) p is om nite mpor a l c on tin ge nt in t he se n se tha t p is c ont inge nt ( c f . ( 9) ) a nd r e pr e se nts a sta te of a f f a ir s w hic h, e ithe r a lw a y s or ne ve r , obta i ns, i. e . w hic h e i the r ob ta ins a ll the ti me or o bta ins ne it he r in the pa st, n or a t pr e se nt, nor w ill obta in in t he f utur e : p = ( ∀t) p C

t or p = ¬( ∃t) pCt I ts sta tu s

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ma y be c a lle d Omnitemporal Contingency. A n e xa mple is the r e a lise d nume r ic a l va l ue of the ma ss ( e ne r gy) of the w ho le uni ve r se . A c c or ding to the r e c e nt unde r sta nd ing, th is va l ue is not de te r m ine d b y la w s of na tur e . A n e x a mple f or a c ontin ge nt s ta te of a f f a ir s, w hic h ne ve r obta ins is a nume r ic a l va l ue w hic h is d if f e r e nt f r om the one r e a lise d. A c c or di ng t o the la w of c onse r va t ion of e ne r gy, suc h a va lue i s c ons ta nt thr ou gh ti me . T hose om nite mpor a l c ont inge nt s ta te s o f a f f a i r s, w hic h ar e re a lise d, c ould a lso be e xpr e sse d a s a c ombina tion of ( 1 2) a nd ( 16) .

A s it w a s sa id a bove , ( 11) a nd ( 12) agr e e in the se nse tha t the ir sta te s of a f f a ir s a r e unpr e ve nta bly ne c e ssa r y. A na logo us ly, ( 13) , ( 14) a nd ( 15) a gr e e in the se nse tha t the ir s ta te s of a f f a ir s a r e f utur e . B ut the y a r e a l so dif f e r e nt c onc e r ning the ir s ta tus : T he sta tus of ( 1 3) a nd ( 14) is Future Necessity a nd i ts r e spe c tive sta te of a f f a ir s is pr e dic ta ble w i th the he l p of d yna mic a l or sta tis tic a l la w s. T he s ta tus of ( 15) i s Future Probabilistic Contingency , its r e spe c tive sta te of a f f a ir s c a n only be pr e dic te d w ith a c e r ta in pr o ba bil ity. O n the ot he r ha nd the r e spe c tive sta te of a f f a ir s of ( 16) – sta tus: Future Contingency – c a nno t be pr e dic te d a t a ll be c a use of the a bse nc e of both dyna mic a l a nd sta ti stic a l la w s. T hu s w e ha ve tw o c a se s of Future Contingency: ( 15) a nd ( 16) . A spe c ia l c a se is the omn ite m por a l c ont inge nc y of ( 17) .

10.32 The necessary status cannot be changed by truth or knowledge ( a ) T he sta tus i s ne c e ssa r y in the str onge s t s e nse if p = pL g or p = pM ( logic a l or

ma the ma t ic a l ne c e ssity) . I f a ll sta te s of a f f a ir s not posse ss ing th is s ta tus a r e ca lle d not necessary , i. e . c ontinge n t ( in this se n se ) , the n a ll la w s of na tur e ( e ve n dy na mic a l or de te r m ini sti c one s) w o uld ha ve t o be c a l le d c ontinge n t. A l so t he e xis te nc e of t h e w or ld ( un ive r se ) is c ont inge n t a c c or ding to thi s te r m ino logy. T h is is impor ta nt in c onne c t ion w ith the Chr is tia n doc tr ine tha t t he c r e a tion of th e unive r se is no t a c onse que nc e of G od's e sse nc e , i. e . ne ithe r s ome t hin g w ha t he ne c e ssa r ily w i lls, nor some t hing w ha t he w ill s t ha t it ha ppe ns ne c e ssa r ily ( se e be low 1 0. 33, c ontinge n t 1) . N ow it is e a sy to unde r sta nd tha t ne ithe r tr ut h, nor know le dge c a n c ha nge the sta tus of log ic a l or ma the ma t ic a l ne c e ssity. A f ir st r e a son f or tha t is tha t in the c a se of logic a l ne c e ssity a logic a l ly va lid pr opos iti on l ike p → p or ¬( p ∧ ¬p) or ( p ∧ ( p → q) ) → q i s a te mpor a l or va lid i n a time le s s w a y . Sinc e a c ha nge r e quir e s a dif f e r e nt sta te of a f f a ir s a t a d if f e r e nt t ime , t he r e c a nnot be suc h a c ha nge of the s ta te

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of a f f a ir s c or r e sponding to suc h l ogic a ll y va lid pr opo sit ions ; i. e . if the y a r e tr ue , the y a r e tr ue a te mpor a lly or e te r na lly. T he sa me ho lds f or ma the ma t ic a lly va li d pr opos iti ons l ike 2 + 3 = 5 or x ⋅ y = y ⋅ x. A se c ond r e a son is t ha t tr u th ( the tr uth pr e dic a te or the tr u th ope r a tor ) i s i tse lf a te mpor a l. Sta te s, sta te s of a f f a ir s a nd e ve nts obta i n a t a c e r ta in time ( of this w or ld) . A nd t he r e f or e pr oposit ions , if the y r e pr e se nt sta te s, sta te s of a f f a ir s or e ve nts, ma y ha ve a time inde x like pt, qt 1 , pt>t 0 . . . e tc . But it ma ke s no se nse to a tta c h a time in de x to the tr u th pr e dic a te or to the tr uth ope r a tor . T hus it is c or r e c t to sa y: "I t i s tr ue tha t W or ld W a r I I e nde d in 1 945 ", bu t not: "I t is tr ue in 1 945 ( or a t so me othe r time ) tha t W or ld W a r I I e nde d in 1945". S inc e the sta te s of a f f a ir s c or r e sponding to lo gic a ll y or ma the ma t ic a lly ne c e ssa r y pr opos iti ons a r e a te mpor a l, too, no time or c ha ng e c a n be invo lve d c onc e r nin g the sta tus of lo gic a l or ma the ma tic a l ne c e ssity a nd the tr ut h of its r e pr e se ntin g pr oposi tio ns. Conc e r nin g hu ma n know le dge , the ope r a tor "k now s tha t " or " the pe r so n a know s t ha t" ma y ha ve a time inde x. B ut a lthough some hu ma n pe r son ma y know a t a c e r ta in ti me tha t a log ic a lly or ma the ma t ic a lly va lid pr opos iti on is tr ue , just by k now in g tha t, the sta tu s ( logic a l or ma the ma tic a l ne c e ssit y) or the r e spe c ti ve sta te of a f f a ir s c a nnot be c ha nge d. O r to sa y it w ith a n e xa mple : T he sta tus ( ma t he ma tic a l ne c e ssit y) of Fe r ma t' s the or e m, i. e . tha t the e qua tio n xn + yn = zn ha s no sol utio n s f or n > 2, i s not de pe nde nt on the f a c t ( a nd c a nnot be c ha nge d by i t) th a t it w a s c or r e c tly c on je c tur e d b y Fe r ma t, but w a s know n only i n 1994, w he n W ile s ha s of f e r e d ( a nd re vise d a nd c omple me n te d) its pr oof . O n the othe r ha nd, a s is c le a r f r o m c h a pte r 3, it doe s not ma ke se nse to a ttr ibute a ti me t o G o d’ s k now le d ge if , f ir st, by ‘ ti me ’ w e un de r sta nd a lw a ys the ti me of our unive r se a nd, se c ond, w e a ssume G od to be ou tsi de time ( if he ha s c r e a te d a c ha nging unive r se w ith ti me ) .

( b) T he sta tus is ne c e ssa r y in a str ong se nse if p = p N or p = p S . Sinc e la w s of na tur e a r e time tr a nsla t ion inva r ia nt, p N ( dyna mic a l la w s) a nd p S ( s ta tis tic a l la w s) hold a ls o in a ti me le ss w a y ; or in t his c a se w e ma y a lso sa y the y h old f or a ll time s ( if ti me is the ti me be long i ng to the unive r se ) . T he r e f or e the r e a sons w hy the sta t us ( na tur a l ne c e ssity) of the sta te s of a f f a ir s r e pr e se nte d by s uc h pr op osi tio ns c a nnot be c ha n ge d by tr ut h or know le dge , a r e simila r a s those give n a bove f or logic a lly a nd ma the ma t ic a lly ne c e ssa r y pr opos it ions.

( c ) T he sta tu s is ne c e ssa r y in a w e a ke r se ns e if p = p NI or p = pt<t0 . I n the c a se w he r e p = p N I , the sta te of a f f a ir s r e pr e se nte d by the pr op osi tion p N I is str ic tl y de te r m ine d b y a n e a r lie r s ta te of a f f a ir s + the d yna m ic a l la w w hic h

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holds w it h na tur a l ne c e ss ity. p NI h ow e v e r holds w ith c on dit iona l ne c e ssity only. Be c a use a lthoug h the la w is na tur a lly ne c e ssa r y a nd a lthough p NI f ollow s w it h lo gic a l ne c e ssi ty f r o m the e a r lie r sta te ( of a f f a ir s) + the la w , it is itse lf ne c e ssa r y only u nde r the c onditi on tha t the e a r lie r sta te ( of a f fa ir s) is ne c e ssa r y in thi s se n se . N ow the e a r l ie r sta te ( of a f f a ir s) is u sua ll y pa st or pr e se nt suc h tha t it p osse s se s un pr e ve nta ble or pa s t ne c e ssi ty. T he r e f or e w e c a n sa y tha t a lso pNI posse sse s Unpreventable Necessity. I n the c a se w he r e p = pt<t 0 ( sta te s of a f f a ir s oc c ur r ing in the pa st or a t pr e se nt) , the s ta tus is a ls o Unpreventable Necessity. O bse r ve t ha t w ha t i s me a nt he r e by "un pr e ve nta ble " is tha t a sta te of a f f a ir s ( e ve nt) p if it ha ppe ns a t t1 ( pt1 ) , c a nnot be ma de not to ha ppe n a t t1 . A nd c onse q ue ntl y tha t i t i s tr ue ( w i tho ut a ny ti me i nde x a tt a c he d to the pr e dic a te ‘ tr ue ’ ) to sa y tha t p ha ppe ne d a t t1 . O n the ot he r ha nd the e f f e c ts of suc h a n e ve nt c a n be r e move d or u ndone a f te r w a r ds. T h us a lthou gh the f a c t tha t the r e w a s a n e a r thqua ke in 1971 in B uc ha r e st is un pr e ve nta ble , ma ny ( e ve n if not a l l hist or ic a l) tr a c e s a nd de str uc tion s c a n be undone in the se nse of be in g r e pa ir e d a nd r e move d. N ow , a ga in, it is e a sy to se e tha t the sta tus of unpr e ve nta b le ne c e ssit y of a sta te of a f f a ir s c a nnot be c ha nge d by tr uth or know le dge : T ha t p ha ppe ne d a t a time t < t0 or tha t p w il l ha ppe n de te r mine d by e a r lie r sta te s a nd dyna mic a l la w s a t a time t > t0 is tr ue ( w ithou t a ny ti me inde x) . A nd mor e ove r it ha ppe ns in de pe nde nt ly of w he the r some one know s it or not.

10.33 Can the status "contingent" be changed by truth or knowledge? Be f or e w e sha ll give so me a nsw e r s t o t his q ue sti on, it sho uld be r e me mbe r e d tha t a c c or ding to the di vis ion i n 10. 31, dif f e r e nt se nse s of "c ontin ge nt " c a n be de f ine d: A sta te of a f f a ir s or its r e pr ese ntin g pr opos iti on p ma y be c a lle d c ontinge n t 1 , if f it is ne it he r logic a ll y nor ma the ma t ic a lly ne c e ssa r y, i. e . if p ≠ pL g a nd p ≠ p M ( c f . 10. 32( a ) ) . A pr opos i tion p ma y be c a lle d c on tin ge nt 2 if f it is c on tin ge nt 1 a nd is no t na t ur a lly ne c e ssa r y in the se nse of a la w of na tur e , i. e . if p ≠ p N a nd p ≠ pS . I n a thir d s e nse a pr oposit ion p ma y be c a lle d c ontinge n t 3 , if f it is c ontinge n t 1 a nd c ontinge nt 2 a nd in a ddit ion i s not ne c e ssa r y in t he se nse of pN I or pS I ( pr e dic ta b le by dyna mic a l or sta t ist ic a l la w s) nor in the se nse of pt≤ t 0 ( de sc r ibi ng a pa st or pr e se nt sta te of a f f a ir s) . Sinc e a ll pa st a nd pr e se nt sta te s of a f f a ir s a r e r ule d out, a pr opos iti on p is c a lle d c ontinge n t 3 , if f it is not ne c e ssa r y in the se nse ( 15) or ( 16) or ( 17) of 10. 31, i. e . if p = ( pt>t0 ∧ pP C ) or p = p C

t>t 0 or p = ( ∀t) p Ct or p = ¬( ∃t) p C

t. I t i s

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only t his t hir d se n se of c ontin ge nc y w hi c h is me a nt i n the que s tion 1 0. 33 a nd w hic h w il l be disc usse d i n this pa r a gr a p h. ( a ) a d ( 15) : Future Probabilistic Con tingency

I f w e mix a l itr e of c ol d a nd a l itr e of h ot w a te r , w e w ill ge t t w o l itr e s of luke w a r m w a te r . T he pr oba bil ity f or t he sta te ( of a f f a ir s) of luke w a r m w a te r a f te r a ce r ta in time of mixi ng w i ll ha ve a c e r ta in ve r y high va lue , c lose to 1, sa y: r . W e c a n pr e dic t the r e f or e the sta te of luke w a r m w a te r w ith t he ve r y high pr o ba bil ity r . T his p r e dic tion, ma de e a r lie r ( sa y a t t1 ) , tha n the oc c ur r ing sta te ( lu ke w a r m w a te r ) a t t2 ( t2 > t1 ) , is a true pr e dic t ion ( sta te me nt) , i. e . it is tr ue tha t a c e r ta in t ime in te r va l a f te r mi xin g the s ta te of luke w a r m w a te r oc c ur s w ith pr oba b i lity r . T he sta te "l uke w a r m w a te r " is a ma c r osta te in t he se nse of the r mo d yna mic s. I t oc c ur s w it h sta t ist ic a l f utur e ne c e ssity. O n the o the r ha nd the oc c ur r ing m ic r osta te w h ic h r e a lise s the ma c r osta te is st ill Probabilistic Contingent s inc e the r e i s a h uge numbe r of po ssi ble m ic r osta te s w h ic h c a n r e a lise the ma c r osta te lu ke w a r m w a te r . T ha t just a pa r tic ula r mic r osta te ( i. e . a pa r tic ula r distr ibu tio n of the a toms or mole c ule s) out of t he hu ge numbe r w ould oc c ur a t t2 ha s a n e xtr e me ly low pr oba b ili ty due to the huge numbe r of possib le mic r osta te s. 1 2 0 N ow thi s ve r y w e a k ( low ) kind of pr o ba bil ist ic c ont inge nc y w hic h is t he onto log ic a l sta tu s of the se mic r osta te s is ju st a f a c t a nd w ill not be c ha nge d w he n t he r e spe c tive pr oposi tio n de sc r ib ing thi s f a c t is ( c a lle d) tr ue . T he r e f or e tr uth doe s not c ha nge the sta t us of pr oba bi lis tic c ontinge nc y. T he sa me hold s f or kno w le dge : T he f a c t t ha t s ome bo dy pr e dic ts c or r e c tly a t t1 tha t a c e r ta in sta te ( of a f f a ir s) – a pa r tic ula r si ngle mic r osta te – w i ll oc c ur a t t2 w i th the s ma ll pr oba bi lity ∆r, d oe s no t a nd c a nnot c ha nge the s ta tus of the pr e d i c te d f a c t ( tha t it is pr o ba bil ist ic c ontinge n t) . T h e sa me r e sult c a n be obta ine d if w e take a sta te of a f f a ir s w hic h ha ppe ns w ith a n othe r ve r y low pr oba bi lit y. A n e xa mple is the s o - c a lle d tu nne l e f f e c t in Q ua ntu m Me c ha nic s : a pa r tic le pa sse s thr o ugh a p ote nt ia l ba r r ie r w ith k ine tic e ne r gy w hic h i s lo w e r th a n tha t of the he igh t of t he ba r r ie r . A ssu me tha t the ve r y l ow pr oba bil ity f o r suc h a n e f f e c t is ∆s . A l so the n a tr ue pr e dic tion f or suc h a sta te of a ff a ir s doe s not c ha nge the pr oba bilit y va lue ∆s of the e ve n t a nd c onse que n tly doe s not c ha n ge its sta tu s of Future Probabilistic Contingency . T he sa me h o lds f or kno w le dge a s i s c le a r if w e spe a k of pr e dic tions.

( b) a d ( 16) : Future Contingency 1 2 0 The number of microstates which can realise the same macrostate was used by Boltzmann to defin e entropy.

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H e r e w e ta ke a sta te of a f f a ir s w hic h ca nnot be pr e dic te d, not e ve n w i th some pr oba b ili ty via unde r l ying s ta ti sti c a l la w s. A n e xa mple is a huma n f r e e w ill de c isi on. T h e hi stor ic a lly f a mous e xa mple is A r i sto tle 's se a ba ttle . 1 2 1 T he r e a r e nume r ous inte r pr e ta tio ns of c ha pte r 9 of A r istot le 's D e I nte r pr e ta tione . S um ma r isi ng t he m, the y c a n be gr oupe d i nto tw o ma in inte r pr e ta tio ns I n t 1 a nd I n t 2. I n t 1 is de f e nde d by the E pic u r e a ns, Boe th ius a nd i n the 20 t h c e ntur y by A n sc ombe , L uka sie w ic z a nd Pr ior . 1 2 2 I nt 1 se e ms to be ba se d f ir st on D e I nt. 19a 4: "W ha t a nyone ha s tr uly sa i d w ould be the c a se , c a nnot not ha ppe n . " I n othe r w or ds: I f p is tr ue , it c a nnot not ha ppe n tha t p. N ow "i t c a nnot not ha ppe n " is i nte r pr e te d by "im pos sib ly not " or "ne c e ssa r ily ", suc h tha t w e ge t the pr inc iple f or f utur e c ontinge n t pr o pos iti ons : I f pt>t0 . is tr u e , the n ne c e ssa r ily : pt>t0 . I nt 1 is f ur the r ba se d on D e I nt. 19a 39: ". . . ye t not a lr e a dy tr ue or f a lse . " I nt 1 sa ys tha t A r i sto tle he ld tha t the pr inc ip le o f biva le nc e ( e ve r y pr o pos iti on is e ithe r tr ue or f a lse ) or the pr inc iple of e xc lude d m iddle ( e ve r y se nte nc e of the f or m ' p or not - p ' i s tr ue ) a r e not va lid f or f u tur e c ont inge n t pr oposi tio ns. I nt 2 is de f e nde d by t he me die va l c o m me nta tor s of A r is tot le , a mong t he m T homa s A qu ina s 1 2 3 , a nd in t he 20 t h c e nt ur y by H int ikka a nd Re sc he r 1 2 4 . A c c or ding t o I n t 2, A r i sto tle d id not gi ve up the pr i nc iple of b iva le nc e or e xc lude d midd le i n D e I n t c h. 9. I n or de r to unde r sta nd t his be tte r , one ha s f ir st to r e a lise the str uc tur e of c h. 9. A lr e a dy a c c or ding to the me die va l c omme n ta tor s, no ta bly T ho ma s A qu ina s in hi s c om me nta r y ( 1 962, A I N ) , - but a l so obse r ve d by H int ikka – A r i sto tle 's te xt ha s thr e e ma i n pa r t s: the f ir st pa r t 18a 28 – 19a 5 c on ta ins a r gu me nts pr o ne c e ssit y a nd de te r mi nis m toge the r w ith i ts un like l y c onse que nc e s ( 18a 28 – 18b25) a nd the n to ge the r w ith its im poss ible ( a bs ur d) c onse que nc e s ( 18b26 – 19a 5) . I nbe tw e e n the r e is a sh or t c ha p te r w he r e A r is tot le sa ys tha t b iva le nc e ha s to be a c c e pte d ( 18b17 – 25) . T he se c ond pa r t c onta i ns a r gu me nt s a ga in st ne c e ssity a n d de te r m ini sm ( 19a 6 – 22) . O nly the thir d pa r t ( 19a 2 3 - 19b 4) c onta ins A r ist otle ' s a nsw e r . I n t his he s a ys tha t p ∨ ¬p is ne c e ssa r ily tr ue , i. e . l ( p ∨ ¬p ) – a lso if ‘ p’ is a f u tur e c ontin ge nt pr o pos itio n – b ut the ne c e ssity ope r a tor mu st no t be distr ibu te d on the pa r ts. T ha t is, w ha t is

1 2 1 Aristotle (Int), ch. 9. 1 2 2 Anscombe (1956, ASB); Lukasiewicz (1958, ASy), p. 155f. ; Prior (1957, TMd), p. 86. 1 2 3 Thomas Aquinas (1962, AIN). 1 2 4 Hintikka (1964, FSF); Rescher (1968, TNT); cf. also Weingartner (1964, VFW), where the same view is de fended. F or an English ver sion of i t see Weingartner (2000, BQT ), ch. 4.

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r e je c te d f or f utur e c on tinge n t pr o pos iti ons is: l p ∨ l ¬p. I f the la tte r i s f a lse , its ne ga tion ha s to be tr ue , i. e . ¬l p ∧ ¬l ¬p or in o the r w or ds mp ∧ m¬p mus t be tr ue f or f utur e c onti nge nt pr oposi tio ns. T he phr a se "ye t n ot a lr e a dy tr ue or f a lse " ( 1 9a 39) i s in te r pr e te d by T h oma s A qui na s 1 2 5 a s ye t not a lr e a dy de te r mi na bly tr ue or de te r m i na bly f a l se . T his r a the r s im ple a nd c onsis te nt i nte r pr e ta tio n w il l be a ls o a dopte d he r e . But f or a mor e syste ma tic sol uti on w e sha ll a ppl y a ga in the tw o pr inc i ple s w h ic h ha ve be e n a pplie d a nd c onf ir me d a lr e a dy in t he f or e going c ha pte r s: P1 T r uth is a te mp or a l. P2 T r uth or know le dge c a nnot c ha nge the ( onto logic a l) sta tu s of a f u tur e c ontinge n t sta te of a f f a ir s w hic h i s r e pr e se nte d by a f utur e c ontin ge nt pr oposi tio n. P1: A s ha s be e n sa id a bove 10. 32( a ) , the tr uth pr e dic a te or the tr uth ope r a tor c a nnot ha ve a t ime inde x ; on l y sta te s of a f f a ir s, e ve nt s or sta te s a r e in spa c e a nd time , w he r e time is u nde r stood a s ti me of this w or ld. 1 2 6 T hus f r om the f a c t tha t sta te of a f f a ir s ( e ve nt) p oc c ur s a t time t ( pt) o ne c a n c onc lude tha t i t is tr ue tha t pt, i. e . Tr ( pt), but not tha t i t w ou ld be tr ue a t a c e r ta in ti me , sa y t or t1 > t tha t pt. Be c a use a c lose d pr op osi tio n p a t t( pt) c onta ini ng n o va r ia b le s, is a lw a ys tr ue o r ne ve r . A nd f ur the r if t he sta te of a f f a ir s p w il l oc c ur a t t > t0 ( t0 = pr e se nt ) in t he f utur e , i. e . pt > t 0 , the n it is tr ue tha t pt > t0 , i. e . Tr( pt> t0 ) . T he da nge r he r e lie s in c omm itt ing a f a l la c y a s f ollow s: S inc e tr uth is a te mp or a l, it is a l so omn ite m por a l. T hus f r om Tr( pt) w e c onc lude : o mni te mp or a l Tr ( pt) . A nd f r om this one ma y w r ong ly c onc lude Tr[ ∀t( pt ) ] , i. e . it is tr ue tha t p oc c ur s a t a ll ti me s or t ha t p i s omni te mp or a lly ne c e ssa r y. T he m ista ke he r e c onsists c le a r ly of smu ggl ing in a unive r sa l qua n tif ic a ti on ove r ti me s ta ke n w r ongly f r om a pr ope r ty of tr uth, i. e . f r om its a te mpor a l c ha r a c te r . Sinc e 'o mni te mp or a l' is de sc r ibe d by ∀t. . . a nd sinc e t c a n be only a ttr ibu te d to sta te s of a f f a ir s, e ve nts a nd sta te s, it is be tte r not to a ttr i bute omnitemporal to tr uth a t a ll, but use only the a ttr ibute atemporal . 1 2 7

1 2 5 Thomas Aquinas (1962, AIN), p. 123. 1 2 6 See chapter 3. 32. For more on time see Mittelstaedt/Weingartner (2005, LNt), chs. 6 and 7. 235. 1 2 7 Applying P1 an d consequently attributi ng time indices o nly to propo sitions representing states o f affairs (eve nts, states) can simplify consid erably certain theses of Tense Logic. For example instead of saying: " If p is true, then it will be true n time units hence that i t was true n time units ago th at p" we may say: "If it is t rue that p at t0 ( t0 = present), then it is true that p at ( t0 + t – t)"; where + t means t time units in the future and –t means t time units in the past.

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P2: I f p = pCt>t 0 ( c f . ( 16) a bove ) , the n the ( ontolog ic a l) sta tu s r e pr e se nte d

by p is Future Contingency. T ha t me a ns p i s ne i the r r ule d, n or r ule d out by a ny la w s a nd its c or r e spond ing sta te of a f f a ir s w il l ob ta in in the f utur e . I f p is n ot r u le d b y la w s, the n p is not ne c e ss a r y ( in t he se nse of la w - ne c e ssity) a nd if p is not r u le d ou t b y la w s or c om pa tible w it h the la w s, the n p i s no t impo ssi ble , he nc e possib le . I n or de r to ma ke this a lit tle bit mor e pr e c ise w e use the te r minolo gy intr o duc e d a bov e : W e de f ine la w - ne c e ssity ( l L ) by sa ying tha t l L p hol ds ju st in c a se tha t p is one of the la w s ( p L g log ic a l, pM ma t he m a tic a l, pN dy na mic a l la w of na tur e , pS sta tis tic a l la w of na tur e ) or r ule d by one of the m, i. e . a c onse que nc e of the m toge the r w ith in itia l c on dit ions ( p NI or pS I ) . l L p if f p is one of pL g , p M , p N , pS , pNI , p S I . 1 2 8 I f p = p C

t>t0 , the n p is not a ny one of those liste d a bo ve ; the r e f or e if p = pC

t>t0 , the n ¬l L p . F ur the r , if p is f utur e c ontinge nt ( p = pCt>t0 ) , the n p is

a lso not r ule d ou t by a ny la w s, i. e . p is c ompa tible w i th a ny of the la w s; the r e f or e if p = pC

t>t0 , the n ◊ L p . Fr om th is it f o llow s tha t if p = p Ct>t 0 , the n

mL p a nd ¬l L p : p = pC

t>t0 → ( mL p ∧ ¬l L p ) or p = pC

t>t0 → ( mL pt>t0 ∧ ¬l L pt>t 0 ) T he imp or ta nt thin g to o bse r ve now is t his: A ppl ying the tr u th pr e dic a te or ( f or r e a sons of simp lic i ty) , the tr uth ope r a tor ' Tr ' to f ut ur e c ontin ge nt pr oposi tio ns doe s no t c ha nge the ir c ontin ge nc y sta tu s sinc e it c a nnot c ha nge the ont olog ic a l sta t us ( of c on tin ge nc y) of the c or r e spond ing sta te of a f f a ir s. Be c a use the obta inin g of the sta te of a f f a ir s is the r e a son f or the pr oposi t io n be ing tr ue a nd not ot he r w ise . Tr( p C

t>t0 ) → Tr( mL pt>t 0 ∧ ¬l L pt>t 0 ) H e r e one ca n a lso distr ibu te Tr to t he pa r ts of the c onse que nt: Tr( p C

t>t0 ) → [ Tr( mL pt>t0 ) ∧ Tr( ¬l L pt>t0 ) ] Fur the r mor e it se e ms to ho ld: Tr( p C

t>t0 ) → Tr( pt>t0 ∧ ¬l L pt>t 0 ) O bse r ve tha t a l so ( p ∧ ¬l p) e xpr e s se s the c ont inge n t sta tus, a lt houg h i n this c a se w e ha ve a c on tinge n t f a c t w h ic h ma y oc c ur a t t0 ( pr e se nt) or e ve n a t t < t0 ( pa st) . If so no pr oble m a r ise s. But in the c a se o f f utur e

1 2 8 For the interrelations of necessity ( l ) and possibility ( m) and the us ual laws of Modal Logic we assume the modest system T (of Feys or v. Wright) and the usual definitions: l p ↔ ¬m¬ p, ¬l p ↔ m¬p etc.

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c ontinge nc ie s, if w e dis tr ibu te now Tr, w e c a n se e im me dia te ly a da nge r f or inte r pr e ta tion: Tr( p C

t>t0 ) → [ Tr( pt>t0 ) ∧ Tr ( ¬l L pt>t0 ) ] T he f ir st pa r t of the c on se que nt : Tr ( pt>t0 ) sugge s ts now t ha t pt>t0 is determinate tr ue . Bu t th is w r on g su g ge stio n c ome s f r o m the f a c t tha t Tr( pt>t 0 ) is a ha lf - tr uth; th is is s o be c a use it is now se pa r a te d f r om ¬l L pt>t 0 , w hic h show s i ts c onti nge nc y, be c a use it lost the ma r k C ( f or c ontinge n t) on the le tte r ' p'. I n or de r no t to f or g e t the sta tu s of c o nti nge nc y a f te r distr i but ion, t he la st tw o f or m ula s sho uld be be tte r r e pla c e d by the tw o f ollow ing one s : Tr( p C

t>t0 ) → Tr( pCt>t 0 ∧ ¬l L pt>t 0 ) a nd Tr( p C

t>t0 ) → [ Tr( p Ct>t0 ) ∧

Tr( ¬l L pt>t0 ) ] W ha t ha s be e n sa id c onc e r ning tr u th, c a n be a na logously sa i d a bout know le dge . W e ma y the r e f or e re pla c e ' Tr' by ' K' ( sta nd ing f or 'know s tha t') : K( pC

t>t0 ) → K( mL pt>t 0 ∧ ¬l L pt>t0 ) K( pC

t>t0 ) → K( pt>t0 ∧ ¬l L pt>t0 ) I f one dis tr ibu te s the ope r a tor ' K' t o the pa r ts of the c onj unc ti on, the n the r e is t he sa me da nge r f or a mi sin te r pr e ta tion a s a bo ve : K( pt>t0 ) ma y be inte r pr e te d w r o ngly a s sa yin g t ha t i t is k now n tha t pt>t 0 is determinate tr ue . But a s a bo ve , K( pt>t 0 ) is a ha lf - tr u th a nd the r e f or e misle a din g, be c a use it is se pa r a te d f r om the pa r t w hic h show s t he c ontinge nc y a nd doe s not ha ve the ma r k ' C' f or 'c on tinge n t'. T he r e f or e t he la st f or mula ha s to be r e pla c e d by K( p C

t>t0 ) → [ K( p Ct>t0 ) ∧ K( ¬l L pt>t0 ) ] .

But if the k now le d ge is huma n know l e d ge , w e migh t a ttr i bute t ime indic e s to the a c tion of know ing. I n thi s c a se on e ma y sa y: T he pe r son a know s a t time t0 ( pr e se nt) tha t p w i ll be the c a se a t t>t0 : aKt 0 ( pt>t0 ) . B ut a l so i n t his c a se know le dge c a nnot c ha nge the sta tus of the sta te of a f f a ir s c or r e sponding t o t he ( f utur e ) pr o pos iti o n pt>t0 . T his c a n be se e n a s f oll ow s: K now in g some thin g be f or e its ha ppe ni n g c a n be know le dge w ith the he l p of la w s ( of na tur e ) in w hic h c a se the f utur e sta te of a f f a ir s ha s a c e r ta in type of ne c e ssi ty. O n t he othe r ha nd i f – a s it i s a ssu me d he r e – i t is know le dge no t w it h the he lp of la w s ( of na tur e ) , but c or r e c t c onje c tur a l know le dge , t he pr e dic ti on pt>t 0 w i ll be tr ue but c ont inge nt, i. e . not ne c e ssa r y a nd the r e f or e c or r e c tly r e pre se nte d by p C

t>t0 . A ls o he r e the d a nge r f or misunde r sta nd ing c ons ist s in only me nt ioni ng a pa r t, i. e. aKt 0 ( pt>t0 ) w it hout t he ma r k ' C', ins te a d of me ntion ing the w ho le w hic h is: aKt 0 ( pC

t>t0 ∧ ¬l L pt>t0 ) . H e r e tha t w ha t is know n r e pr e se nts the sta tu s of the

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r e spe c tive sta te of a f f a ir s: Future Contingency. A nd the obta in ing sta te of a f f a ir s w ith t his ont olog ic a l s ta tus is the r e a son f or the c or r e sp ondi ng pr oposi tio n be ing tr ue a nd not the ot he r w a y r ound. Fr om the se c on side r a tio ns i t i s c le a r th a t ne ithe r tr u th nor know le dge c a n c ha nge the sta tus of Future Contingency of the r e spe c tive sta te s of a f f a ir s. A pply ing a ll thi s now t o the pr ob le m of the se a ba ttle or to tha t of a ( f utur e ) f r e e w ill de c i sion, it sho uld be c le a r tha t " it is tr ue tha t the r e w ill be a se a ba tt le t omor r ow " or " it is tr u e tha t the r e w il l be th is f r e e w i ll de c ision ne x t w e e k" a r e inc om ple te pr e dic tio ns in the f oll ow in g se nse : T o ma ke the m c omp le te w e ha ve to a d d, i. e . to e xplic itl y me nt ion, the c ontinge nc y of t he f utur e e ve nt. T hus w e ma y f or mula te the tw o e xa mple s a bove a s f oll ow s: "I t is tr ue , thou gh no t ne c e ssa r ily, t ha t the r e w i ll be . . . " or : "I t i s tr ue , b ut not de te r m ine d b y a ny la w , tha t the r e w i ll be . . . ". Si mila r l y f or k now le d ge : "I t i s k now n n ow , but not w i th t he he lp of la w s, tha t t he r e w ill be . . . " or : "I t is kno w n n o w tha t the r e w il l be this c ont inge n t ( not ne c e ssa r y) e f f ec t".

( c ) a d ( 17) Omnitemporal Contingency T he r e w e r e vie w s in A r is tot le a nd in D i odor u s a nd the Me ga r ia n Sc hoo l to de f ine tha t w ha t i s ne c e ssa r y ( p oss ible ) a s tha t w hic h is tr ue a t all ( a t some) time s : l tp ↔ ( ∀t) pt mtp ↔ ( ∃t) pt A some w ha t w e a ke r de f ini tion is by de f i ning t he ne c e ssa r y a s tha t w hic h i s the c a se now a nd e ve r a f te r a nd the po ss ible a s t ha t w h ic h i s the c a se e it he r now or a t so me f utur e t ime . But a lr e a dy the me die va l c o mme n ta tor s, e spe c ia lly T ho ma s A qui na s a nd Ca je ta n us poin te d out tha t the r e c a nnot be a n e quiva le nc e , but only a n i mpl ic a tio n. Mor e a c c ur a te ly: Pr ovide d t ha t the a bove e quiva le nc e s a r e not unde r st o od a s de f ini tio ns of a ne w ki nd of a time de pe nde nt w e a ke r ne c e ssit y a nd s tr onge r p oss ibi lit y, bu t a r e unde r stoo d a s ne c e ssity of la w s a nd c o mpa ti bil ity w ith la w s, the n the r e a r e no e quiva le nc e s: " For some thin g is n ot ne c e ssa r y be c a use it a lw a ys w il l be , but r a the r , it a lw a ys w ill be be c a use it is ne c e ssa r y; thi s ho lds f or the possi ble a s w e ll a s the impo ssi ble . " 1 2 9 I n or de r to show w ha t i s me a nt i n the a bo ve quo ta tio n ne c e ssi ty ( ne c e ssa r ily: p) ha s t o be unde r st ood he r e sole ly a s ne c e ssit y of la w s, i. e . a s pL g or pM or p N or p S , w hic h w ill be a bbr e via te d a s l L * p, w he r e mL * p ↔ ¬l L * ¬p. T he n the thr e e pr inc i ple s a dopte d in the quota t ion a r e the f ollow ing one s ( w he r e the se c ond a nd thir d f ollow f r om t he f ir st) :

1 2 9 Thomas Aquinas (1962, AIN), p. 113.

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l L * p → ( ∀t) pt l L * ¬p → ( ∀t) ¬pt ( ∃t) pt → mL * p Fr om the la st pr inc ip le one r e c ogn ise s i mme d ia te ly tha t the r e c a n be c a se s w he r e some thin g ( some sta te s of a f f a ir s) is possib le w ith out be in g r e a lise d a t so me t ime suc h tha t the o ppos ite im plic a tio n a nd the e q uiva le nc e doe s not ho ld. T he r e a r e e xa mple s in mo de r n c osmo logy : the nu me r ic a l va lue of the a mou nt of e ne r gy ( ma ss) of the w hole un ive r se is a n om nite mpor a l c ontinge nc y. T he la w of c onse r va t ion o f e ne r gy ( in a c l ose d syste m) sa y s tha t th is a moun t ( nu me r ic a l va lue ) m us t be c onsta n t. Bu t the la w doe s not sa y how la r ge th is n ume r ic a l va l ue is. T he la w sa ys if t he va lue is M, the n M i s c ons ta nt thr ou gh ti me . Bu t t h e f a c t tha t it is jus t M, is a n omni te mp or a l c ontin ge nc y be c a use it is not r ule d by la w s. A nd sinc e thi s f a c t is not r ule d b y la w s, it i s not ne c e ssa r y in the se n se of l L * . N ow a va lue M', w hic h dif f e r s a lit tle bi t f r om M is p oss ible , be c a use c ompa t ible w ith the la w s, bu t it w il l ne ve r be r e a lise d. A not he r e xa mple c onc e r ns r a tiona l be ing s like ma n so me w he r e in the unive r se . A s w e know so f ar , othe r r a tiona l be in gs like me n a r e not d e te r mine d, ne it he r r ule d n or r ule d out by the la w s of na t ur e . T hus it is p os sible tha t the y mi ght e xi st; b ut on the othe r ha nd the ir e xis te nc e ma y ne ve r be r e a lise d dur ing the lif e ti m e of the unive r se , i. e . f or a ll time s. I n t his c a se the ir e xiste nc e i s pos sib le , but is not r e a lise d a t a ny time . T he pr inc iple l L * p → ( ∀t) pt sh ow s a lr e a dy tha t the imp lic a ti on goe s onl y in one dir e c tio n, i. e f r om the f a c t tha t so me sta te s of a f f a ir s a r e o mni te mp or a l, one must not c onc lu de tha t the y a r e nec e ssa r y. A nd thus if it is tr ue tha t ( ∀t) pt it d oe s no t f ol low f r om t his tha t p is ne c e ssa r y. O n t he c ontr a r y, a c c or ding to t he a bove e xa m ple p ( sa yi ng t ha t the ma ss of the w hole un ive r se e qua ls M) i s tr ue a nd hold s o mni te mp or a lly, bu t c ontinge n tly s uc h tha t the w hole tr u th is e xpr e sse d thus : ( ∀t) pt ∧ ¬l L * p T his show s a ga in tha t tr uth c a nn ot c ha nge the s ta tus of a sta te of a f f a ir s w hic h is in th is c a se Omnitemporal Contingency. Su mma r is ing c h. 10 w e ma y sa y tha t it w a s show n f ir s t tha t tr uth a nd know le dge do not c ha nge the ( on tol ogi c a l) sta tus of ne c e ssity of sta te s of a f f a ir s c or r e spondin g t o la w s of log ic , of ma the ma tic s a nd of la w s of na tur e . T he n i t w a s sh ow n tha t tr ut h a nd kn ow le dge do not c ha nge t he s ta tus of a c ondi tio na l a nd of a w e a ke r kind of ne c e ssit y of sta te s of a f f a ir s w hic h a r e pa st ( pt>t 0 ) or w h ic h c a n be de t e r minis tic a ll y pr e dic a te d ( p NI , pS I ) . Fina l ly i t w a s show n t ha t a lso t he sta tus of c onti nge nc y ( be it Future Contingency or Omnitemporal Contingency) c a nnot be c ha nge d by tr uth or

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know le dge . T his r e su lt a mou nts a lso t o a simple sol uti on of the pr oble m of the "se a ba ttle " a nd a na logo us que s tion s.

10. 4 A n sw e r t o t he O b je ct i on s

10.41 Only closed proposition can be true (ad 10.11) T he e xpr e ssi on " A w in s t he e le c tio n" is not a c lo se d pr o pos iti on ( se n te nc e ) , but in f a c t a pr oposi tiona l f unc tio n or a se nte ntia l f unc ti on, i. e . it c onta ins some va r ia ble s or so me in de f inite pa r ts or la c ks so me pa r ts. A s suc h i t c a nnot be tr ue or f a lse . W e ma y c onstr uc t a c lose d se nte nc e ou t of it by a dd ing c onc r e te spa c e a nd t ime in dic e s a nd a ss umin g tha t ' A' r e f e r s to a r e a l pe r son : A w ins t he e le c tion a t t ime t a nd pla c e x. I f this pr oposi tio n – tha t a c e r ta in e ve nt oc c ur s a t t ime t a nd p la c e x – is tr ue , the n it is a lw a y s tr ue a nd not onc e f a lse a nd onc e tr ue . Mor e ove r , tr uth is not the r e a son f or the r e spe c tive e ve nt or sta te of a f f a ir s to obta i n. O n the othe r ha nd the o bta in ing sta te of a f f a ir s is the r e a son f or the c lo se d pr o pos iti on be ing tr ue . T he r e f or e tr uth c a nnot c ha nge the sta tus of a sta te of a f f a ir s.

10.42 Truth does not destroy contingency (ad 10.12) T he a nsw e r to A r ist otle ' s pr ob le m of the se a ba ttle ha s be e n give n i n de ta il in c h. 10. 33. T he ma in p oin t is f ir st tha t tr uth i s a te m por a l a nd t he r e f or e a ny c lose d pr opo sit ion pt i s e ithe r a lw a ys tr ue or ne ve r . A nd se c ond, the sta tus of the sta te of a f f a ir s w h ic h c or r e spond s to the tr ue pr opos it ion pt – if i t is c ontinge n t – c a nnot c ha nge i nto ne c e s sa r y; be c a use the c ontin ge nt sta te of a f f a ir s is the r e a son f or this r e spe c tive pr oposi tio n be ing tr ue .

10.43 The reason for truth is the obtaining fact, not the other way round (ad 10.13) I f it is c or r e c tly know n a t t1 < t0 t ha t pt 2 > t0 , the n – sinc e ge nui ne huma n know le dge ne e ds jus tif ic a ti on – it c a n b e know n e ithe r w i th the he lp of la w s or w itho ut. I f it is know n w ith the he lp of dyna mic a l or sta ti stic a l la w s, the n the know n pr e dic ti on pt 2 > t0 is c onditio na lly ne c e ssa r y ( r e c a ll 10. 31 ( 5) , ( 6) , ( 13) , ( 14) ) . I f it is a si ngle s ta te a nd is k now n w i th the he lp of sta t ist ic a l la w s, the n the pr e dic tio n pt2 > t0 is pr oba b ili stic a lly c on tin ge nt ( r e c a ll 10. 31 ( 7) , ( 15) ) . I f it c a nnot be know n w it h the he lp of la w s, the n pt 2 >t0 is a f utur e c ontinge n t sta te me nt, w h ic h is c or r e c tly c onje c tur e d ( poss ibl y by g ivin g othe r r e a sons w hic h a r e not la w - li ke ) ( r e c a ll 10. 31 ( 9) , ( 16) ) . But the f a c t tha t it i s

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c or r e c tly c onje c tur e d c a nnot c ha nge i ts c ontinge nc y, sinc e the r e a son f or the c onje c tur e be ing tr ue is the ob ta ini ng of th e c onti nge nt f u tur e sta te of a f f a ir s a nd this – the ob ta ini ng of the c ontin ge n t f utur e sta te of a f f a ir s r e pr e se nte d by pt 2 >t 0 – is w ha t is know n; if othe r w i se it w ould no t be know le dge , but e r r or .

10.44 God’s knowledge does not change the ontological status of a state of affairs (ad 10.14) T he ont olog ic a l s ta tus of t he sta te of a f f a ir s tha t Soc r a te s is sit tin g a t so me f utur e ti me t > t0 or a ls o of the s ta te of a f f a ir s tha t S oc r a te s is n o t si tt ing a t t > t0 is ( in both c a se s) c on tin ge nt. Bu t G od's k now le d ge doe s no t c ha nge the ( ontol ogic a l) s ta tus of a sta te of a f f a ir s . T his c a n be s ubs ta ntia te d by t hr e e r e a sons a s f ollow s : ( 1) G od's kno w le dge c a n be be st r e pla c e d by tr uth: gKp ↔ Tr( p) . A s it w a s

show n in 1 0. 33, tr ut h doe s no t c ha nge t he sta tu s of c on tin ge nc y: ( Tr( p) ∧ pC ) → Tr( p C ) . T he r e f or e G od's kno w le dge doe s no t c ha nge the s ta tus of c ontinge nc y, i. e . if G o d kn ow s tha t p a nd if p i s c on tin ge nt, t he n G o d know s tha t the c ontin ge nt pr opo sit io n p is tr ue : ( gKp ∧ p C ) → gK[ Tr( p C ) ] . A pplie d to the e xa mple the f ir st jus tif ic a tio n i s t his : L e t ' p ' be the pr oposi tio n tha t Soc r a te s is s itt ing a t t > t0 . A c c or ding t o c h. 1 w ha te ve r G od know s is tr ue . T hu s if G od k now s tha t p, the n p is tr ue ( Tr( p ) ) a nd G od know s t ha t p is tr ue ( gK[ Tr( p) ] ) . But if p is tr ue , ( Tr( p ) ) a nd the sta tus of p is c ontinge n t ( St( p) = p C ) , the n th e c ontinge nt pr op osi tio n p C is tr ue ( Tr( p C ) ) . N ow w e c a n a ssu me tha t G od know s of e ve r y sta te of a f f a ir s ( a nd of its r e pr e se nt ing pr opo s it ion) w he the r it i s c ont inge n t or no t. T hu s if t he sta tus of p is c on tin ge nt, the n G od kn o w s this : gK[ St( p) = p C ] . T he r e f or e G od know s tha t the c ontinge n t pr o posi tion p C is tr ue gK[ Tr ( pC ) ] . Sy mbol ic a lly : 1. gKs ( w he r e ' s' is the pr oposi tio n tha t S oc r a te s is sitt ing a t t > t0 ) 2. gKs → gK[ Tr( s) ] 3. ( Tr( s ) ∧ St( s) = s C ) → Tr ( s C ) 4. gK[ St( s ) = s C ] 5. gK[ Tr( s) ] ∧ gK[ St( s) = sC ] f r om 1. /2. a nd 4. 6. gK[ Tr( s) ∧ St( s) = sC ] D istr i but ion ( ∧) 5. 7. gK[ Tr( sC ) ] f r om 3. a n d 6. by the pr inc ip le of E pi st e mic

L ogic : [ ( p → q) ∧ Kp] → Kq.

( 2) T h e se c ond r e a son is this : G od' s know le dge doe s not c ha nge the c ontin ge nt sta tus e ve n if he k now s w ith ne c e ss ity w ha te ve r he know s ( c f . c h. 2) . T hus

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if he knows that p and p is future contingent (p = pCt>t0), then he necessarily

knows that pCt>t0. And since the contingency of pt>t0 can be expressed by

not-necessarily pt>t0 (Âl pt>t0), God necessarily knows that not-necessarily pt>t0: l gK[Âl pt>t0]. From this it is seen that even God's necessary kind of knowledge does not change the contingent status: what he necessarily knows, is the contingency of the future state of affairs expressed by pC

t>t0, i.e.: Âl pt>t0. Moreover if we add to l gK[Âl pt>t0] as a second premise: Necessarily: whatever God knows is the case (l (gKp " p)), then the conclusion is: Necessarily: (not-necessarily pt>t0); i.e. l Âl pt>t0. Independently, this can be received by a theorem of the modal system S5 from Âl pt>t0. This theorem is also used as an additional axiom leading from the weaker modal system T (Feys and v. Wright) to S5: Âl p " l Âl p.130

(3) A third reason is this: Every obtaining state of affairs (every fact) is either willed by God or permitted by God and therefore its respective ontological status is also either willed or permitted by God. But if the status of any state of affairs is either willed by God or permitted by God, then God's knowledge cannot change this status. Otherwise his knowledge would be inconsistent with his will which is impossible.

130 For details of this kind of argumentation recall ch. 1, objection 1.14 and the answer to it (1.44).

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11. Whether God Knows Future States of

Affairs

11.1 Arguments Contra

11.11 If an event E is a future state of affairs and is not determined by dynamical laws, then the ontological status of E is not yet actual and still open. But what is not yet actual, can only be possible or possibly not. Therefore it cannot be known as (actually) occurring or known as (actually) not occurring and consequently God cannot know it in this sense. Therefore God cannot know future states of affairs as obtaining or not obtaining if they are not yet actual. 11.12 If God knows future states of affairs, then he knows them either in their causes or in their actuality. But since they are not yet actual, he cannot know them in their actuality. However, to know them in their causes would mean that they are determined, which is not the case of those states of affairs which are not ruled by dynamical laws, like free human actions. Therefore God does not know future states of affairs like free human actions. 11.13 If God knows the future in the sense that he foreknows all human actions, then they cannot happen otherwise then he foreknew. For example, if he knows that Judas will be a traitor, it is impossible for him not to become a traitor, that is, it is necessary for Judas to betray. Thus the actions of men follow by necessity from the foreknowledge of God;131 and consequently there are no free human actions and man is not responsible for them such that court and criminal law (and many other institutions) are in vain. But this seems to be absurd. Therefore God does not foreknow all human actions. 11.14 If a proposition is true, then it represents a fact (a state of affairs that obtains). If a proposition is known, then it is true. If a proposition is future

131 Cf. the argument by Lorenzo Devalla in his Dialogue on Free Will, reprinted in Dworkin (1970, DFW), p. 111-118, p. 111. Cf. further objection 13 of Thomas Aquinas (Ver) 24.

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c ontinge n t, the n it doe s n ot ( ye t) r e pr e se nt a f a c t ( a sta te of a f f a ir s tha t obta in s) . T he r e f or e : I f a pr oposit ion is f u tur e c ontin ge nt, the n it is not know n. A nd c onse que ntl y it is no t know n by G od. 1 3 2 11. 15 ( 1) A ss ume t ha t G od know s the f utur e sta te of a f f a ir s t ha t pe r son a a c ts ( in suc h a w a y) tha t p ( is the c a se ) a t t ime t3 > t0 ( w he r e t3 is i n the f ut ur e r e la tive to t0 a t pr e se nt) . ( 2) A c c or ding to c h. 2 it holds t ha t w ha te ve r G od know s, he ne c e s sa r ily k now s. ( 3) M o r e ove r , it holds tha t w ha te ve r G od know s i s ( or w il l be ) the c a se ( is tr ue ) – a c c or ding to c h. 1. ( 4) T he r e f or e if G od know s tha t pe r son a a c t s ( in s uc h a w a y) tha t pt 3 > t 0 , the n it is ne c e ssa r y tha t pe r son a a c ts t ha t pt3 > t 0 . ( 5) I f it i s n e c e ssa r y tha t pe r son a a c ts tha t pt3 > t 0 , the n pe r son a doe s not a c t f r e e ly tha t pt3 > t0 . ( 6) H e nc e : I f G od know s tha t a a c ts tha t pt3 > t0 , the n a doe s not a c t f r e e ly tha t pt 3 > t 0 . ( 7) T he r e f or e : I f pe r son a doe s a c t f r e e ly tha t pt3 > t0 , the n G o d doe s n ot k now ( the f utur e sta te of a f f a ir s) tha t pe r so n a a c ts f r e e ly ( in s uc h a w a y) tha t pt3 >

t 0 . 1 3 3 11. 16 ( 1) A ssume tha t p i s a c ontinge nt f utur e sta te of a f f a ir s. ( 2) T he n it holds : poss ible p a t t2 ( mpt2 ) a nd pos sibl e not - p a t t2 ( m¬pt2 ) , w he r e t2 > t0 , i. e . t2 is in the f utur e r e la t ive to the pr e se nt point of t ime t0 . ( 3) Co nse que n tly it is possi ble tha t G od k now s tha t pt2 a nd it is possib le tha t G od kno w s tha t no t - pt2 . ( 4) N ow by the la w of e xc lu de d m idd le e ithe r G od k now s tha t pt2 or G od d oe s n ot kn ow t ha t pt2 . ( 5) ( a ) A c c or ding t o c h. 2 it hol ds t ha t w ha te ve r G o d know s, he ne c e ssa r ily kno w s. A nd w e migh t a dd ( b) : W ha te ve r G od doe s no t know he ne c e ssa r ily doe s not kn ow . ( 6) T he r e f or e , ( f r om ( 4) a nd ( 5) ) it f ollow s tha t e ithe r ne c e ssa r ily : G od kn ow s tha t pt2 or ne c e ssa r ily: G od doe s n ot k now tha t pt2 . But ( 6) c ontr a dic t s ( 3) 1 3 2 Cf. Thomas Aquinas (Ver) 2, 12, objection 9. 1 3 3 An argument with a similar structure is discussed by Linda Zagzebski (1997, FHF), p. 291f. The difference is that there, time ind exes (of the past ) are attribu ted to God' s knowing and so necessity is introduced as necessity per accidens as William of Ockham called the nece ssity of the p ast. Here the vie w is defended t hat time in dexes cannot be applied to God' s actions and they cannot be applied to truth (or a truth operator) either because God and truth are timeless. Time can only be applied to events or states which are in spacetime of this world (creation). Ho wever, necessity can be introduced here via premise (2) according to ch. 2. This leads to the same difficulty of God' s knowledge (of future state of affairs) and human freed om as in the case of the argument discussed by Linda Zagzebski.

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w hic h se e ms to sh ow tha t G od’ s kn o w le dge of futur e sta te s of af f a ir s is inc ons iste n t. 1 3 4 11. 2 A r gu m en ts P ro

I f one know s all t he ca use s of the cont inge nt fu tur e eve nts, the n on e kn ow s the obta ini ng of the se continge n t futu r e eve nts. Now God know s all the ca use s of eve r y eve nt and co nse que n tly also tho se of eve r y co nti nge nt futur e eve nt. The r e f or e God know s the obta ini ng of eve r y continge nt futur e eve nt. 1 3 5 11. 3 P rop os ed A nsw er

U sing a dis tinc t ion of Tho ma s Aqui na s , we ca n sa y tha t the r e ar e two wa ys how God know s futur e sta te s of af f a ir s: he ma y know the m " in the ir ca use s" and he ma y know the m in the ir ac tua lit y. 1 3 6 He ca n know the futur e sta te s in the i r ca use s be c a use he know s the ca use s of the eve nts (sta te s) in the uni ve r se and be c a use he know s h is po w e r and th e pow e r of eve r y cr e a tur e, espe c ia lly also t ha t of ma n. He ca n know the f u tur e sta te s in the ir ac tua lit y as he i s outs ide time . The r e f or e we ma y distingu ish thr e e ca se s: Fir s t (11. 31) , he know s the futur e sta te s of af f a ir s of the unive r se and of all cr e a tur e s be longin g to it by know ing i ts ca use s. Se c ond (11. 32) , he know s the m be c a use he kn ow s his pow e r and t he pow e r of cr e a tur e s espe c ia lly t ha t of ma n. Thir d (11. 3 3) , be c a use he migh t ha ve a pos sib ili ty t o know eve r ything in i ts ac tua l sta te if he is out s ide time .

11.31 God knows the future states of affairs of the universe and of the creatures belonging to it by knowing their causes 11. 311 Fu tu r e sta te s of af f a ir s rule d by la w s of na tur e . Conc e r nin g t he fut ur e sta te s of af f a ir s of the unive r se we migh t d ist ing uis h dif f e r e nt ca se s in ac c or da nc e with cha pte r 10 above . If the fu tur e sta te s of

1 3 4 An argument with similar but more complicated structure is discussed by Linda Zagzebski(1997, FHF) p. 297. But the respective inconsistency can also be seen by the simplified argument above. Again the necessity introduced here is that defended in ch. 2 for God’s knowledge, whereas the necessity in Zagzebski(1997, FHF) is introduced as necessity of the past. Moreover we replaced ‘belief’ by ‘knowledge’ because we defended in ch. 1 that there is no belief in God but just knowledge in the strict sense (i. e. : &p(gKp ! p)). 1 3 5 Cf. Thomas Aquinas, (Ver) 2, 12. To the contrary 6. 1 3 6 Cf. Thomas Aquinas (STh) I, 14, 13.

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a f f a ir s a r e r ule d by dyna mic a l or by s ta ti stic a l la w s, t he y a r e pr e dic ta ble ( e ve n f or huma ns) w ith the he l p of la w s a nd i nitia l c ondi tio ns ( c a se s ( 13) a nd ( 14) of 10. 31, sta tus: f utur e ne c e ssity) . H um a ns how e ve r , a lthough the y c a n know in pr inc ip le suc h c a se s ( pt >t 0 # p NI ) a nd ( pt >t 0 # pS I ) , the y w ill k now on ly a ve r y sma ll pa r t of a ll t he f utur e sta te s of a f f a ir s w hic h a r e r ule d by d yna m ic a l a nd sta tis tic a l la w s. But if w e a ss ume tha t G od ha s c r e a te d the unive r se w i th it s la w s a nd w i th the c os molo gic a l i nit ia l c ondit ions, he mus t kn ow a ll tho se f utur e sta te s of a f f a ir s. T he sa me h old s f or f utur e s ta te s of a f f a ir s pr e dic ta ble w ith the he lp of sta t ist ic a l la w s ( ma c r ost a te s) . I n the c a se of dyna mic a l la w s, a n e a r lie r sta te w il l be c a lle d the c a use of a la te r sta te w h ic h f ol low s f r om the e a r lie r one w i th t he he lp of the la w ( dif f e r e ntia l e qua ti on) . I n the c a se of sta t istic a l la w s, a n e a r lie r mic r osta te w il l be c a lle d the c a use of la te r mic r o st a te s, w hic h r e sul t s ta tis tic a lly in a ma c r osta te , e ve n if no t e ve r y ind iv idua l e le me n t of t he m i s the r e by de te r mine d ( c a se : p t >t 0 # pS I , sta tu s: c on diti ona l na tur a l ne c e ssit y ( sta tis tic a l) ) . I n both c a se s a lso t he la w ma y be vie w e d a s a "c a use " in a dif f e r e nt se nse . I n the t r a di tion c o ming f r om A r is tot le i t w a s te r me d "c a usa f or ma li s". Sinc e a tr ue la w of na tur e de sc r ibe s a c e r ta in s tr uc tur e of r e a lity, thi s s tr uc tur e ma y be vie w e d a s a c a use , w hic h toge the r w it h the ini tia l s ta te ( a s a c a use , te r me d "c a usa e f f ic ie ns") le a ds to the f ina l sta te a s the e f f e c t. T ha t G od know s the f utur e sta te s of a f f a ir s "in the ir c a use s" me a ns the n tha t he know s the la w s of na tur e , the dif f e r e nt sta te s of the unive r se , plus it s e le me nts dow n to the sing ula r c a use s, a nd its boun da r ie s ( like c on sta n ts of na tur e ) . Conc e r nin g suc h c a use s e ve n ma n c a n f ind ou t a lot of thin gs: A s a n a na lys is of the c a usa l r e la tion s show s, the r e is a plur a lis m 1 3 7 of c a usa l r e la tions a nd e spe c ia lly a lso of th ose w hic h a r e r e pr e se nte d by la w s of na tur e : c a usa l r e la tions w hic h a r e r e pr e se nte d by dy n a mic a l la w s of Cla s sic a l Me c ha nic s, E le c tr odyna mic s a nd the T he or y of Re la tiv ity, by s ta ti stic a l la w s of T he r mody na mic s a nd Ra dia t ion, by dy na mic a l la w s un de r lyin g D yna mic a l Cha os, b y dyna mic a l a nd sta ti st ic a l la w s of Q ua ntum T he or y. Suc h a n a na l ysi s sho w s f ur t he r tha t t he se c a usa l r e la tion s ha ve a nu mbe r of impor ta nt pr ope r tie s w h ic h c a n be subdi vide d int o:

( a ) L ogic a l pr ope r tie s l ike ir r e f le xivi ty, a sy mme tr y, tr a ns itiv ity, w he r e the r e la tion c a n be one - one , o ne - ma ny or m a ny - one . H e r e tr a nsit ivi ty is not ge ne r a lly sa tisf ie d, but o nly w . r . t. dyna mic a l la w s.

1 3 7 Cf. Weingartner (2005, PCC).

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( b) I ntr ins ic pr ope r tie s l ike c om ple te ne s s of c a use s, r obustne ss a nd ne c e ssity. H e r e c o mple te ne s s i s n ot s a tisf ie d a n d r ob ust ne ss is not ge ne r a lly sa ti sf ie d ( f or e xa mple no t in c ha otic moti on) . I n c a usa l r e la tions w hic h a r e r e pr e se nte d by la w s of na tur e , the ne c e ssity of the c a usa l r e la tion is ju st the ne c e ssi ty of th e r e spe c tive la w . T h is d oe s n ot me a n how e ve r tha t e ve r y c a use is a ne c e ss a r y c ondi tion, a s c la ime d by the so - c a lle d C ounte r f a c tua l T he or y of Ca usa lit y. I n t he c a se of sta tis tic a l la w s, the c a use s a r e usua lly n e ithe r ne c e ssa r y c ondit ion s, nor suf f ic ie nt c ond itio ns.

( c ) Spa ti o - T e mp or a l pr ope r tie s li ke c on tinu ity, n o c lose d ti me - like c ur ve s 1 3 8 , te mpor a l or de r , f inite l im ita t ion of c a usa l pr opa ga t ion, obje c tiv ity of c a usa l or de r i ng. H e r e c ontin uit y is not ge ne r a lly sa tisf ie d. 1 3 9

I n a n a na logo us w a y a n a na ly sis c o uld b e give n f or Si ngle E ve nt Ca usa l ity. I n c a se s of si ngle e ve n t c a usa l ity, w e do n ot a ss ume unde r ly ing la w s of na tur e . A nd this ma inl y f or tw o r e a sons: Fir st, be c a use the y ma y be c omple te ly hidde n suc h tha t w e do not ha ve a ny k now le dge of the m. Se c on dly, be c a use the y ma y o nly pa r tia l ly e x ist si nc e the e ve nt i s a f r e e de c is ion of h uma n w i ll ( se e 11. 312 be low ) . T he a na lysi s of c a usa l r e la tion s s how s the huge mul tip lic i ty a nd r ic hne ss of the str uc t ur a l va r ie ty of our u nive r se . A nd t he pa r t of i t w h ic h c a n be unde r stoo d by ma n w ith the he lp of la w s – though a c ons ide r a ble pa r t – is s t il l r a the r sma ll in c o mpa r iso n to the ma n y ne w thi ngs d isc ove r e d a nd the ma n y ne w que st ion s w h ic h a r e st ill una n sw e r e d. W e ma y sa y like E ins te in tha t w he n one que s tio n is a n sw e r e d by sc ie nc e , te n ne w pr oble m s tur n up w h ic h nobody ha s e ve r dr e a me d of be f or e . Thus if w e sa y tha t ma n c a n know the f utur e sta te s of a f f a ir s by know in g the i r c a use s a nd by know ing t he c a usa l r e la tions r e pr e se nte d by la w s of na tur e , the mor e we ha ve to sa y tha t the c r e a tor of the unive r se w ill know the f ut ur e sta te s of a f f a ir s "in t he ir c a use s". 11. 312 Fu tur e sta te s of a f f a ir s only pa r ti a lly r ule d by la w s of na tur e . T he mor e pr oble ma t ic c a se s how e ve r a re those w he r e the sta te s of a f f a ir s ar e only pa r tia lly r ule d b y la w s of na tur e , i . e . c a se s w he r e a single f utur e e ve nt ( sta te of a f f a ir s) is a f r ee huma n a c tion a nd de c ision. Bu t a lso in the se c a se s 1 3 8 For more about closed time - like cu rves, for causality in General Relativity an d for the question o f singularities in our universe see Hawking, Ellis (1973, LSS). 1 3 9 For a detailed analysis of t he causal relati ons represented by laws of nature see Mittelstaedt, Weingartner (2005, LNt), ch. 9, Ruse (2001, CDC).

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G od c a n know t he f r e e f utur e a c tions a n d de c ision s of ma n w . r . t. the ir c a use s. T he r e a sons f or this a r e the f ollow ing :

( 1) Fir s t, w e ha ve to r e me mbe r f r om c ha pte r 10 tha t no kind of k now le dge c a n c ha nge the ontologic a l sta t us of a sta te of a f fa ir s. T hus if H is a fr e e huma n a c ti on ( a f r e e a nd c ontinge n t de c ision of the hu ma n w il l) the f a c t tha t th is e ve nt i s ( or c a n be ) know n by a ny othe r pe r son ( inc ludi ng G od) , doe s not c ha nge thi s f r e e de c isi o n of the w ill a nd his c ont inge n t sta tus.

( 2) I n or de r to sh ow tha t G od c a n k now a ls o f r e e f utur e a c tions or de c is i ons of the h uma n w il l, w e ha ve to show th a t w it h r e spe c t to a l l i mpor ta nt c ondit ions f or suc h a c tion s:

( a ) A f r e e a c tion or de c ision of the hu ma n w ill ( FADW ) is one w i thou t c ompul sio n f r om out side . O n the a ssu m ption tha t G od ha s c r e a te d this w or ld ( inc lu din g m a n) 1 4 0 , he w ill know a ll pos sib ili tie s of c o mpu lsi on hinde r ing FADW .

( b) FADW im plie s de l ibe r a tio n a nd pla nn i ng w ith the he lp of r e a son. But f or G od the r e a son w hic h a hu ma n pe r son is ta king into c on side r a ti on ma y be e ve n mor e tr a nspa r e nt to him tha n to the pe r s on him se lf .

( c ) For so me of the FADW e th ic a l a nd mor a l r e a sons l ike the c omma nd me nt s a r e c onside r e d a s r e a sons or mot ive s. A lso c onc e r nin g the se r e a sons G od c a n know the m be t te r tha n the indivi dua l hu ma n pe r son him se lf .

( d) FADW i mp lie s inde te r mina c y c o nc e r nin g di f f e r e nt a s pe c ts of the a c tion or de c ision. For e xa mp le , a lthough ma n is usua l ly not f r e e to c hoose he a lth or not he a lth, ma n i s la r ge l y f r e e in c hoos ing the me a ns, e spe c ia lly if se ve r a l me dic a me nt s a r e a va ila ble a nd he lpf ul. Bu t w e ha ve to a ssu me t ha t G od know s a ll c ounte r f a c tua ls of the ty pe if A w ould oc c ur , ma n w o uld c ho ose B , a nd if C w ou ld oc c ur , ma n w oul d c hoose D … e tc . T he know le dge of a ll possi ble c ounte r f a c tua ls by G o d w a s de f e nde d by Molina w ho c a lle d it middle knowledge. T his poin t w a s a lr e a dy e l a bor a te d a nd de f e nde d in c h. 9. 44 a bove .

∉∉⋅32 God knows his power and the power of the creatures including man I n c h. 5 it w a s show n tha t G od' s kno w le dge e xc e e ds his pow e r e spe c ia lly be c a use of the f a c t tha t he know s a lso t he f r e e immor a l a c tions of ma n w h ic h 1 4 0 We do not enter here the question on how G o d has created the world (universe). There is, however, no difficulty that God has created the universe as a universe in evolution. Cf. Weingartner (2000, EVS).

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do not c o me unde r his pow e r e ve n if he pe r mits the m ; a s sta te s of a f f a ir s w hic h he kn ow s a nd pe r mit s, the y c o me unde r hi s pr ov ide nc e . But G od know s a lso the pow e r of hi s c r e a tur e s. I n th is se nse h e kno w s a l l the a bi li tie s, not onl y of ma n in ge ne r a l, but a lso of e ve r y pa r tic ula r pe r son.

( a ) FADW i mpl ie s the pe r son's a bil ity of a utono mou s a c tion s a nd se lf de te r mina t ion w . r . t. the pe r so n's de c isi on. Bu t a lso he r e w e ha ve to a ssume tha t G od ha s a de ta ile d know l e dge of the a bilitie s of ma n in ge ne r a l a nd of e ve r y pa r tic ula r huma n pe r son.

( b) FADW im plie s r e sp ons ibi lity of the pe r son's a c ti ons in c onne c ti on w i th the e vide nc e tha t the de c ision w a s in h i s pow e r a nd tha t he c a use d the a c tion. 1 4 1 I n othe r w or ds : f r e e a c tions a nd de c ision s of the hu ma n w i ll a r e not w ithout c a use s. T he f r e e ly a c ting a nd de c iding hu ma n pe r son know s tha t he hi mse lf is t he c a use of those a c tions a nd de c isi ons. Bu t w e ha ve to a ssu me t ha t t he pow e r a nd a bili ty to c a use f r e e de c ision s a nd a c ti on s in ma n is know n t o G o d f a r be tte r tha n to the pe r so n him se lf .

( c ) For s ome FADWs i t ho lds tha t the r e a r e inne r a c tions goin g on – some t ime s no t w ith out in ne r c onf lic t – in pr e pa r a tion f or a fr e e w ill de c ision. I n suc h c a se s t he r e spe c tive pe r son m ight e ve n h im se lf not f or e know w ha t he is go ing t o de c ide . But f r o m thi s it d oe s not f ol low tha t a c lo se f r ie nd of h im c o uld not kn o w hi m be t te r a nd f or e kn ow w ha t he w ill de c ide . S o muc h t he m or e w e h a ve to a ssu me t ha t G o d w i ll be a ble to know his f ut ur e de c ision.

( d) For s ome e ve nt s, w hic h a r e or ha ve be e n f utur e e ve nts f or me n, i t ho lds tha t t he y a r e bo th in G od's pow e r a n d w i lle d b y G o d. I n s uc h a c a se i t i s e a sy to unde r sta n d tha t t he y a r e know n by G od. A n e xa mp le w oul d be the bir th of Chr is t w hic h is pr e dic te d b y Je sa ja ( 7, 14) : "T he vir gi n w ill give bir th to a c hild …"

Su mm ing up c ha p te r 11. 31 a nd 11. 32 w e ma y sa y tha t G o d c a n know f utur e sta te s of a f f a ir s "in the ir c a use s", bo th, if the c a usa l c onne c tion is ba se d o n la w s of na tur e , a nd if i t is ba se d on h is pow e r or on the pow e r a nd inne r a utono mous se lf de te r mina t ion of ma n in a c ti ons or de c isi ons of f r e e w il l ( FADW) . H ow e ve r , the r e is st ill a r e ma i ning dif f ic ulty w i th those f utur e sta te s of a f f a ir s – e spe c ia lly FADWs – f or w hic h no c a use s ( mo tive s, pla n s, c onside r a ti ons, inte nt ions … e tc . ) e xis t so f a r . O ne s im ple r e a son f or tha t c ould be tha t the pe r son in que s tion is no t ye t bor n. Fr om suc h c ons ide r a tio ns it se e ms to 1 4 1 This condition was stressed already by Aristotle in his Metaphysics (982b25).

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f ollow t ha t kno w ing the f utur e sta te s o f a f f a ir s "in the ir c a use s" – thou gh a good e xp la na tio n f o r ma ny c a se s – w ill not be a ppl ic a ble to a ll c a se s of know in g c onti nge nt f utur e sta te s of a f f a ir s. T his is the r e a son w hy T ho ma s A quina s pr opo se d a f ur the r e x pla na ti on f or G od' s f or e know le dge w h ic h w ill be tr e a te d in the ne xt c ha pte r 11. 33.

11. 33 God migh t hav e a possi bil ity to kn ow fu ture sta te s of af fai rs in the i r ac tual st ate s T he e xpla na t ion T ho ma s A q uina s gi ve s f or th is is c o nta ine d in the f o llo w ing quota t ions : "I n e vide nc e of this, w e mus t c onsi de r tha t a c ontinge n t thi ng

c a n be c onside r e d in tw o w a y s; f ir s t, in itse lf , in so f a r a s it is now in a c t: a nd in this se nse it i s not c onside r e d a s f utur e , but a s pr e se nt; ne ithe r is it c ons ide r e d a s c ontinge nt ( a s ha vin g r e f e r e nce ) to one of tw o te r ms, but a s de te r mine d t o one ; a nd o n a c c ount of this i t c a n be inf a llibl y the obje c t of c e r ta in know le dge … I n a nothe r w a y a c ontinge n t thi ng c a n be c onside r e d a s i t is in its c a u se ; a nd i n t his w a y it i s c ons ide r e d a s f utur e a nd a s a c o nti nge nt th ing not y e t de te r mi ne d t o o ne … a nd in thi s se nse a c ontinge n t thi ng is n ot sub je c t to a ny c e r ta in know le dge . H e nc e , w h oe ve r kno w s a c ontinge n t e f f e c t i n i ts c a use only, ha s me r e ly a c onje c tur a l kn ow le dge of i t. N ow G od know s a ll c ont inge n t thi ngs no t only a s the y a r e in th e ir c a use s, but a lso a s e a c h one of the m is a c tua lly in itse lf . A nd a ltho ugh c ontinge n t t hing s c a n be c ome a c tua l su c c e ssive ly, ne ve r the le s s G od know s c ont inge n t th ings not suc c e ssive ly, a s t he y a r e in the ir ow n be ing, a s w e do; bu t si mul ta ne ously. T he r e a s on is be c a use H is know le dge is me a sur e d b y e te r nity, a s i s a l so H is be ing; a nd e te r n ity be i ng s imu lta ne ou s ly w ho le c ompr i se s a ll time , a s sa id a bove . " 1 4 2

"…bu t the r e la ti on of t he divi ne k now le dge to a n yth ing w ha tsoe ve r is like tha t of pr e se nt to pr e se nt. T his ma y be unde r stoo d by the f oll ow in g e xa mple . I f some one w e r e to se e ma ny pe ople w a lk ing s uc c e ssive l y dow n a r oa d dur ing a give n pe r iod of t ime , in e a c h pa r t of t ha t t ime he w ould se e a s pr e se nt some of th ose w ho w a lk pa s t, so tha t in the w hole pe r iod of h is w a tc hing he w ou ld se e a s pr e se nt a ll of tho se w ho w a lke d pa st

1 4 2 Thomas Aqu inas (STh) I, 14, 13. With the phrase "above" he refers to (STh) I, 10, 2.

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him. Y e t he w o uld not si mul ta ne ous ly se e the m a l l a s pr e se nt, be c a use the ti me of hi s se e in g is not c o mple te l y si mu lta ne ou s. H ow e ve r , if a ll his se e ing c ould e xi st a t onc e , he w ould sim ul ta ne ou sly se e a ll the pa sse r s - by a s pr e se nt, e ve n though the y the m se lve s w ou ld not a l l pa ss a s sim ulta ne o usl y pr e se nt. " 1 4 3 "Jus t a s he w h o g oe s a lo ng the r oa d, doe s no t se e tho se w h o c ome a f te r him; w he r e a s he w ho se e s the w hole r oa d f r o m a he ight, se e s a t onc e a ll tr a ve lling by the w a y. " 1 4 4 "T he r e f or e , sinc e the vision of divine know le dge is me a sur e d by e te r nity, w hic h i s a ll si mul ta ne ous a nd ye t i nc lude s the w hole of t ime w ith out be ing a b se nt f r om a ny pa r t of it, i t f ollow s tha t G od se e s w ha te ve r ha ppe ns in time , not a s f utur e , but a s pr e se nt. For w ha t is se e n by G od is, inde e d, f utur e to some othe r thi ng w hic h it f oll ow s in t i me ; to the d ivi ne vi sio n, how e ve r , w hic h is not in ti me but ou tsi de time , it is not f u tur e but pr e se nt. " 1 4 5

11. 331 G od doe s no t know the f utur e sta te s of a f f a ir s a s f utur e . ( 1) G od ne ithe r know s the pa st e ve nts ( sta te s of a f f a ir s) a s pa st, nor doe s he know t he f utur e e ve nt s ( s ta te s of a f f a ir s ) a s f utur e . T hi s c a n be su bsta n tia te d a s f ollow s :

( 1a ) I f x know s the oc c ur r e nc e of a n e ve nt e a s pa st ( f or him, f or x ) , the n the r e mus t be a ti me i nte r va l be tw e e n t he poin t of t ime of his a c tion of know in g ( t 1 ) a nd the oc c ur r e nc e of e (the pa st e ve nt) ( t 2 ) , w he r e t 1 is la te r tha n t 2 ( t 1 > t 2 ) .

( 1b) I f x know s the oc c ur r e nc e of a n e vent e a s f utur e ( f or him, f or x ) , the n the r e mus t be a ti me i nte r va l be tw e e n t he poin t of t ime of his a c tion of know in g ( t 1 ) a nd the oc c ur r e nc e of e ( t he f utur e e ve nt) ( t 3 ) , w he r e t 1 i s e a r lie r tha n t 3 ( t 1 < t 3 ).

( 2) I t f ol low s f r om ( 1a ) a nd ( 1 b) : I f t he r e is a ti me in te r va l be tw e e n the poin t of time of the a c tion of know ing of x a nd the oc c ur r ing e ve nt, t he n the a c ti on of know ing of x oc c ur s a t a ce r ta in point of time . ( 3) But i t w a s sh ow n in c h. 3 t ha t it is n ot th e c a se tha t G od know s so me thi ng a t some ti me . O r in othe r w or d s: N o t i me inde x c a n be a ttr i bute d to G od's a c tion of know i ng; a lth ough G o d c a n know tha t so me e ve nt ha ppe ns a t some 1 4 3 Thomas Aquinas (Ver) 2, 12. 1 4 4 Thomas Aquinas (STh) I, 14, 13 ad 3. 1 4 5 Thomas Aquinas (Ver) 2, 12.

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time ( i n t his w or ld) i. e . time i ndic e s mu st be a t tr ibu te d to e ve nts of th is w or ld ( the y a r e in spa c e - time ) , but not to a ny a c tion of G od. ( 4) T he r e f or e : G od doe s no t kno w the oc c ur r e nc e of a n e ve nt a s pa st ( f or him) ; nor doe s he kno w the oc c ur r e nc e of a n e ve nt a s f utur e ( f or him) . H ow e ve r , G od doe s kn ow t he oc c ur r e nc e of a n e ve nt of t his w or ld a s pa s t ( or f utur e ) w ith r e s pe c t to some p oin t of r e f e r e nc e ( or r ef e r e nce syste m) of this w or ld; or mor e s pe c if ic a lly G od doe s kn ow the oc c ur r e nc e of a n e ve n t of th is w or ld ( sa y a huma n a c tion) a s a pa st or a s a f utur e e ve nt w ith r e spe c t to a point of t ime ( sa y L ondo n ti me ) of a gr oup of me n in thi s w or ld. T he de e pe r r e a son f or tha t is t ha t the r e i s no a bs olu te ti me a s a ls o the T he or y of Spe c ia l Re la t ivi ty te ll s us. T i me is the time of thi s w or ld ( uni ve r se ) . But w e c a nnot e ve n sa y tha t the r e is one ti me f or the w hole w or ld ( uni ve r se ) ; sinc e e ve r y r e f er e nc e syste m ( a s a pa r t of the unive r se ) ha t its ow n ti me . H ow e ve r sinc e G od is no t ide nt ic a l ( or pa r t of ) this uni ve r se ( or not ide ntic a l w i th hi s c r e a tion) , he is out side t ime . O n t he o the r ha nd, the ti me of th is w or ld i s r e la tive in the se nse of the T he or y of Re la tivit y. T his me a ns :

( 1) T he r e is no de signa te d poi nt of ti me , but only ti me inte r va ls. 1 4 6 ( 2) T he time sc a le a nd si mul ta ne ity a r e not the sa me in dif f e r e nt r e f e r e nc e

syste ms w hic h a r e moving w i th di f f e r e nt ine r tia l move me nt or a c c e le r a tion.

( 3) T ime d oe s n ot pa ss e q ua bly f or dif f e r e nt r e f e r e nc e syste m s. W he the r time pa s se s m or e slow ly or mor e quic kly de pe nds both on t he move me n t of t he r e f e r e nc e sys te m a nd on the gr a v ita io na l f ie ld in w hic h it is l oc a te d. Fr om th is it f ol low s :

( 4) For a r e f e r e nc e syste m ( obse r ve r ) mo ving w ith ve loc i ty of lig ht ( in va c uum) no ti me pa sse s.

11. 332 T he sa me e ve nt ma y be pr e se nt a nd f utur e f or tw o d if f e r e nt obse r ve r s or r e f e re nc e syste ms. 1 4 7

1 4 6 It may seem that a designated p oint of time i s the point of ti me of the Bi g Bang whi ch is – according to the Standard Theory of Cosmology – about 15 billion years in the past. But although the Standard Theory is well supported b y the cos mic backgroun d radiation (discovered by Penzias and Wilson in 1965), the theory is still controversial because there are competitors that seem at least mathematically correct though without empirical test or confirm ation so far. Furtherm ore, this point of time is not very pr ecise. It rests on a number of theoretical assumptions. For instance, on the assumpt ion that the cosmic background radiation cooled down uniformly to the magnitude 2, 7 K at this time. 1 4 7 This is a result of the theory of Special Relativity.

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A sta r e xplos ion of t he Sir ius ( A l pha - Ce nta ur i) i s pr e se nt f or a n obse r ve r the r e ( or c lose to it) , bu t i s f ut ur e f or u s on e a r th, sinc e w e c o uld obse r ve it only a bou t 4 ye a r s la te r ( sinc e the di sta nc e is a bout 4 l igh t ye a r s) . T he r e spe c tive sta r ma y be f ur the r a w a y, s a y 1000 l ight ye a r s. I t ma y e ve n no t e xist a ny mor e w he n w e ob se r ve it in a c e r ta in sta te . I ma gi ne a n ob se r ve r ( A) ( or r e f e r e nc e syste m) , w ho i s l oc a lly pr e se nt w he ne ve r a c o sm olog ic a l e ve nt like a sta r e xplosio n is a c tua lly ta k ing pla c e . H e the n know s the se e ve nts in the ir a c tua li ty; w he r e a s ot he r obse r ve r s B1 … Bn , w hic h a r e f ur the r a w a y, w il l obse r ve the se e ve nts in the ir f utur e ; w he r e the time inte r va l de pe nds o n the dis ta nc e the l ight ha s to r un thr ou gh. U nde r this s uppo sit ion obse r ve r A, w ho se e s a ll the se e ve nts in i ts pr e se nt a c tua lity, w i ll kno w a lso ( a nd c a n pr e dic t) the f utur e obse r va ti ons ( e ve nts) of a ll th e othe r ob se r ve r s B1 … Bn . T his sh ow s a c onsiste nt p oss ibi l it y tha t a n om nipr e se nt be ing c a n know e ve nt s in the ir pr e se nt a c tua lity, w hic h a r e future e ve nts f or huma n ob se r ve r s. Suc h e ve nts a r e not r e str ic te d to c os molo gy, but i nc lude a lso e ve nt s like h uma n a c tio ns, w he r e the slighte s t mot ive mi ght be c om e a w a r e on ly a f te r some time . H ow e ve r , the huma n ob se r ve r c a nnot se e the dista n t obje c t ( or e ve nt) un til the ligh t r a ys of i t or the r e s pe c tive c a usa l p r opa ga tion r e a c h his te le sc ope a nd h is e ye s w ith f in ite ve loc i ty ( li ght ve loc ity) , w h ic h ne e ds ti me . O n the ot he r ha nd, G od doe s not ne e d f or hi s kn ow le dge li ght r a ys or c a usa l pr opa ga tion c om ing f r om the e ve nt; a nd the r e is ne ithe r spa t ia l nor te mpor a l di sta nc e be tw e e n his know le dge a nd a ny e ve nt, be c a use he is outs ide spa c e a nd time . A nd be ing omni pr e se nt by his know le dge 1 4 8 , G od c an know e ve n ts ( sta te s of a f f a ir s) of this uni ve r se ( a nd of e ve r ythi ng he ha s c r e a te d) in it s pr e se nt a c tua li ty. U nde r the se e ve nt s t he r e a r e some w hic h a r e f utur e e ve nt s f or huma n s. T h us in thi s se nse G od c a n k no w e ve n ts in the ir a c tua lity w h ic h a r e f ut ur e e ve nts f or huma ns. I t is a not he r c onse que nc e of t he T he or y of S pe c ia l Re la tiv ity t ha t t ime ( of t he unive r se ) doe s not "f lo w e qua bly " a s N e w ton t houg ht 1 4 9 , but tha t it c a n be "str e tc he d " a nd "c o mpr e sse d ": Cl oc ks, w he n tr a nspor te d w it h hi gh s pe e d, go

1 4 8 According to Thomas Aquinas God "is" in all creatures by his power, by his presence and by his e ssence; by his po wer in s o far everythin g is s ubject to his powe r, by his presence in so far all things are bare and open to his "eyes" (i. e. his knowledge), by his essence, inasmuch as he is the cause of their being. 1 4 9 Cf. Newton (Princ), Scholium: "Abs olut e, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external…"

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mor e sl ow ly r e la tive to t hose tr a nspor te d w it h lo w spe e d. 1 5 0 L ivin g or ga n ism s ( inc ludi ng me n) , w he n the y a r e tr a nspor te d w i th high spe e d, gr ow or be c ome olde r mor e sl ow ly tha n othe r s w hic h a r e "a t r e st" or a r e tr a nspor te d w i th l ow spe e d. A c onse que nc e of th is is t he so - c a lle d " c loc k pa r a dox" or "tw in pa r a dox ": a n a str ona ut sta r t ing a t the a ge of 20 f or tr a ve llin g in spa c e w ith v = 12 /13c f or 20 ye a r s ( a c c or ding to h is c l oc k a nd a g ing pr oc e ss) w he n c o ming ba c k me e t s hi s tw in br o the r , w ho be c a me 52 ye a r s old e r me a nw hile ( a c c or ding t o the t ime pa sse d on c loc ks a t the e a r th a n d a c c or ding to h is a g ing pr oc e ss) . T hus the me e ting of the tw in br o the r s is f ur the r in the f utur e f or the one w ho sta ys on e a r th a nd ne a r e r in the f u tur e f or the on e w ho tr a ve ls ; i. e . the s pa c e tr a ve lle r know in g a nd pr e dic ti ng the me e t ing 20 ye a r s a he a d ( his time ) c a n know a nd pr e dic t the f u tur e e ve nt of the me e t ing 5 2 ye a r s a he a d r e la tive to the r e f e r e nc e syste m e a r th, i. e . r e la tive to the c loc ks of his tw i n br ot he r on e a r th. I ma gine n ow a n o bse r ve r f or w h om no t ime pa sse s be c a use he is tr a ve lling w ith ve loc ity of lig ht ( in va c uum) . H e know s e ve nts a s pr e se nt, a lthoug h the y a r e f ut ur e f or dif f e r e nt r e f e r e nc e syste ms ( obse r ve r s) m ovi ng mor e slow ly. N ow f or G od no ti me c a n pa ss not be c a use he w ou ld mo ve w ith the spe e d of l igh t bu t be c a use he is out si de time . H e c a n kno w the r e f or e e ve r y e ve nt a s a c tua l ( pr e se nt) , si nc e he is omni pr e se nt ( in thi s w or l d, or in h is c r e a tion) by his kn ow le dge . O n the othe r ha nd, the se e ve nts, w hic h a r e pr e se nt a nd a c tua l t o hi s k now le d ge , c a n be f utur e f or us a n d mor e ove r f utur e in a dif f e r e nt se nse f or dif f e r e nt obse r ver s or r e f e r e nc e syste ms in th is w or ld, de pe nding on t he dis ta nc e f r om t he e ve nt; a nd the y c a n a lso be ne a r e r or f ur the r in t he f utur e de pe nd ing on t he m ov e m e nt of the o bse r ve r ( r e f e r e nc e syste m) or on the gr a vita tiona l f ie ld in w hic h he is loc a te d. 11. 333 T he obse r ve r w ho be long s to the w or ld ( unive r se ) c a nnot ha ve a c omple te kno w le dge a bout t he w or ld ( unive r se ) . T he obse r ve r of a doma in of r e a lity ma y ha ve a n inc omple te know le dge f or dif f e r e nt r e a sons: Fir s t, be c a use c onc e r ning the doma in o bse r ve d only sta tis tic a l la w s a r e know n ; a nd s ta tis tic a l la w s do not a ll ow pr e d i c tin g w ith c e r ta inty a n ind ivi dua l c a se ( a sin gula r e ve nt, a pa r tic u la r m ic r osta te … e tc . ) , but on ly t he be ha vio ur of the w h ole e nse mble ( the a ve r a ge ove r the i ndiv idua l c a se s, the ma c r osta te ) . Se c on d, be c a use the s yste m ob se r ve d be ha ve s c ha otic a lly ( in the se nse of dyna mic a l c ha os) a nd the r e f or e no pr e dic tion s a r e 1 5 0 This effect was first confirmed wi th atomic clocks in airplanes by Hafele an d Keating (1971) and by the Maryland Experiment in 1975/76.

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possi ble , e xc e pt f or a ve r y sh or t tim e , a lthough the unde r ly ing la w s a r e dyna mic a l la w s. 1 5 1 T hir d, be c a use ne ithe r the initia l c ondi tion s, nor the de ve lopme n t of the sys te m in its lo ng hist or y i s k n ow n e noug h i n or de r to ma ke e xa c t pr e dic tio ns a bo ut t he f utur e a s it is the c a se w it h the be g inn ing a nd f ur the r e volutio n of the w hole unive r se . Mor e ove r , the r e is a f ur the r se nse , a c cor ding to w h ic h a n obse r ve r c a nnot ha ve a c om ple te know le dge a bou t t he w or ld ( u nive r se ) . I t i s be c a use he be longs a s a pa r t to t his ve r y w or l d w hi c h he tr ie s to obse r ve , to de sc r ibe a nd to e xpla in. Mor e spe c if ic a ll y i t c a n be pr ove d tha t u nde r c e r ta in nor ma l c on dit ions ( li ke a c onsis te nc y c ondi tio n a nd a de te r mi n istic v iz . dyna m ic a l ti me e volu tion be tw e e n the me a sur e d sta te of the syste m S a t t0 a nd the a ppa ra tus sta te ( s) a t t1 ) the a ppa r a tus ( o bse r ve r ) c onta ine d in S c a nnot me a sur e a t t ime t1 a ll sta te s of S a t t0 . I n c onse q ue nc e of tha t, the r e s pe c t ive a ppa r a tus ( obse r ve r ) w hic h is c onta ine d in S c a nno t d ist ingu ish a t ti m e t1 c e r ta in sta te s of S a t t0 . 1 5 2 Bu t he ma y ( in pr inc i ple ) ha ve a c omple te kno w le dge a bout S in a n e xte n de d sys te m S' of S. T hu s if t he sys te m S is the w ho le w or ld, the o bse r ve r c a nn ot ha ve a c omple te kno w le dge of the w hole w or ld to w hic h he be longs a s a pa r t. N ow G od is no t a pa r t of t he w or ld. T he r e f or e he is not s ubje c t to t his r e str ic tion. M or e ove r , w e c a nnot a ssum e tha t he ha s some ki nd of inc o mple te know le dge of t he sor t de sc r ibe d. N ot be longi ng to the w or ld me a ns t ha t G od c a n ha ve a "point of vie w " of the w or ld w hic h is i mpo ssi ble f or a huma n obse r ve r . H e c a n know e ve nts of th is w o r ld w hic h ha ppe n a t a c e r ta in p oin t of time r e la tive to a r e f e r e nc e syste m of this w or ld a nd w h ic h a r e ne a r e r in the f utur e f or some obse r ve r s a nd mor e re mote in the f utur e f or some othe r obse r ve r s be long ing to th is w or l d. 11. 4 A n sw e r t o t he O b je ct i on s

11.41 ÒPresentÓ or Òactual eventÓ is ambiguous (to 11.11) T he e xp r e ssion "a n e ve nt E ( of this w or ld) is a c tua l or pr e se nt" is a mb iguo us sinc e it ha s to be r e la tiv ise d t o a r e f e r e nc e syste m ( to a n obse r ve r ) . I n pa r tic ula r w e ha ve t o di sti ngui sh the r e f e r e nc e syste m RI, w h ic h is the spa c e -

1 5 1 Recall the respecti ve discussio n about dyna mical and statisti cal laws i n ch. 7 above. 1 5 2 For proof and further discussion see Breuer (1995, IAS) and (1997, IOP).

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time poi nt w he r e E oc c ur s f r om a n y oth e r r e f e r e nce syste m R w he r e E c a n be obse r ve d. I f R is dis ta nt f r om RI, a n e v e nt w h ic h i s a c tua l ly oc c ur r ing in RI ma y be f utur e ( no t ye t a c tua l) in R. T hu s G od c oul d e a si ly k now a n e ve nt a s a c tua l ( pr e se nt) w . r . t. RI a nd know th a t thi s e ve nt is n ot ( ye t) a c tua l, b ut f utur e to us a t R. O n the ot he r ha nd c onc e r ning e ve n ts w hic h a r e not a c tua l ( pr e se nt) in a ny r e f e r e nce syste m of thi s w or ld, G od c a n know the m in the ir c a use . T his is a l so possi ble w . r . t. suc h e ve nts w hic h a r e not r ule d by dyna mic a l la w s, a s ha s be e n e la bor a te d in 11. 31 2 a nd 11. 32 a bo ve . Mor e ove r , suc h e ve nts c a n a lso ha ve the sta tu s of f utur e pr oba b ili stic c ont ing e nc y ( r e c a ll 10. 31( 15) a bove ) . I n this c a se G od doe s no t kno w the se e ve nt s a s a c tua lly oc c ur r ing so me w he r e , but only a s po ssi bl e a nd pos sib le no t or a s pr oba ble a nd pr oba ble not. Bu t f r om this i t doe s no t f oll ow tha t h is kno w l e dge a bout the se c onti nge nt f a c t is c ontinge n t too ( c f . 11. 46 be low ) .

11.42 Future events $ determinate events (to 11.12)

I t is no t c or r e c t, a s sa id in the o bje c ti on, tha t to know c ont inge nt f ut ur e e ve nts ( like f r e e huma n a c tions a nd de c is ion s) in the ir c a use s w ou ld me a n tha t the y a r e de te r mine d. A s show n in c h. 10 a b ove , ne ithe r tr u th n or kno w le dge c a n de te r mine ( or c ha nge ) the ont olog ic a l s t a tus of a n e ve nt or sta te of a f f a ir s, be it ne c e ssa r y or c ontinge n t or f utur e c ontin ge nt. T he r e f or e , sinc e a w r ong a ssump tio n is use d a s pr e mi se in obje c ti on 11. 12, its c onc lu sion i s not pr ove d.

11.43 ÒForeknowsÓ is inadequate for God (to 11.13) T he obje c tion 1 1. 13 c onta in s tw o f la w s . T he f ir st is ba sic a lly the sa me a s in the obje c tio n 11. 12: kn ow le dge doe s no t de te r mine the ont olog ic a l sta tu s of a sta te of a f f a ir s ( c h. 10) . T hus sinc e Juda s' a c tion of be tr a ying is a f utur e c ontinge n t a nd f r e e a c tion of Juda s, thi s c ontinge n t ont olog ic a l sta tu s is no t ta ke n a w a y or c ha nge d by the f a c t tha t some one or G o d kno w s tha t thi s w i ll ha ppe n ( a t a c e r ta in ti me unde r c e r ta i n c ir c ums ta nc e s in t his w or ld) . A nd c onse que ntl y the r e spons ibi lit y f or this a c tion is a ls o not ta ke n a w a y. T he se c ond f la w is the e xpr e ssion "f or e k now s" w . r . t. G od. Suc h a n e xpr e ssio n f its to hu ma n know le dge sinc e ma n c a n foreknow in t he se nse tha t he know s a t time t1 t ha t a n e ve nt w ill ha ppe n a t ti me t2 . But G od' s a c tivi ty of kn ow in g c a nnot r e c e ive a time inde x, sinc e it d oe s not ha ppe n a t a c e r ta in ti me ( c f . c h. 3) . T he r e f or e , the e xpr e ssion "f or e kno w s" is ina de qua te f or G od; the mos t a de qua te e xpr e ssion f or G od is ju s t knows in the pr e se nt te n se .

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Be c a use of the se t w o e r r or s in the a ss umpt ion s the c onc lusi on of o bje c ti on 11. 13 is not pr o ve d.

11.44 “Is a fact” is ambiguous (to 11.14) T o thi s ob je c tion a s im ila r a nsw e r c a n be give n a s t ha t gi ve n to o bje c tio n 11. 11. T he e xpr e ssi on " is a f a c t" or "i s f a c tua l" is a mb iguo us i n a si mi la r w a y a s "i s a c tua l ". I t ha s to be r e la tiv ise d to a r e f e r e nc e syste m i n t he sa me w a y. A n e ve nt w hic h is a f a c t ( f a c tua lly) oc c ur r ing in one r e f e r e nc e syste m, ma y be not ( ye t) f a c tua l in a dif f e r e nt r e f er e nc e syste m. But the r e spe c tive c ont inge n t f utur e pr oposi tion ma y be know n a nd c a n be pr e dic te d in ma ny c a se s. I f the r e spe c tive e ve nt is a f a c t w . r. t. to a t le a st one r e f e re nc e syste m, the n it is possi ble in pr inc i ple e ve n f or ma n to know it a nd to pr e dic t it f or othe r r e f e r e nce syste ms. So muc h t he mor e it c a n be know n by G od f or e ve r y r e f e r e nce syste m. I f , on the o the r ha n d, it is not ye t f a c tua l in a ny of t he r e f e r e nce syste ms it ma y be kno w n in it s c a use s by G od.

11.45 Does foreknowledge destroy free will decisions? (to 11.15) I n or de r to show the mis ta ke in ob je c tio n 11. 15 w e sha ll p ut the a r gu me nt in to symb olic f or m : ( 1) gK(aApt3>t0) aAp … a a c ts ( suc h) tha t p ( 2) gKp ' l gKp de f e nde d in c h. 2 ( 3) gKp ' p de f e nde d in c h. 1 ( 4) gK(aApt3>t0) ! l aApt3>t0 ( 5) l aApt3>t0 ! ÂaAFpt3>t0 aAFp … a a c ts f r e e ly tha t p ( 6) gK(aApt3>t0) ! ÂaAFpt3>t0 ( 7) aAFpt3>t0 " ÂgK(aApt3>t0) Conc e r nin g this a r gu me nt w e sha ll a s k tw o que st ions : ( a ) I s the a r gume nt va lid, i. e . doe s the c onc lusi on ( 7) a n d a lso ( 6) lo gic a lly f ol low f r o m the pr e mise s ( 1) , ( 2) , ( 3) a nd ( 5) . I t is e a sily se e n tha t the a n sw e r is : Y e s, pr ovide d tha t w e use a w e l lkno w n pr i n c iple of Moda l L ogic w h ic h sa ys: I f l p (necessarily p) a nd if p ' q ( p necessarily implies q ) the n l q (necessarily q). T he se c ond que s tion ( b) is the q ue stio n w he t he r the pr e mi se s a r e tr ue . Sinc e onl y the n t he c onc lusi on is pr o ve d to be tr ue by thi s a r gume n t. But i n this r e spe c t w e f ind a n i mpor ta n t ne gle c t: W ha t kin d of a c tion is A in “ aApt3>t0 ” . T he time inde x te l ls us tha t t he a c tion w ill ta ke pla c e in the f ut ur e ( point of ti me t3 ) r e la t ive t o t he pr e se nt point of ti me t0 . But i t d oe s n ot te ll us w he the r the a c tion i tse lf i s c ont inge nt a n d ha r dly pr e dic ta b le or de te r mine d by

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dyna mic a l la w s a nd the r e f or e str ic tly pr e dic ta ble . I f the a c tion is a n a c tion of f r e e w ill the n it is c onti nge nt a nd not de te r mine d by dyna mic a l la w s. A nd a c c or ding to c h. 1 0 k now le d ge c a nnot c ha n ge the ont olo gic a l sta tu s ( c ontinge nc y or f r e e w ill a c tion) of sta te of a ff a ir s ( he re of the f r ee w ill a c tion) . T hus the e pis te mic ope r a tor ‘ K’ c a nnot c ha nge the a c tion ope r a tor ‘ A ’ . I n or de r to c or r e c t the a r gu me nt by c or r e c ting the pr e m ise s w e f ir st ha ve to c omple te pr e mise ( 1) by c ha nging ‘ A ’ ( sta nding f or a ny a c tion, de te r mine d or f r e e ) to ‘ AF ’ ( sta nding f or a c ontinge nt a c tion of f r e e w ill) . T he n the c or r e c te d a r gume nt r e a ds a s f ollow s: ( 1’ ) gK(aAFpt3>t0) ( 2’ ) = ( 2) a nd ( 3’ ) = ( 3) ( 4’ ) gK(aAFpt3>t0) ! l aAFpt3>t0 W e c a n e a sily se e now tha t pr e mi se ( 5) be c ome s f a lse : “ I f ne c e ssa r ily pe r son a a c ts f r e e ly tha t pt3>t0 the n pe r son a doe s not a c t f r e e ly tha t pt3>t0 . ” A nd so w e c a nnot use pr e mise ( 5) a n ymor e . A nd he nc e c onc lusio ns ( 6) a nd ( 7) c a nnot be de r ive d a nymor e . T he w hole a r gume n t s tops t he n w ith c onc l usi on ( 4’ ) : I f G od know s tha t pe r so n a a c ts f r e e ly tha t pt3>t0 the n ne c e ssa r ily pe r son a a c ts f r e e ly tha t pt3>t0 . T h is c or r e c ts the a r gu me nt a nd solve s the r e spe c tive dif f ic ul ty c onc e r ning hu ma n f r e e dom a nd G od ’ s know le d ge of c ont inge n t f utur e e ve nts. 1 5 3 O bse r ve f ur the r tha t m ixe d moda l itie s like lm p ( necessarily possibly p ) or ml p ( possibly necessarily p) a r e w e l lk now n in M oda l L ogic s. For e xa mp le the pr i nc iple mp ! lm p is use d a s a n a xio m, w hic h, w he n a dde d to sys te m T , le a ds to s yste m S 5. W e ma y the r e f or e c or r e c t the a r gume nt in 11. 15 by r e w r iting pr e m ise ( 1) w ith the he lp of e xplic ite ly sta t ing the c ontinge nc y of tha t s ta te of a f f a ir s p br ought a b out b y the a c tion of f r e e w ill of pe r son a. I n a bbr e via te d f or m pr e mise ( 1) c a n the n be f or mula te d thus : ( 1’ ’ ) gKopt3>t0 w he r e op " def mp # mÂp I n this c a se the a r gume nt e nds w it h ( 4’ ’ ) : ( 4’ ’ ) gKopt3>t0 ! l (opt3>t0) tha t is: I f G od know s tha t the c onti nge nt s ta te of a f f a ir s p w ill obta in a t t3>t0 the n ne c e ssa r ily the c ontin ge nt sta te of a f f a ir s p w ill obta i n a t t3>t0. A lso w it h t his in te r pr e ta tion of the f ir s t pr e mise the que sti on of c om pa tib ili ty of c ontinge n t f ut ur e s ta te s of a f f a ir s a nd know le dge of f ut ur e sta te s of a f f a ir s is r e solve d.

1 5 3 The argument discussed by Linda Zagzebski can also be corrected along these lines. Then her premise (7) becomes false and conclusion (8) is no more derivable.

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11.46 Is knowledge of contingent future propositions inconsistent? (to 11.16) For r e a sons of c la r if ic a tion w e sha ll f ir st pu t the a r gu me nt in 11. 1 6 in to symb olic f or m : ( 1) pt2 is a c ontinge nt f utur e sta te of a f f a ir s ( 2) mpt2 ∧ m¬pt2 ( w he r e t2 is in the f utur e w . r. t. t0 , pr e se nc e ) ( 3) mgKpt2 ∧ mgK¬pt2 ( 4) gKpt2 ∨ ¬gKpt2 ( 5) ( a ) gKp → l gKp ( b) ¬gKp → l ¬gKp ( 6) l gKpt2 ∨ l ¬gKpt2 Z a gz e b ski w r ite s ( 6) a s ¬m¬gKp t2 ∨ ¬mgKpt2 w hic h is log ic a lly e qui va le nt to ( 6) . She c la ims tha t ( 6) a nd ( 3) c ontr a dic t e a c h othe r w hic h is how e ve r not the c a se ; sinc e the ne ga tion of ( 6) is: mgKpt2 ∧ m¬gKpt2 A s c a n be se e n the se c ond pa r t m¬gKpt 2 is not e qui va le nt to mgK¬p t 2 . I n the f ir st, the ne ga ti on i s a tta c he d t o the a c ti on of kno w ing, i n the se c ond, to t ha t w ha t is know n. H ow e ve r one c a n de r ive a c ontr a dic t ion inde pe nde nt ly f r o m ( 3) a nd ( 5) . Fr o m ( 5b) it f ollow s tha t mgKp → gKp, by c ontr a pos iti on. A nd by sub sti tut ing ¬p f or p it f o llow s tha t mgK¬p → gK¬p. W ith t he he lp of the se w e c a n de r ive f r om the tw o pa r ts of ( 3) : gKpt2 ∧ gK¬pt2 T his le a ds to the c o ntr a dic t ion pt2 ∧ ¬pt2 by the pr inc ip le K T : gKp → p w hic h w a s de f e nde d in c h. 1. A lt hough the c l a im t ha t ( 6) a nd ( 3) a r e c on tr a dic tin g e a c h othe r is too str on g, the w e a ke r c la im ( ma y be Z a gz e bski d idn’ t w a n t to c la im mor e ) tha t ( 6) imp lie s the ne ga t io n of ( 3) is c or r e c t pr o vide d w e a s su me the pr inc iple of moda l logic : “ I f it holds tha t p s tr ic tl y i mpl ie s q t he n it ho lds tha t mp im plie s mq” : Si nc e gK¬p str ic t ly im plie s ¬gKp, m gK¬p impl ie s m ¬gKp a nd the r e f or e ( 3) imp lie s ( 3*) : ( 3*) mgKpt2 ∧ m¬gKpt2 Sinc e ( 6) im plie s t he ne ga ti on of ( 3*) a nd the ne ga tio n of ( 3*) i mp lie s the ne ga tion of ( 3) , it f ollow s t ha t ( 6 ) impl i e s the ne ga tion of ( 3) . I n this w a y w e ma y de r ive a c ontr a dic tion of the f or m “ ( 3) a nd non - ( 3) ” . We ar e now tur ning to inspe c t the pr e m ise s.

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T he pr e mi se s a r e ( 1) , ( 2) , ( 4) a nd ( 5) . N ow ( 4) i s a la w of lo gic , it c a nnot be f a lse . 1 5 4 ( 1) a nd ( 2) ar e a ssu mptio ns w hic h a r e a c ce pte d sinc e the e xiste nc e of c ontinge n t sta te s of a f f a ir s is e m pir ic a ll y w e ll c onf ir me d. D e nyin g ( 1) a nd ( 2) w ould me a n to c la i m so me kind of ne c e ssity ( be it ne c e ssit y of the pa st or ne c e ssity b y de te r m inis tic la w s) f or e ve r y sta te of a f f a ir s of th is w or l d – w hic h se e ms a bsur d. O bse r ve in th is c onne c t ion t ha t, f or mor e a c c ur a c y, w e c ould qua nt if y pr e mise s ( 1) a nd ( 2) a nd c onse que n tly ( 3) w ith the qua nt if ie r ‘ (∃p) ’ , i. e . ‘ f or some p’ a nd a lso ( 4) , ( 5) a nd ( 6) w ith the qua ntif ie r ‘ (∀p) ’ , i. e . ‘f or a ll p ’ . T his w ou ld not c ha nge the si tua ti on: ( 6) stil l the n i mpl ie s the ne ga tion of ( 3) . Pr e mi se ( 5a ) w a s de f e nde d a t f ul l le ngth in c h. 2. I n the a r gu me nt by Z a gz e bski pr e mise ( 5) is sup por te d by th e pr inc iple of ne c e ssity of the pa st. But w ha t a bout pr e mise ( 5b) . I s it de f e n sible i n a sim ila r w a y a s ( 5a ) ? Fir st of a ll ( 5b) is i nde pe nde nt f r o m ( 5a ) . ( 5a ) sa ys tha t f or G od’ s know le d ge know in g a nd ne c e ssa r il y k now in g is e q uiva le nt, sinc e l gKp → gKp is va li d by the la w l p → p of M oda l L ogic . N o w ( 5 b) sa ys tha t f or G o d’ s kn ow le dge a lso kno w ing a n d po ssib ly k now i ng i s e quiva le n t; s inc e p → mp is a ls o a la w of Moda l L o gic . Bu t this doe s not se e m so e a sily de f e nsib le si nc e G od’ s a c tivity is pur e l y a c tua l w it hout po te nc y it is ve r y que st iona ble w ha t ‘ mgKp’ shoul d me a n. I n a ny c a se it is e a sy to se e tha t w ith out ( 5b) ne i the r of both c ontr a dic tio ns me n tione d c a n be de r ive d. A f ur the r c onside r a tion c onc e r ns ( 3) w hic h f or Z a gz e bski f oll ow s f r om ( 2) a nd the pr e mise : t he r e is ( a nd w a s in the pa st) a n e sse ntia l o mni sc ie nt kn ow e r . ( 3) c a nnot be de r ive d f r om ( 2) mpt2 ∧ m¬pt2 a lone . T o de r ive ( 3) fr om ( 2) one ne e ds in a dd it ion the tw o pr inc i ple s of omn isc ie nc e : p → gKp a nd ¬p → gK¬p. T he se pr inc ip le s a r e disc usse d a t the be ginni ng of the ne xt c ha p te r 12. But the r e ( a nd in the a xioma t ic the or y, c h. 13) the y a r e not use d. I nste a d of the m t he f oll ow in g w e a ke r pr inc ip le is use d: G o d kn ow s e ve r yt hing ( e ve r y tr uth) a bout h imse lf , a bout L ogic a nd M a the ma tic s a nd a bou t his Cr e a ti on. N ow , a ssu ming tha t the se s tr onge r pr i nc ipl e s a r e str ic tly va lid, ( 3) f o llow s f r om ( 2) w i th t he he lp of the la w of Mo da l L og ic p ⇒ q | - mp → mq. But a lso he r e the pr oble m is w he the r the se pr i n c iple s a r e too s tr ong. Sinc e i t is not pla usi ble tha t f r om the c on tinge nc y of p ( if p i s a f utur e - pr opo si ti on) w hic h is e xpr e sse d by mp ∧ m¬p w e sho uld de r i ve the c ontin ge nc y of the know le dge of p, e xpr e sse d by mxKp ∧ m¬xKp. O bse r ve mor e ove r tha t th is w ou ld not

1 5 4 We assume here Classical Logic in which the tertium non datur is universally valid. An exception would be Intuitionistic Logic where the principle is not universally valid .

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e ve n be ge ne r a lly tr ue f or ma n’ s know le dge . A s it w a s show n i n c h. 2 ( a nsw e r to the se c ond obje c ti on 2. 4 2) tha t a lth ou gh w ha t is pr ove d c a n be a c onti nge nt f a c t, the pr oof pr oc e ss ( w ith the he lp of la w s a nd logic a l de r iva tion r u le s) is ne c e ssa r y a nd c a n be ne c e ssa r ily kno w n; in thi s c a se a lso the so de r i ve d c onc lusio n, a ltho ugh itse lf c on tin ge nt c a n be ne c e ssa r ily kn ow n. T he r e f or e : Sinc e the m ove f r om the c o nti nge nc y of p to the c on tin ge nc y of the know le dge of p is no t e ve n ge ne r a lly v a lid f or ma n’ s k now le d ge it ne e d no t be va lid f or G od’ s know le d ge ; i. e . the r e is no hin de r a uc e tha t G od ne c e ssa r ily know s s o me th ing w h ic h is c onti nge n t a nd ne c e ssa r ily know s tha t it is c ontinge n t. T h is is a lso su ppor te d by c h . 10, w he r e i t ha s be e n de f e nde d tha t ne ithe r know le dge nor tr u th c a n c ha ng e the onto logic a l sta tu s of a sta te of a f f a ir s ( he r e of a c ontinge nt sta te of a f f a ir s) . Su mma r iz in g w e ma y c onc lu de tha t t he a r gume nt in 11. 46 ( a d 11. 16) r e sts on tw o pr oble ma tic pr e m ise s: O n ( 5b) a nd on the move f r o m “ c ontin ge nt p to c ontinge n tly know n tha t p” . T he r e f or e the c onc lusi on in 11. 16 tha t G od’ s know le dge of c ont inge n t f ut ur e sta te s o f a f f a ir s is i nc onsi ste n t is no t pr ove d by this a r gu me nt.

11.47 Free actions ≠ non-causal actions (to 11.2) T o this a r gu me nt w e sho uld a dd t ha t a lso f r e e a c tions a nd de c isions of ma n ( FADW) a r e not non - c a usa l. T he f r e e ly a c ting a nd de c id ing pe r son k now s tha t he is the c a u se a nd tha t he i s r e sp ons ible f or the se a c t ions a nd de c isi ons. Mor e ove r , the r e a r e dif f e r e nt kinds of r e a sons w hic h a r e c a use s w ithou t be ing the only o ne s a nd w i thou t be ing de te r mi ning c a use s l ike tho se lis te d in 1 1. 312 ( 2b - d) a bove . A nd th us G od c a n k now a lso a c e r ta in pe r son a s t he c a use f or a c ontinge n t a c tion in t he f utur e .

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12. Whet her God K now s E ver yt hi ng T hat i s

T r ue T his q ue sti on i s the op pos ite to the one in c ha pte r 1: W he t he r e ve r ything is tr ue w ha t G od k now s. Sy mbo lic a lly, th e que sti on of c ha p te r 1 i s f or m ula te d a s: ∀p( gKp → Tr( p) ) ? T hu s que stio n 1 2 c a n be f or m ula te d a s: ∀p ( Tr( p ) → gKp) ? 12. 1 A r gu m en ts C on tr a

12. 11 I f G od is omn isc ie n t , the n he k now s e ve r yt hing w ha t is tr ue , or he know s a ll t he tr uth s. N ow a ll tha t is tr ue or a ll the tr uths c a n be c ompr e he nde d in the se t of a l l tr u ths. But the r e is no se t of a ll tr u ths. Si nc e if w e a ssu me one , sa y Tr = { tr 1 , tr 2 , …} , t he n to e a c h s e t of the p ow e r se t of Tr the r e w il l c or r e spond so me tr u th ( f or e xa m ple t o θ the tr ue pr o posi tio n tr 1 ∉ θ ) a n d by Ca ntor ' s a r gume nt t he pow e r se t of Tr is la r ge r tha n Tr. T he r e f or e G od c a nnot know e ve r ythi n g w ha t is tr ue a nd c o nse que nt ly he c a nnot be omni sc ie nt. 12. 12 T o kn ow e ve r yt hin g t ha t is tr u e , is t o k now a n inf ini te nu mbe r of pr oposi tio ns. T hus if G od kno w s e ve r ythin g tha t is tr ue , he must kno w a n inf ini te nu mbe r of pr opos it ions. N o w to kno w a n inf in ite nu mbe r of pr oposi t io ns se e ms to be p oss ible onl y b y kno w ing t he a xio ms ( the a x io ma tic syste m) f r om w hic h the y f oll ow by the la w s of logic . But e ve r ythin g tha t is tr ue , i. e . a ll tr ue pr opositi ons, a r e not a xioma ti sa ble . 1 5 5 T he r e f or e G od c a nnot know e ve r ything t ha t is tr ue . 1 2. 13 T o know e ve r ythi ng w ha t is tr ue , me a ns to be a ble to e f f e c tive ly lis t a l l tr ue pr oposi tio ns. T hus if G o d know s e ve r ything t ha t is tr ue , he is a ble to e f f e c tive ly lis t a ll tr ue pr op osi tio ns. N o w a ll tho se pr opos iti ons w h ic h c a n be e f f e c tive ly liste d a r e r e c ur sive ly e nume r a ble . But ( the se t of ) a ll tr ue pr oposi tio ns a r e not r e c ur sive ly e nume r a ble . 1 5 6 T he r e f or e G od c a nnot know e ve r ything t ha t is tr ue . 1 5 5 This is a result (theorem) of metamathematics by Tarski and others; cf. 12. 342(2). 1 5 6 This is a result (theorem) of metamathematics by Tarski and others; cf. 12. 342(2).

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12. 14 T o know e ve r ythi ng t ha t i s tr ue me a ns t o kn ow a ls o a ll the l ogic a l c onse que nc e s of tr ue pr oposi tio n s a c c or ding t o the pr inc ip le DO a nd DI ( r e c a ll c h. 1) . But sinc e the r e a r e a lot of supe r f luou s ir r e le va nt a nd r e dun da nt pr oposi tio ns a mon g t he c onse q ue nc e s o f tr ue pr op osi tio ns, i t me a ns to k now a lso a lot of s upe r f luou s, ir r e le va nt a n d r e dunda n t tr u ths. Bu t t his doe s no t se e m to be c ompa tib le w ith the pe r f e c t know le dge of G od. T he r e f or e G od c a nnot know e ve r ything t ha t is tr ue . 12. 15 T o ha ve a pe r f e c t a nd c ompr e he nsive k now le dge of e ve r ythi ng t ha t is tr ue , me a ns to kno w of the tr ue pr opo sit ions t ha t the y a r e tr ue a nd of the f a lse pr oposi tio ns tha t the y a r e f a lse ( no t t r ue ) . But t his me a ns to be a ble t o e f f e c tive ly list a l l tr ue pr opos iti ons ( t he or e ms) on the one ha nd, a nd to e f f e c tiv e ly li st a l l f a lse pr opo sit ions ( non - the or e m s) on the othe r ha n d in w hic h c a se both, the sy ste m of t he t r ue pr oposit ion s ( the or e ms) a nd t he syste m of the f a lse pr o pos iti ons ( no n - th e or e ms) , a r e r e c ur sive ly e nume r a ble . T his a ga in i mpl ie s tha t the sy ste m of a ll tr ue a nd a l l f a lse pr opo sit ion s is de c ida ble a nd r e c ur sive . Bu t it is know n by pr oof tha t t he sys te m of a l l tr ue a nd a ll f a lse pr oposit ion s is not de c ida b l e a nd not r e c ur sive . 1 5 7 T he r e f or e one c a nnot know of a ll tr ue pr oposi tio ns tha t the y a r e tr ue a nd of a ll f a lse pr opos it ions tha t t he y a r e f a lse . A nd thu s G od c a nno t kno w the m a l l a nd so he c a nnot be omnisc ie n t. 12. 2 A r gu m en ts P ro

E ve n if in the inf ini te se r ie s of numbe r s the r e is no highe st nu mbe r , f or w hom w hose know le dge is inf in ite , the inf in ite ne e d not be inc ompr e he ns ible . 12. 3 P rop os ed A nsw er

12. 31 I ntr oduc t ion T he se t the or e t ic a l pa r a doxe s sh ow tha t one ha s to be c a r e f ul w ith e xpr e ss ion s like 'e ve r ythin g', 'a ll' a nd mor e spe c if ic a lly w it h e xpr e ssion s like 'a ll se ts ', 'a ll tr uth s ', 'a ll pr e dic a te s', 'a ll f unc t ion s' … e tc . A s is w e ll - know n, suc h e xpr e ssion s – w he n use d unc r i tic a lly a nd unr e str ic te dly – le a d to c ontr a dic tio ns. T o a void s uc h c ontr a dic t ions, ma i nly thr e e me th ods ha ve be e n use d in se t the or y : to inc or p or a te a type the or y, to r e str ic t the a xio m of c ompr e he nsi on by the a xi om of se pa r a tion or f i na lly to d ist ing uish se ts ( w hic h c a n be me mbe r s) f r om c la s se s ( w hic h c a nnot be me mbe r s) . T he f ir st

1 5 7 This is a result (theorem) of metamathematics by Gödel and Church; cf. 12. 342(2).

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me thod w a s a pp lie d by Rus se ll a nd Q uine , the se c ond by Z e r me lo a nd Fr a e nke l, the thir d by von N e u ma nn, Be r na ys a nd G öde l. T he pr oble ms j ust me nti one d ha ve nothin g spe c if ic a lly t o do w it h omni sc ie nc e or G od 's kn ow le dge . T he y a lw a ys c o me up w he n e x pr e ssio ns like 'a ll se ts', 'a ll tr ut hs' a r e use d unc r it i c a lly or unr e str ic te d ly. T he r e f or e the y a r e r e la te d to o mn isc ie nc e or to G od' s k now le dge only to tha t e xte n t t o w h ic h ma n use s suc h e xpr e ssio ns unc r it ic a lly in the a pplic a tion to G o d or to H is know le dge . T he r e a r e , it se e ms, tw o w a ys to a vo id the a bo ve me nt ione d c ontr a dic tio ns w he n spe a kin g of G od's k now le dge or of omni sc ie nc e :

( 1) T o use suc h e x pr e ssi ons in one of the r e str ic te d w a y s a s is done in se t the or y or in a c onsiste nt t he or y of tr uth.

( 2) N ot t o use suc h e x pr e ssio ns w . r . t. que stio n 12, b ut to e nu me r a te the dif f e r e nt doma in s w hic h a r e c om pr e he nde d by G od's kn ow le dge .

I n this c ha p te r w e sha ll a pp ly t he se c ond po ssi bil ity. T h is doe s not me a n how e ve r tha t w e f ind w a y ( 1) ina ppli c a ble . Re c a ll how e ve r the pr oble ms disc us se d in se c ti on 11. 4 6 a bove . I n the a ppe ndix of my bo ok on e vi l 1 5 8 I ha ve use d ∀p( p ↔ gKp) a s a de f inie ns f or be ing o mnisc ie nt in t he se nse of ha ving both, soun d a nd c omple te know le dge , w hic h is r e pr e se nte d by ∀p ( gKp → p ) a nd ∀p( p → gKp) , w he r e the la t te r is a n a nsw e r to que s tio n 12. A n d the n it is show n the r e tha t the r e a r e c ons ist e n t ( a xioma tic ) the or ie s w hic h ha ve the f ollow ing the si s a mo ng t he ir the or e m s: G od e xis ts, G o d is om nisc ie n t, G od is omni pote n t, G od is nor ma t ive a nd vo lit ive c onsis te nt, w ha te ve r G od w ill s or c a use s is goo d, w ha te ve r G od c a n w il l o r c a n c a use is go od, t he r e a r e e vils of dif f e r e nt kinds, i nc lud ing mor a l e vil s. O ne c ould a lso s ta r t w it h the c onjunc t ion ∀p[ ( gKp → p ) ∧ ( gKp ∨ gK¬p) ] us ing i t a s a de f inie ns f or omni sc ie nc e . Fr om th is one c a n de r i ve ∀p( p → g Kp) . O n t he othe r ha nd w a y ( 2) by de sc r ib ing the mo st i mp or ta nt d oma in s of G od' s kn ow le dge , ne e ds to obse r ve the c r itic a l r e str ic tion s a lso w . r . t. the tr uths of e a c h doma in. But w a y ( 2) is m or e inf or ma tive t ha n w a y ( 1) in the se nse tha t it inc or por a te s the dif f e r e nt doma in s a nd give s so me de ta ils a bout the m. I n ge ne r a l, pa r a doxe s of se t the or y or of the the or y of tr uth ( f or e xa mple L ia r pa r a doxe s 1 5 9 ) only s how t ha t our w a y of e xpr e ssing some mor e c omp lic a te d pr oposi tio ns ( like tho se in vol ving se lf r e f e r e nc e ) is insuf f ic ie nt or ma ke s f a lse hidde n a ssu mpt ions or d oe s n ot m a ke e xplic i t so me c or r e c t h idde n pr e suppos iti ons. T ha t is, t he dif f ic ul ti e s a r e on the side of o ur i mpe r f e c t

1 5 8 Weingartner (2003, Evil), p. 137. 1 5 9 Cf. ch. 1 for a specific case. For a simple solution of different kinds of Liar paradoxes cf. Weingartner (2000, BQT), ch. 7. cf. Plantinga/Grim (1993, TOC)

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know le dge a nd t he r e is not e no ugh r e a son to bla me r e a lity f or it, m uc h le ss t o bla me G od. I f G od is inf inite , the n it is not a stoni shi ng t ha t e ve n ma ny de sc r iptio ns f r om ma ny d if f e r e nt poin ts of vie w w il l gi ve – if c or r e c t – only a tiny a nd ve r y pa r tia l pic t ur e of H im via a na logy.

12.32 God's knowledge about himself T he r e a r e thr e e c ompr e he nsive do ma ins of G od' s know le dge : G od's know le dge a bout H i mse lf , G od' s k no w le dge a bou t h is c r e a tion a n d G o d's know le dge a bou t L o gic a nd Ma the m a tic s. T he la tte r d oma i n d oe s n ot ne c e ssa r ily se e m t o be inc lu de d in th e tw o f or me r do ma i n s. W e c a n sa y, the r e f or e , G od is omni sc ie nt if f he kno w s a ll the tr ut hs a bou t H im se lf , a bout c r e a tion a nd a bout logic a nd ma the ma t ic s. G od's k now le d ge a bout H im se lf c a n be c onsi de r e d unde r tw o a spe c ts: f i r st ( 1) , in sof a r a s it is a b out hi mse lf inde pe nde nt ly of his r e la tio n to c r e a tion, se c ond ( 2) , insof a r it is know le dge a bout h is r e la t ion to c r e a tio n. A nd the la tte r ma y be sub div ide d a ga i n in to tw o subdo ma in s: ( 2a ) I nto hi s kno w le d ge a bout h is r e la t ion to c r e a tion inde pe nde nt ly of t his pa r t ic ula r c r e a tion he ha s be e n doin g; a nd t o th is pe r ta ins h is know le dge a bou t h is omn ip ote nc e . ( 2b) I nto his kno w le dge a bo ut his r e la tio n to th is pa r tic u la r c r e a tion; a nd to this subd oma i n be long s his know le dge a bo ut h is be ing t he f ir st c a u se , a nd f ur the r a bout h is l ove , j us tic e , me r c y, pr ovide nc e , c onse r va tion a nd gove r nme nt w . r . t. his c r e a tion. ad (1) Co nc e r ning G od's kno w le dge a bout h im se lf , inde pe nde n tly of h is r e la tion to c r e a tio n, w e ha ve to sa y t ha t it is ne c e ssa r y in tw o w a ys: F ir st, in the se nse t ha t w ha te ve r he know s a bou t hi mse lf , he ne c e ssa r il y kno w s, a nd se c ond in the se nse tha t w ha te ve r he know s a bout hi mse lf i s some t hing w h ic h is ne c e ssa r ily the c a se . U nde r the a ssump tio n t ha t to spe a k a bou t G od ( inde pe nde nt ly of hi s r e la tio n to c r e a tio n) me a ns the sa me a s to spe a k a bo ut his e s se nc e , w e ma y f or mula te w ha t h a s be e n sa id a bove i n t he f ol low in g w a y: I f p be lo ngs to the the or e m s ( tr u e pr opos iti ons) a b out G od 's e s se nc e , the n both : G od ne c e ssa r ily k now s t ha t p a nd G od know s t ha t ne c e ssa r ily - p. Sy mbol ic a lly : ∀p [ pεTg's E sse nc e → ( l gKp ∧ gKl p ) ] 1 6 0 1 6 0 As was pointed out alrea dy in ch. 7. 43, to use propositio ns in such formulation s does not mean that God' s thinking or knowing uses propositions. We cannot assume of him that he has to split up subj ect and predica te and to affirm a property of an in dividual or such similar things which are basic for hum an knowled ge. But we humans can only say something true about God by forming propositions.

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W e do no t a ss ume the o ppos ite imp lic a tion to be va li d, too. For e xa mple a sim ple log ic a l ta utol ogy li ke p → p or a pr op osi tio n of the mul tip lic a tio n ta ble a r e suc h tha t both l gKp a nd gKl p w ill ho ld. Bu t to sa y tha t the se pr oposi tio ns a r e the or e m s a bout G od' s e sse nc e w oul d a mou nt t o a ve r y spe c ia l vie w a bout L og ic a nd Ma the ma t ic s w hic h w e do not pr e sup pose he r e . A ll the or e m s a bou t G o d's e sse nc e G o d not on ly know s w i th ne c e ssit y, but a lso w i th pe r f e c tion, i. e . in a mos t p e r f e c t w a y. W ha t it me a ns t o kn ow some t hing in a pe r f e c t w a y w e ma y u nde r sta nd i n a n a na lo gous w a y w i th r e spe c t to our ( huma n) know le d ge : A mong t he pr oposi ti o ns w hic h a r e in pr inc iple pr o va ble ( de mo nstr a b le ) those a r e most pe r f e c tly kn ow n to us ( f or e xa mple to a ma the ma t ic ia n) w hic h ha ve be e n in f a c t pr ove d – c om pa r e d to those w hic h c o uld not be pr o ve d so f a r suc h tha t on ly pr oba ble r e a son s w e r e give n. N ow a lt houg h G od doe s not ne e d to ma ke a pr oof in or de r to know pe r f e c tly, – his know le dge is not kn ow le dge w ith the he lp of pr oof s a nyw a y – he ne ve r the le ss know s him se lf in the m ost pe r f e c t w a y. A nd simi la r ly to w ha t ha s be e n sa id a bove a bout ne c e ssity, it holds f or pe r f e c tion: I f p be longs t o the the or e m s ( tr ue pr o posi tio ns) a bo ut G od's e s se nc e , the n bo th: G od mo st pe r f e c tly know s t ha t p a nd G o d kno w s tha t w ha t he kn ow s i s mo st pe r f e c t. Mor e ove r , w e ma y a dd tha t e ve r y thin g w ha t i s tr ue a bout G od 's e sse nc e , G od k now s a lso i n a most c omp le te w a y. Aga in, to unde r sta nd w ha t it me a ns to know s ome t hing in a c o mple te w a y, w e ma y use a n a na l ogy w . r . t. hu ma n know le dge . A n a xiom s yste m or a the or y ( c onsist ing of la w s + init ia l c ondit ions) a bo ut a do ma in D i s c omp le te if f a ll tr ue pr opo sit ions a b out D a r e de r iva ble f r om the a xio m sy ste m or the o r y. T hus to ha ve c omp le te kno w le dge a bout D me a ns to k now the c om ple te a x iom sys te m or the or y plu s a ll the tr ue pr oposi tio ns a bo ut D w hic h a r e de r iva bl e f r om it ; bu t s inc e the y inc lu de a lso the a xiom s or the la w s ( + in itia l c o ndi ti ons) of the t he or y w e ma y j ust sa y it me a ns t o kn ow a l l tr ue pr opo sit ions a bout the do ma in D . T hu s G o d ha s c omple te k now le d ge a bout his e s se nc e me a ns tha t he know s a ll the tr ue pr oposi tio ns a bout h is e sse nc e . 1 6 1 ad (2a) I f G od ne c e ssa r ily pe r f e c tly a nd c omple te l y know s hi mse lf ( viz h is e sse nc e ) , it f ollow s tha t he mu st a l so ne c e ssa r ily a nd pe r f e c tly a nd c o mp le te ly know hi s pow e r a nd tha t me a ns a lso to know to w ha t his pow e r e xte nds. 1 6 2 N ow hi s pow e r e xte nd s f ir s t of a ll to t h e w hole c r e a tion, i. e . to th is pa r t ic ula r unive r se a nd t o a ll othe r sp ir itua l c r e a tur e s. But it e xte n ds f ur t he r to the 1 6 1 Concerning irrelevant and re dundant con seq uences of true propositions see ch. 7. 42 and the answer 12. 44 to objection 12. 14 below. 1 6 2 Cf. the argument in Thomas Aquinas (ST h) I, 14, 5.

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possi ble c r e a tion, to c r e a tur e s he doe s not c r e a te ( c a use ) , but c a n c r ea te ( c a use ) . A cc or ding to T h oma s A q ui na s, the lim it f or th is do ma in of possi bil it ie s is on ly lo gic a l inc on sis t e nc y. 1 6 3 But T ho ma s A qu ina s ha s c e r ta inly in mind tha t to c r e a te ( c a use ) some th ing i nc onsi ste nt w ith his e sse nc e or w ith hi s goo dne ss or w ith h i s c omma n dme n ts, w oul d be a logic a l inc ons iste nc y f or G od. ad (2b) C onc e r ning his pa r tic ula r c r e a ti on, he ne c e ssa r ily kn ow s h is be ing t he f ir st c a use , his love , jus tic e , me r c y, pr ovide nc e , c onse r va tion a nd gove r nme nt. H ow e ve r , it ha s to be obse r ve d tha t the c r e a tion is n ot a ne c e ssa r y outc ome of his e sse nc e , bu t a f r e e de c ision a nd the r e f or e the ne c e ssity doe s not r e f e r to h is a c tion of c r e a tion. A l thou gh he ne c e ssa r ily know s tha t he i s a c ting a s a c r e a tor , it doe s no t f ol low f r om tha t t ha t he ne c e ssa r ily is a c ting a s a c r e a tor .

12.33 God's knowledge about his creation G od's know le dge a bout hi s c r e a tion c a n be divi de d in to tw o do ma in s: i nto his know le dge a bou t the unive r se a nd into his know le dge a bout othe r c r e a tur e s, e spe c ia lly spir itua l c r e a tur e s, like the a nge ls. A c c or ding to c ha pte r 2. w e ha ve to sa y tha t w ha te ve r G od know s, he n e c e ssa r ily kno w s. T he r e f or e it mus t hold: W ha te ve r G od kn ow s a bout t he unive r se , he ne c e ssa r ily know s. A ga in f r om this i t doe s not f oll ow tha t w ha t h a ppe ns in the u nive r se , ha ppe ns w ith ne c e ssity. S inc e so me e ve nts a r e gov e r ne d by dyna m ic a l la w s a nd t he se ha ppe n by a c e r ta in kind of c onditio n a l ne c e ssity a nd the la w s of na tur e the mse l ve s ho ld a lso w it h a c e r ta in ki nd of ( na tur a l) ne c e ssi ty. Bu t ot he r e ve nts ha ppe n in mos t c a se s a c c or ding to sta ti stic a l la w s a nd the se ha ppe n w ith a w e a ke r k ind of ne c e ssit y. S til l o t he r e ve nts ha ppe n r a the r a c c ide nta lly a nd sti ll othe r s a c c or din g to f r e e w i ll de c ision ; bo th of the se e ve nts do n ot oc c ur ne c e ssa r ily ( r e c a ll c h. 10 f or de t a ils) . T o put i t in o the r w or ds, w e ma y sa y tha t G od ha s c hose n ne c e ssa r y la w s a nd ne c e ssa r y c a use s f or some e ve nts in the unive r se a nd sta t is tic a l la w s a nd c a use s w it h w e a ke r ne c e ssit y f or ot he r e ve nts a nd stil l othe r c a use s like c onsid e r a tion a nd ba la nc i ng mot ive s f or f r e e w ill de c isi ons … e tc . A na lo gous ly w e c a n sa y a ls o c onc e r nin g the othe r c r e a tur e s tha t e ve r yth ing G od kno w s a b out the m ( w ho a r e a l so h is c r e a tur e s) he ne c e ssa r ily kno w s a bou t the m. A lt hough not e ve r yt hing w ha t ha ppe n s a mong the m ha ppe n s n e c e ssa r i ly; o nly some e ve nts c onc e r ning the se 1 6 3 Cf. Thomas Aquinas (STh) I, 25, 3; "Whatever implies a contradiction does not come within the scope of divine omnipotence. "

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c r e a tur e s w ill ha ppe n ne c e ssa r ily, but othe r s w i ll n ot ha ppe n ne c e ssa r ily. A c c or dingly, w e ma y f ir st sa y tha t G od's know le dge a bou t h is c r e a tion e nc ompa sse s the kn ow le dge of a ll the l a w s c onc e r ning our unive r se a nd the othe r c r e a tion, it e nc ompa s se s f ur the r t he know le dge of a ll the la w gove r ne d sta te s a nd e ve nts inc l udin g ini tia l a nd r a ndom c ond iti ons a nd the know le dge of the c onsta nts of na tur e . So me ha ve sa i d t ha t G o d's know le d ge a bout his c r e a tur e s is la w - li ke know le dge suc h tha t G od c a nnot kn ow si ngu la r e ve nts w hic h a r e not ha ppe ning a c c or din g to la w s or he c oul d not k now in div idua l s a s ind ivi dua ls. But th is w ou ld me a n tha t G od ha s only impe r f e c t k now le dge a bout his ow n c r e a tur e s w hic h is r a the r a bsur d. A nd in c ha pte r 7 it w a s a lr e a dy de f e nde d in de ta il tha t G od k now s a lso si ngula r tr ut hs. T he r e f or e w e ha ve to sa y tha t G od ne c e ssa r ily kn ow s a ll e ve n ts of th is unive r se a nd a ll e ve n ts of h is o the r c r e a tur e s be the y r ule d by la w s or not. G od's kn ow le dge a bout the un ive r se inc lude s a lso h is know le dge a bout ma nkin d a nd a bo ut e a c h in divi dua l h u ma n pe r son. A n d th is me a ns t ha t G od ne c e ssa r ily know s a ll pa s t a nd pr e se nt e ve nts inc ludi ng the r e spe c ti ve huma n a c tions ( w he r e 'pa st' a nd 'pr e se nt' r e f e r to the time of the e a r th) ; this w a s show n in ge ne r a l a lr e a dy in c ha pte r 4. But G od ma y know a lso f utur e sta te s of a f f a ir s inc l udi ng f r e e de c is ions of ma n. W ith r e spe c t to both pa s t ( pr e se nt) a nd f utur e hu ma n a c tion s it is i mpor ta nt to r e a li se tha t G o d kno w s a ll the c a pa bilit ie s a nd a bi lit ie s of e ve r y pa r tic ula r huma n pe r son. T he kn ow le dge of c ontinge n t f ut ur e sta te s of a f f a ir s is a ki nd of kn ow le dge w hic h is s pe c if ic a lly posse s se d by G od. Sinc e to pr e dic t the f utur e w ith the he lp of dyna m ic a l or sta tis tic a l la w s i s a ls o a n a b ili ty of m a n. A nd w e c ou ld i ma gi ne tha t th is a bilit y ma y be posse s se d in a sti ll muc h mor e pe r f e c t w a y by spir itua l c r e a tur e s like a nge ls. But t o know f u tur e f r e e de c isions of in div idua l pe r so ns, is s ome th ing w hic h be lon gs to G o d a l one . O the r w ise h is know le dge w ou ld not c om ple te ly sur pa ss the kno w le dge of ma n a nd sp ir it ua l c r e a tur e s. H ow this i s poss ible w a s show n in mor e de ta il in c ha pte r 11 a bove . T hus w e ha ve to sa y tha t G od ne c e ssa r il y know s a ll tr u ths a bou t his c r e a tur e s.

12.34 God's knowledge about Logic and Mathematics I t is w e ll - know n tha t hu ma n know le d ge a bout logic s a nd ma the ma t ic s is lim ite d. Spe c ia l l im ita t ion s a r e e xpr e sse d by the so - c a lle d li mi ta tive the or e m s in the f ounda t ions of lo gic s a nd ma the ma tic s. O n the a ssu mpt ion tha t G o d is the c r e a tor of the unive r se inc lu din g ma n a nd c onse que nt ly a ls o the c r e a tor of

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the hu ma n mi nd a nd br a in, w e ha ve t o sa y tha t G o d's know le dge supe r se de s e sse ntia l ly – not on ly gr a dua ll y – huma n know le dge . A nd th is w il l hol d not only f or kno w le dge in ge ne r a l, but s p e c if ic a lly a lso f or know le dge a bout logic s a nd ma the ma t ic s. T he r e f or e G od's know le dge a bou t l ogic s a nd ma the ma t ic s – if it is l im ite d a t a ll – c a nnot be l im ite d i n the sa me w a y a s huma n kno w le dge a bout l ogic s a nd ma t he ma tic s.

12. 341 L e ibn iz 's ide a of huma n kno w le d ge c onc e r ning L ogic a nd Ma the ma t ic s L e ibniz th oug h t tha t hu ma n kn ow le dge is not l im ite d in the w a y w hic h w a s disc ove r e d onl y in the la s t c e ntur y. H is vie w w a s tha t c onc e r nin g the so -c a lle d ( by hi m) veritees de raison ( tr ut hs of r e a son) ma n c a n ( in pr inc ip le ) build up sc ie nt if ic sys te ms w hic h h a ve the f ol low in g thr e e pr ope r tie s be low . 1 6 4 T he tw o hu ge do ma ins of sc ie n c e w hic h c ons ist only of tr u ths of r e a son a r e logic s a nd ma the ma t ic s on t he one ha nd a nd me ta phys ic s on the othe r . T he thr e e pr ope r tie s a r e :

( 1) A ge ne r a l c onc e ptua l f r a me w or k w hic h c onta ins a ll the i mpor ta n t ba sic te r ms ( ba s ic c onc e pts) a n d a ll the de r ive d te r m s ( de r ive d c o nc e pts) w hic h a r e built up f r o m the ba sic te r ms by de f in iti ons. T he ge ne r a l c onc e ptua l f r a me w or k is c a lle d characteristica unive rsalis . I n f a c t L e ibniz th ough t the characteristica universalis c a n be ma de sti ll mor e pr e c ise by ma the ma t isi ng i t: A sc ie n ti f ic te r m ( c onc e pt) c a n be f ir st a na lyse d a s be i ng e i the r ba sic ( pr i mi tiv e ) or e lse be ing r e duc i ble t o a ba sic ( pr imit ive ) te r m w ith the he lp of a c ha in of de f inition s. T he ma the ma t isa t ion the n pr oc e e ds in t w o ste p s: Fir s t e ve r y ba s ic ( pr imi tive ) te r m c a n be r e pr e se nte d by a c ha r a c te r istic ba sic numbe r ( or by a c ha r a c te r istic pa ir of ba sic num be r s) . Se c ondly e ve r y c omp oun d te r m c a n be r e pr e se nte d by a c ha r ac te ristic nu mbe r w hic h is e qua l t o the r e sult of a ppl ying a c e r ta in ma t he ma tic a l f unc tio n to nu mbe r s ( pa ir s of numbe r s) w hic h r e pr e se nt pr im iti ve te r ms.

( 2) T he sc ie nt if ic sy ste m s of tr ut hs of r e a son ( i. e . L ogic s, Ma the ma t ic s a n d Me ta phys ic s) c a n be bu ilt up more geometrico , tha t is a s a xi om syste ms. E ve r y tr ut h of the se sy ste ms is f ini te ly a na lyt ic in the f ollow ing se nse : e ve r y tr uth c a n be tr a c e d ba c k in a f inite numbe r of ste ps ( in w hic h a l so de f in iti ons ma y be invol ve d) to t he a xio ms. A nd the a xio ms the m se lve s a r e f in ite i n nu mbe r . I n mo de r n te r m s L e ib niz w ould ha ve to sa y tha t a ll the se s yst e ms a r e f inite l y a xio ma ti sa ble

1 6 4 For details cf. Rescher (1979, LIP) and Weingartner (1983, IMS).

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( w hic h is not c or r e c t, se e be low ) : T his, how e ve r , doe s not hold f or the sc ie ntif ic sys te ms of phy sic s or of th a t of jur ispr ude nc e a nd e t hic s. Sinc e he r e c ontin ge nt pr e mi se s e nte r , the sys te ms a r e not f in ite ly a na lytic ( f ini te ly a x ioma tisa b le ) f or m a n. O nly G od know s the tr ue a xiom s.

( 3) T he sc ie ntif ic sys te m of tr ut hs of r e a son ( i. e . ) L ogic s, Ma the ma tic s a n d Me ta phys ic s, w he n b uil t up more geometrico, i. e . a s a xio m sy ste m s, ha ve the f ur the r pr ope r tie s of be ing c ons iste nt a nd c o mple te . T he f ir st i s imp lie d by L e ibn iz 's pr i nc iple : A ll f i n ite ly a na ly tic pr op osi tio ns a r e ne c e ssa r ily tr ue . A s ha s be e n sa id a bove, a f inite ly a na lyt ic pr oposi tio n is one t ha t c a n be tr a c e d ba c k to or de r ive d f r om t he a xio ms i n a f ini te numbe r of ste p s. T h is pr inc ip le is the r e f or e a soun dne ss pr inc i ple f or a n a xioma t ic sys te m. T he se c ond pr ope r ty, the c omp le te ne ss of the a xio m syste m i s i mpl ie d b y L e ib niz 's pr inc i ple of s uf f ic ie nt r e a son w hic h r e a ds in it s l ogic a l f or m: E ve r y tr ut h ha s it s pr oof ( f r o m the a x iom s + de f in it ions) . 1 6 5 T ha t me a ns t ha t L e i bniz c la ime d f or the d oma i ns o f logic , ma the ma tic s a nd me ta p hysic s c omple te ne ss in the f ol low i ng se nse : E ve r y tr uth in the do ma in of logic ( in t he do ma in of ma the ma t ic s, in the d oma i n of me ta p hysic s) i s de r iva ble f r om the a xiom s of the sy ste m of logic ( ma the ma tic s, me ta phy sic s) i n a f in ite numbe r of ste ps. Fur t he r the r e spe c tive a xioms c a n be f ound in pr inc iple by ma n f or t he se do ma in s of t r uths of r e a son. L e ibniz did no t c la im c o mple te ne s s f or the d oma i n of ph ysic s, n or f or tha t of jur ispr u de nc e a nd e th ic s. I n the se do m a ins on ly G od k now s the r i ght a xiom s, w he r e a s f or huma ns ma n y tr ut h s in the se d oma i ns a r e inf ini te ly a na lytic f or w h ic h a n inf ini te nu mbe r of ste ps w ould be ne c e ssa r y suc h tha t ma n i s no t a ble in pr inc ip le to tr a c e ba c k ( or de r ive ) t he r e spe c tive tr uth to ( f r om) the a xio ms.

W he the r L e ibniz thou ght tha t t he sc ie ntif ic ( a xio ma tic ) syste ms of log ic , ma the ma t ic s a nd me ta ph ysic s a r e a lso d e c ida ble , is not a n e a sy que sti on. O n a c lose r look how e ve r it se e ms tha t he c la ime d de c ida b ili ty o nly f or pa r t s. T hus he f ound hi mse lf a ma the ma tic a l de c is ion pr oc e dur e f or syl log ist ic s. 1 6 6 H e se e ms to ha ve hope d to e xte nd suc h a de c ision me t hod to o the r doma in s of logic a nd to pa r ts of ma t he ma tic s, but h e did n ot r e a ll y c la i m de c ida b ili ty of the f ull doma ins.

1 6 5 Leibniz (GP) 2, p. 62. 1 6 6 Leibniz (OF), p. 77 - 8 4. Cf. Wei ngartner (19 8 3, IMS), p. 175 and M arshall (197 7, LLA).

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I f w e now a sk the que s tio n w h ic h of t h e f e a tur e s of L ogic a nd Ma t he ma tic s pointe d o ut by L e i bniz c ould illu mina te our vie w c onc e r nin g G od' s know le dge of L og ic a nd Ma the ma tic s, w e ma y give the f ollow i ng a n sw e r : Conc e r nin g the ge ne r a l c onc e ptua l f r a me w or k, G od w ill of c our se know w ha t the c or r e c t ( e xplic it) de f in iti ons of a l l t he dif f e r e nt logic a l a nd ma the ma tic a l c onc e pts a nd str uc tur e s a r e , but w e c a nnot the r e f or e a ssume ( i. e . it doe s not f ollow f r o m t ha t) tha t G od thi nks in de f init ion s ( a s w e kn ow the m) or t ha t he ne e ds de f init ions a nd s pli tti ng up de f inie ndu m a nd de f in ie ns in or de r to think. 1 6 7 Conc e r nin g a xio ma tisa b il ity t he c om me nt is sim ila r : A ltho ugh G o d w i ll kn ow the a xiom s of tho se syste ms of l ogic a nd ma the ma tic s w h ic h a r e a xioma t isa ble e ve n if the se w e r e inf in it e ly ma ny a x io m sc he ma ta ; but f r o m this it doe s n ot f ol low t ha t G od' s kn ow le dge of the tr u ths of l ogic a nd ma the ma t ic s c ons ist s of know ing a x iom syste ms, de r iva tio n r ule s a nd de r i ve d the or e ms . H e w i ll k now the se tr u ths in one a c tion of know ing a n d no t a f te r one a nothe r , if he is outs ide ti me a s w a s de f e nde d in c h. 3. A lso c onc e r ning c onsis te nc y a nd c omple te ne ss w e ha ve to sa y tha t G od w i ll kn ow the c onsis te nc y of t hose s yste ms w hic h a r e in f a c t c ons iste n t, e ve n if ma n c a nnot pr ove this w ith the he lp of t he r e spe c tive syste m – a c c or ding to the li mita tion s pr ove d by G öde l's se c on d inc o mple te ne ss the or e m – a n d ma y no t be a ble to pr ove it a t a ll. Si mi la r ly, G od w il l kn ow w hic h sys te ms a r e c omple te a nd w hic h a r e not, e ve n if ma n w ill not f ind out this f or a ll pos sib le syste m s. But w e mus t n ot a s su me tha t G od kn ow s th is b y ma king the usua l c ons iste nc y – or c omple te ne s s pr oof s. H e doe s not ne e d t o ma ke pr oof s ( á la ma the ma t ic ia ns or l ogic ia n s) in or de r t o know ; w hic h i s sup por te d by be ing outs ide time a nd by th ink ing pur e ly a c tu a lly a nd not in a disc ur s ive w a y.

12. 342 T he li mita t ion s disc ove r e d in the 20 t h c e ntur y. W e sha ll disc us s the s e li mita t ions i n thr e e ste ps sim ila r to tho se of L e ibniz .

1 6 7 The definitions which are at stake here a re not those which are arbitra rily introduced into a conte xt like definitions as co nvenient abbreviati ons (for example DNA), but those which are tr ue statements describi ng the essential features o f the con cept or structure in question, like the definition of circle. That the important and interesting definitions in the sciences ar e true or false can be substantiated with a nu mber of reasons. Cf. for definitions in mathematics: Kreisel (1981, BMD). For definitions in general : Weingartner (1989, DRV) and (20 00, BQT) ch . 5 (Are definitions true or false?). See also 12. 342(1) below.

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(1) T he r e a r e limi ta ti ons to a mo st unive r sa l c o nc e ptua l f r a me w or k a s L e ibniz 's characteristica universalis . I mpor ta n t e xa mple s a r e the f ollow in g one s: ( a ) T a r s ki disc ove r e d tha t the c onc e pt of tr uth ( or the tr uth pr e dic a te ) w he n

a pplie d t o a ( suf f ic ie nt ly r ic h) f or ma l ise d sys te m of se n te nc e s of la ngua ge le ve l n is not de f ina b le in n, b ut in l a ngua ge le ve l n +1 ( me ta la ng ua ge inc lud ing la ng ua ge n) . W e ha ve to a dd: pr ovide d tha t the unde r ly ing lo gic is tw o - va l ue d c la ssic a l pr e dic a te log ic w ith ide n ti ty ( PL 1=) . 1 6 8 O r in othe r w or ds: T he not ion of tr uth ( the se t of a ll tr ue se nte nc e s) of a c onsiste nt f or ma lise d s yste m c onta i ning r e c ur si ve numbe r the or y is no t de f ina b le i n this sy ste m.

( b) N ot e ve r y c onc e pt or se nte nc e ca n be a r bitr a r ily e xpr e sse d or r e pr e se nte d. For e xa mple if the a xio m syste m of Z F se t the or y is c o nsi ste nt, it c a n be pr ove d t ha t t he r e is a se nte nc e of se t t he or y w hic h i s no t a r it hme t ic a lly e xpr e ssible . 1 6 9 A f ur the r r e la te d the ore m is T a r ski's U n de f ina bil it y T he or e m. 1 7 0

( c ) E ve n ve r y pre c ise e quiva le nc e - tr a nsf or ma tion s or c oding sy ste m s a r e not c omple te l y uniq ue . For e xa mp le , one c a n show tha t if tw o la ngua ge s S1 a nd S2 a r e logic a l ly e quiva le nt, t he usua l de f ini tion of ve r is i mil itu de ( a nd othe r de f in it ions) a r e not inva r ia n t w . r . t. to a tr a nsf or ma tion f r om S1 to S2 ; suc h tha t i n S1 A > B ( A is ne a r e r to the tr uth t ha n B) hol ds w h e r e a s in S2 A < B holds. 1 7 1 A nothe r e xa mple is the f a c t tha t e ve n so pr e c ise c oding syste ms li ke G öde l numbe r s a r e no t c o mple te l y un ique : F or ins ta nc e one c a n show tha t the e xiste nc e of ungr ounde d a n d pa r a doxic a l se nte nc e s ( in the se nse of K r ipke ) is no t in va r ia nt a ga i nst the ki nd of G öde l num be r ing w hic h is c hose n if inste a d of the str ong 3 - va l ue d logic of K le e ne the w e a k 3 - va lue d logic of K le e ne is ta ke n. 1 7 2

1 6 8 Cf. Tarski (1935, WBF). It is know n that by d eviating from PL1=, for i nstance b y dropping negation (Myhill, 1950, S DT) or by introducing truth value gap s (Kripke, 197 5, OTT) or by constructing a logic with independ ent quantifiers, which is weaker than PL1= (Hintikka, 1996, PMR) the truth predicate is definable in the object language. 1 6 9 A sentence of set theory is arithmetically expressible iff it is demonstrably equivalent (within set theory under ZF) to some sentence of elementary arithmetic. 1 7 0 Cf. Fraenkel et al. (1973, FST), p. 312. 1 7 1 Cf. Schurz (1990, SAE). For ano th er example cf. Weingartner (2000, BQT), p. 178 (where it should read in line 7 from below: ( p ∧ ¬ q )* < ( ¬p ∧ ¬q)*). 1 7 2 Cf. Cain, Damnjanovic (1991, WKS). Cf. also Weingartner (1997, LCD). These and related pro blems were observed by Kre i sel much earli er. C f. Kreisel (1 953, PHk), Kreisel, Takeuti (1974, FSR).

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A f te r givin g the se e xa m ple s f or l im its t o a mo st u nive r sa l c onc e pt ua l f r a me w or k w e ma y a sk w he the r G od' s know le dge c o uld be s ubje c t to suc h lim ita t ions. Fir s t of a ll, if G od i s the c r e a tor of the w or l d inc l udin g ma n, t he n he w ill k now the l im its of the hu ma n mind c o nc e r ning un ive r sa l c onc e ptua l f r a me w or ks. Se c ondl y, he w ill know t ha t a nd how ma n ne e ds c onc e ptua l f r a me w or ks to thin k a nd e spe c ia l ly t o s olve m or e c ompl ic a te d pr oble ms. But f r om a ll thi s it doe s n ot f ol low tha t G od hi mse lf is bo und t o c onc e ptua l f r a me w or ks or c oding sy ste m s in or de r to t hink. U si ng c onc e ptua l f r a me w or ks or c o din g s yste ms im plie s t ha t suc h a t hin king i s d isc ur si ve , i. e . invol ve s suc c e ssi on; sinc e the c onc e ptu a l f r a me w or k or the c oding sys te m i s f ir st u nde r sto od a nd c ons tr uc te d a nd the n u se d f or the pr oof . Bu t G o d's know le d ge is no t di sc ur si ve a nd doe s not i nvol ve suc c e ssio n. 1 7 3 T he r e f or e G od's t hin king d oe s no t ne e d or use c onc e ptua l f r a me w or ks or c odin g syste ms. A f ur the r suppor t f or this i s th a t disc ur si ve a nd suc c e ssive th inki ng ne e ds ti me . But if G od i s ou tsi de ti me , the n the r e c a nnot be di sc ur sio n or suc c e ssion in h is a c tion s. Conc e r nin g the spe c if ic l im ita ti ons a bo ve it c a n be sa id: A l tho ugh G o d w il l know T a r ski 's r e sul t ( like he w il l kno w a ny othe r c or r e c t r e sult pr ove d by ma n) , his kn ow le dge is no t b ound to the spe c if i c l im ita t ion si nc e he c a n c ompr e he nd a r bi tr a r ily ma ny la n gua ge le ve ls e ve n a n inf i nite n um be r of the m. T ha t e ve r y s yste m of la ngua ge ( b e it na tur a l or sc ie nt if ic ) ha s it s l im its of e xpr e ssibi lit y me a ns a r e str ic t ion f or huma ns in so f a r a s the y ha ve to use syste ms of sign s ( of la ngua ge s) in or de r to think in a pr e c ise w a y. But w e c a nnot a ssu me of a mo st pe r f e c t be in g tha t he w o uld ne e d suc h sc ie n tif ic la ngua ge sys te ms, li ke tha t of a r ith me ti c or se t the or y, in or de r to thin k mor e pr e c ise ly. T he f ir st e xa mp le in ( c ) just s how s th a t logic a l e qu iva le nc e is no t a ve r y str ong no tio n if the usua l Fir st O r de r P r e dic a te L ogic w ith ide n tit y is use d. T he se c ond show s t ha t e ve n G öde l nu m be r s a r e not c o mp le te ly uni que w he n a pplie d to c e r ta in d oma in s. Bu t w hy shoul d thi s be a pr oble m f or the know le dge of a most pe r f e c t be ing w h o doe s not ne e d to use e ithe r logic a l e quiva le nc e s or some c odin g syste m in or de r to know a nd to c ompr e he nd. (2) T he r e ar e limita tio ns c onc e r ning a xi om sys te ms. ( a ) Fir st of a l l t he sys te m of Cla s sic a l tw o - va l ue d Pr o pos iti ona l L o gic i s

a xioma t isa ble , de c ida b le a nd c o mp le te . Fir s t O r de r Pr e dic a te L o gic i s a xioma t isa ble a nd c o mp le te , but n ot d e c ida ble . A lso N e u ma nn - Be r na y' s

1 7 3 Cf. Thomas Aquinas (STh) I, 14, 7: "In the divine knowledge there is no discursion. "

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a nd G öde l's se t the or y a r e f inite ly a xio ma tisa b le , but Z e r me lo Fr a e nke l se t the or y Z F is n ot.

( b) T he tr ue se nte nc e s ( w ff s) of e le me nta r y a r ithme tic ( Pe a no A r ith me tic ) a r e not a xi oma t isa ble ( a nd n ot de c ida b le ) . Z e r me lo - Fa e nke l ( Z F) se t the or y a nd N e uma nn - Be r na ys ( N B) a nd G öde l ( G ) se t the or ie s a r e a ll e sse ntia lly unde c ida ble ; i. e . the y a r e unde c ida ble a nd e ve r y c onsiste n t e xte nsi on of the m is a ls o unde c ida ble . 1 7 4

( c ) N o a xio ma tisa t ion of ma the ma t ic s c a n e xa c tly c a ptur e a l l tr ue sta te me nts of ma the ma tic s, sinc e i t c a nno t e ve n c a ptur e a ll tr ue s ta te me n ts of e le me nta r y a r ithme t ic . Mor e ge ne r a lly : N o a xio ma ti sa ti on c a n c a ptur e a ll sta te me nts w h ic h a r e tr ue ; i. e . the se t of tr ue se nte nc e s is no t a xioma t isa ble a nd t he r e f or e a lso not r e c ur s ive ly e nu me r a ble . W e ma y a sk now the q ue sti on i n w ha t s e nse G od mus t be f r e e f r om the se a nd simi la r lim ita t ions c onc e r nin g a xio ma tisa b lit iy a nd de c ida bl ity : ( i) E ve n if the syste m is a xio ma ti sa ble a nd ma y be de c ida ble ma n

know s a nd c om pr e he nds ( to so me e xte nt ) the a xioms a nd se ve r a l the or e ms. Bu t he is not a ble to c o mpr e he nd a ll the the or e ms s inc e the y a r e inf ini te in nu mbe r ; a lt houg h a ny spe c if ic the or e m ( if t he syste m is de c ida ble , the n a lso a ny sp e c if ic non - the or e m) c a n be me c ha nic a lly c a lc ula te d. H ow e ve r , of G od w e mus t a ssu me tha t he c a n c ompr e he nd inf ini te ly ma ny t he or e ms a nd a xio ms a t onc e .

( ii) Ma n c a nnot c om pr e he nd a t onc e m a ny th ings : he unde r sta n ds dif f e r e nt subje c t s ( the or e m s) a f te r one a nothe r a nd pr oc e e ds f r o m the a xiom s ( pr e mise s) to the the or e ms ( c o nc lusio n) . H ow e ve r , this c a nnot ho ld f or G o d f or tw o r e a sons : if G od is ou tside ti me , he doe s not unde r sta n d one thin g ( the or e m) a f te r the othe r . Fur the r to pr oc e e d f r om a xio ms or f r o m one t he or e m to t he othe r w o uld me a n to pr oc e e d f r om no t - know ing ( the ne w the or e m t o be pr ove d) t o know in g i t ( w he n the pr oof is e s ta bli she d) . But th is is im poss ible f or the know le dge of G od.

1 7 4 A formalised system of sentences is axio matisable if its sentences can be effectively listed, i. e. if they are recursively enumerable; in this case the sentences of the system are provab le (under s ome specified rul es of proof) fr om a fini te subset called the axioms. The system is decida ble if both it s theorems and its n on - theorems can be effectively listed or if bo th its theorems and it s non - theorems are recursively enumerable. In this latter ca se the syst em is recur sive. In o ther words: a s ystem S i s decidable if there exists an effective, uniform method (decision method) of determining whether a given sentence of S is valid in S (otherwise undecidable).

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( iii) For ma n so me pr opos iti on ma y be pr ova ble or know a ble in pr inc i ple , but no t ( ye t) pr o ve d a nd n ot ( ye t) k now n . For G od the r e is not suc h a dist inc ti on: w ha t i s pr ova ble or know a bl e , is know n by him.

( iv) So me syste ms a r e a xioma t isa ble , so me othe r s e ve n de c ida ble ; tha t is the ir the or e m s a r e r e c ur sive ly e nume r a ble or e ve n r e c ur sive . T ha t me a ns the r e is a me c ha nic a l pr oc e du r e or c ompute r pr ogr a m to c a lc ula te the the or e ms or bot h t he the or e ms a nd non - the or e ms. O the r r ic he r syste ms, e spe c ia ll y tho se of hi ghe r or de r logic a nd ma ny syste ms in ma the ma t ic s 1 7 5 a r e unde c ida ble a nd a lso not a xioma t isa ble . I n the se la tte r c a se s i t i s m or e c omp lic a te d to ge t a s uita b le or suf f ic ie nt know le d ge of the the or e ms of the syste m. H ow e ve r , w e c a nnot a s sume tha t a n i m ma te r ia l pe r f e c t be in g w o uld ne e d a c ompute r pr ogr a m or a me c ha nic a l pr oc e dur e in or de r to know the the or e ms; a nd t his ho lds in de pe nde ntly of w he the r the sys te m is a xio ma ti sa ble or de c ida b le or ne ithe r . T hus G od a l so doe s not ne e d a n a x io ma tisa t ion or pa r tia l a xi oma ti sa tio n in or de r to know the ma t he ma tic a l the or e m s. H e c a n know a ll the or e m s of ma the ma t ic s w it hout pr o of or a xioma ti s a tion.

(3) T he r e ar e limit a tio ns c onc e r ning c on siste nc y a nd c om ple te ne ss. ( a ) T he r e a r e f inita r y pr oof s of c o nsis te nc y of ( c la ssic a l tw o - va l ue d)

Pr opo sit iona l L o gic a nd of some ve r y w e a k syste ms of se t the or y ( f or e xa mple : the si mple the or y of ty pe s w it hout a n a xiom of inf ini ty) . But the c onsis te nc y of a sys te m of se t the or y w hic h i s r ic h e nough to be suf f ic ie nt f or a re a sona ble pa r t of ma the ma tic s ( e ve n f or the ve r y r e str ic te d pa r t of Pe a no a r ithme t ic ) c a nnot be p r ove d by f inita r y me a ns, sinc e it c a nnot be pr ove d e ve n in the the or y itse lf . 1 7 6

T he r e a r e, how e ve r , r e la tive c onsiste nc y pr oof s in a tw of o ld se n se : F ir st, in the se nse tha t in a str on ge r the or y on e ma y pr ove the c ons iste nc y of a w e a ke r one ; f or e xa mple in the se t the o r y of Q uine - Mor se the c onsis te nc y of the se t t he or y of Z e r me lo Fr a e nke l c a n be pr ove d. Se c ondly, i n the se nse tha t if one the or y is c o nsi ste nt, the str onge r one w hic h is r e c e ive d by a dding a n a dd iti ona l a x io m i s a l so c o nsi ste nt: T h us f or e xa mp le if G öde l 's

1 7 5 Exceptions are for example Elementary Ge o metry and the Theory of Real Closed Fields which are both decidable. 1 7 6 This is a result of Gödel' s second incomplet eness theorem: the consistency of a sufficiently rich theory cannot be proved with the means of that theory.

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se t the or y is c ons iste n t, the n so is the the or y e xte n de d by the A xi om of Cho ic e a nd the Conti nuu m H ypo the si s. 1 7 7

I n a mor e ge ne r a l se nse w e ha ve t o sa y t ha t f or suc h r ic h the or ie s the r e a r e no dir e c t or a bsolu te c onsis te nc y pr oof s . Fr om th is i t a ls o f oll ow s tha t f or the syste m of ( a ll) e sta blishe d ma the m a tic a l the or e ms the r e c a nnot be a c onsis te nc y pr oof , sinc e w e c a nnot i ma gine a str on ge r ma the ma tic a l syste m. A nd by w e a ke r me a ns the poof c a nnot be c a r r ie d out a s it f ollow s f r om G öde l' s se c ond inc o mp le te ne ss th e or e m. Mor e ove r it f ollow s tha t a c onsis te nc y pr oof of a ll sc ie nt if ic w e ll - c onf ir me d sc ie n tif ic r e sul ts is impo ssi ble f or ma n; it tr a nsc e nd s ma n's a bilit y.

( b) A sc ie ntif ic the or y T w hic h de sc r ibe s a doma in D of obje c ts ( ma ybe a lso c onc e p tua l) or of r e a lity is c a lle d c ompl e te if e ve r y tr ue sta te me nt a bout D is de r iva b le f r om T. 1 7 8 Cla ss ic a l tw o - va lu e d Pr op osi tiona l L og ic a nd Fir s t O r de r Pr e dic a te L ogic a r e c omple te i n a ll thr e e se nse s. Bu t str on ge r the or ie s a r e usua lly inc o mple te . T h us L e ib n iz w a s r igh t w . r . t. the c omple te ne s s of L og ic if he me a n t S yll ogis tic s a nd e ve n if he w ou ld ha ve me a nt Fir s t O r de r Pr e d ic a te L ogic ( w hi c h he did not know ) . But he w a s not c or r e c t w . r . t. ma the ma tic s sinc e a lr e a dy e le me nta r y a r ith me tic ( Pe a no A r ith me tic ) is inc o mple te .

W e ma y now a sk a ga in the que s tion in w ha t se nse G od i s not a f f e c te d by the se a nd sim ila r lim ita t ions c onc e r nin g c onsis te nc y a nd c omple te ne s s. ( i) For ma n f ini ta r y c onsis te nc y pr oof s m i ght be mor e tr a nspa r e nt a nd

be tte r c ompr e he nd ib le . For G od, how e v e r , the r e is no dif f ic ulty w i th inf ini ta r y me a ns, f ir st of a ll be c a use he doe s not ne e d a ny "me a ns " or "pr oof pr oc e dur e s " in or de r to k now ; se c ondly, be c a use he c a n c ompr e he nd inf in ite ly ma n y le ve ls of str o nge r sy ste m s w h ic h inc lude the c ons iste nc y of the w e a ke r syste m s. But a ga in he doe s not ne e d suc h le ve ls of sys te ms in or de r to know .

( ii) For hu ma n kn ow le dge mos t do ma in s D of know le d ge a r e inc omple te in the se ma nt ic se nse ( se e a bo ve ) ; th us the do ma in of ma the ma tic s, of phy sic s, of c os mol ogy, of bi olog y e tc . a r e a ll inc o mple te . H ow e ve r , of G od w e ha ve to a ssume tha t he know s a l l the tr ut hs be longi ng to suc h a doma in D .

1 7 7 Cf. Fraenkel et al. (1973, FST) ch. V. and Gödel (1940, CAC). 1 7 8 This is called semantic completeness. A theo ry T is called formally complete, i f there is no proper consisten t extension of T (with the same vocabulary). T is complete concerning derivability if for every (closed) sentence s well - formed in T, either s or non - s is derivable from (the axioms of) T.

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( iii) Ma n c a nnot c ompr e he nd the inf i n ite c omple te l y, but only "pote n tia l ly". T ha t is by s ome r e c ur siv e pr oc e dur e like "1, 2, 3, … a nd so on" or by a n instr uc t ion w h ic h le a ds to a n inf ini te se r ie s like ( α ) 0 is a f igur e ( β ) if x is a f igur e , the n so is + x+ H ow e ve r , w e ha ve to a ss ume tha t G od c a n c ompr e he nd t he inf i nite c omple te l y a nd w itho ut pr oc e e ding f r om one ste p to the othe r . Mor e ove r , it is know n tha t be yond the f i r st le ve l of the inf inite in t he se nse of the denumerable infinite t he r e a r e highe r le ve ls of the tr a nsf ini te r e a lm w hic h a r e or de r e d by the c ontinuu m hyp othe s is. A ltho ugh in t his tr a nsf in ite do ma in the r e se e ms to be c onsi de r a ble f r e e dom c onc e r ning the f ur the r de ta i ls of t he or de r ing r e la ti ons. 1 7 9 T his show s tha t ma n is r a the r uns ur e a bout t he or de r ing la w s in thi s doma in. A l so he r e w e ha ve to a ssume tha t G od doe s not ne e d to pr oc e e d le ve l by le ve l a nd doe s not ne e d the c ontinuu m hy pothe s is or a nothe r or de r ing pr inc iple f or c ompr e he ndin g the tr a nsf ini te doma in ( e ve n if he d oe s kn ow w ha t pr inc iple s a r e use d by hu ma n ma the ma t ic ia ns) .

12. 4 A n sw e r t o t he O b je ct i on s

12. 41 ( to 12. 1 1) Sinc e t he se t of a l l tr uths is i nf ini te , the r e i s a si mila r situa t ion a s w it h the se t of a ll ( na tur a l) numbe r s ; you c a n a lw a ys a dd one , i. e . the r e is no highe st nu mbe r a nd sim ila r ly the r e is no la st ( ulti ma te ) tr uth. O r if tr a nsc e nding the de nu me r a ble do ma in, the r e a r e a lw a ys highe r pow e r s or le ve ls. Bu t f r om t his o ne c a nnot c onc lu de tha t G od c ou ld no t kno w thi s. O n the c ontr a r y w e ha ve to a ssume tha t he , a s a n inf inite be ing, pos se ssi ng inf ini te know le dge , c a n c ompr e he nd inf inite l y ma ny n umbe r s a nd tr uths a n d a lso inf in ite l y ma ny pow e r s of the c onti nuum ( c f . 12. 342( 2) ) . 12. 42 ( to 12. 12) Sinc e ma n c a nnot kno w a n inf i nite n um be r of pr opo sit ion s c omple te l y, he c a n he lp himse lf b y kn ow ing t he a xiom s ( pr e mise s) of t he syste m a nd the de d uc tion r ule s f or de r iving the the or e ms. I f the s yste m i s c omple te , a ny spe c if ic the or e m c a n be de r ive d a ltho ugh nobo dy c a n c ompr e he nd or inf e r the i nf ini te num b e r of a ll the or e ms of the r e spe c ti ve a xiom s. I f the syste m is no t a xio ma tisa b le , only a pa r t of the the or e ms c a n be de r ive d f r om the a xiom s or a xiom sc he ma ta . But a ll the se r e str ic t ions d o not hold f or G od ( c f . 12. 342( 2) ) , w ho c a n c ompr e he nd inf in ite ly ma ny the or e ms 1 7 9 Cf. the remarks of Gödel in the Addenda of his (1940, CAC), p. 70.

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a nd w ho doe s not ne e d a xioms or de r iva tio n r ule s in or de r to know the se tr uths. 12. 43 ( to 12. 13 ) T he a n sw e r to thi s ob j e c tion i s si mi la r to tha t of the f or me r : G od doe s not ne e d the se t of tr ue pr oposit ions t o be r e c ur sive ly e nume r a ble ( to be e f f e c tive ly l iste d) in or de r to k now t he m. T h is ( a xio ma tisa b ili ty) is c e r ta inly a he lp f or ma n, but G od doe s not ne e d it. 12. 44 ( to 12. 14) I t is tr ue tha t a mo ng t he c onse que nc e s of tr ue pr opos it ions the r e a r e a lot of supe r f luous, ir r e le va nt a nd r e dunda nt tr ue pr oposi tio ns. N ow a lthoug h suc h ir r e le va nt tr uths di str a c t ma n a n d so me ti me s le a d a lso to pa r a doxe s w hic h ne e d t o be solve d b y ma n, s uc h ir r e le va nt tr u ths do n ot distr a c t or d ist ur b G o d in his thi nkin g. L ike w ise , G od c a nnot be se duc e d or mis le d by his kn ow le dge of the mor a l e v ils c om mi tte d by ma n. 12. 45 ( to 1 2. 15) T he a nsw e r to th is ob je c tion is s im ila r to tha t of o bje c tio n 12. 12. a nd 12. 13: A s yste m or me r e ly se t of tr uth s ne e d not t o be de c ida ble in or de r to be know n by G od. G od doe s not ne e d a ny me c ha nic a l pr oc e dur e of c a lc ula tion or a c ompute r pr ogr a m in or de r to know ( c f . a lso 12. 342( 2) a bove ) .

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13. A T heor y of Om ni sc i ence 13. 1 I nt ro du ct io n

T he pur pose of the f oll ow in g f or ma l s yste m i s to s how tha t – c on tr a r y to oppos ite c la im s – the r e a r e the or ie s of omni sc ie nc e w hic h a r e built up a x ioma t ic a lly a nd a r e a ppe a r e ntly c onsis te nt c on ta ini ng the f ol low i ng impor ta nt the or e m s: ( 1) G od ( a s a per son) e xists ( 2) G od is omni sc ie nt ( 3) G od is omni pote n t ( 4) W ha t e ve r G od know s ist tr ue ( 5) W ha te ve r G od know s he ne c e ssa r ily know s ( 6) G od’ s know le d ge is te n se le ss a nd de duc tive l y inf a lli ble ( 7) G od know s a ll the or e m s a bout hi mse lf ( 8) G od know s a ll the or e m s a bout lo gic a nd ma the ma t ic s ( 9) G od know s a ll t he or e ms a b out the uni ve r se ( i. e . a bout it s la w s, sta te s, init ia l c ondi tion s, c onsta nt s a nd e ve nts) ( 10) G od kno w s a l l pa st, pr e se n t a nd f utur e e ve nts r e la tive to a r e f e r e nc e f r a me of the unive r se ( 11) G od know s a ll un ive r sa l a nd a ll sin gula r tr uths a bou t the uni ve r se ( 12) A lt houg h G od is o mni sc ie nt a n d o mnip ote nt he i s ne i the r a llw il ling nor a llc a using ( 13) G od kn ow s a l l mor a l e v il of thi s w or ld bu t ne it he r he c a n w ill it n or he c a n c a use it; he pe r mits it ( unde r the c onditi on of c r e a ting ma n w ith f r e e w ill) T he une r lyin g lo gic is ( tw o va l ue d) Pr opo sit iona l L ogic e xte n de d by the Moda l Sys te m T ( of Fe ys ) + e piste mic a nd othe r ope r a tor s a nd a sma ll pa r t of Pr e dic a te L ogic ( of Fir s t O r de r ) . T he te rmino log y is a s f ollow s: ( 1) T he c opula ‘ is’ is e xpr e sse d by tw o p r imi tive s ∈ a nd e w he r e ∈ is use d f or indiv idua l va r ia ble s ( r e pr e se nting in divid ua ls) a nd e f or pr o pos iti ona l va r ia ble s r e pr e se nti ng sta te s of a f f a ir s . For e xa mple : ‘ x ∈ OS’ f or ‘ x is omni sc ie nt’ or ‘ x ∈ H ’ f or ‘ x is huma n’ ; ‘ p e ME’ f or ‘ the sta te of a f f a ir s p is a mor a l e vil’ . ( 2) W ith r e spe c t to sta te s of a f f a ir s a lso the se t the or e tic a l e le me ntho od r e la tion ε i s u se d a s f or e xa mple : ‘ p ε T(LM)’ , ‘ p ε T(CR)’ , ‘ p ε Tg’s essence ’ ,

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‘ p ε Tg’s Commands ’ sta nd ing r e spe c t ive ly f or ‘ the s ta te of a f f a ir s p is a n e le me nt of the the or e m s of L og ic s a n d Ma the m a t ic s’ , ‘ p is a n e le me n t of the the or e ms of c r e a tio n’ , ‘ p is a n e le me n t of the the or e m s of G o d’ s e sse nc e ’ , ‘ p is a n e le me nt of the the or e ms of G od’ s Co mma nd s’ . ( 3) T he r e a r e dif f er e nt ope r a tor s a tta c he d to pr opo si tiona l va r ia ble s by w hic h ne w sta te me n ts ( t r ue or f a l se ) a r e f or me d. E xa mple s a r e : K, W, C, CW, CC, A, P, SW, SA r e pr e se nting r e spe c tive ly: k no w s, w ills, c a use s, c a n w ill, c a n c a use , a c ts, pe r mits, shoul d w il l, should a c t. ( 4) T he r e a r e the moda l ope r a tor s ‘ ’ ( sta ndin g f or ‘ ne c e ssa r y’ ) a nd ‘ m’ ( st a ndin g f or ‘ poss ible ’ ) in a c c or da nc e w ith t he unde r ly ing s yste m of M oda l L ogic T of Fe ys. ( 5) U nive r sa l a nd e xiste nt ia l qua nt if ie r s a r e use d f or both type s of va r ia ble s: ∀x, ∃x, ∀p, ∃p. T he q ua ntif ie r ‘ E ! x’ use d in A xi om A 1 r e a ds : the r e i s e xa c tl y one ( i. e . a t le a st one a nd a t most one ) x. ( 6) T he f or ma l syste m pr opose d he r e c onsis ts of a xiom s A 1 - A 8, de f init ions D 1 - D 25 a nd the or e ms T 1 - T 135. 13. 2 T h eo ry o f O mn i sc ien ce D 1 x ∈ Person ↔ [(∃p)xKp ∧ (∃p)xWp] K … know s ( tha t) W … w ills ( tha t) x ∈ … x is ( ha s) D 2 x=g ↔ x ∈ Person ∧ x ∈ OS ∧ x ∈ OM ∧ x ∈ AG ∧ x ∈ CT g … G od OM … omn ipote n t OS… omni sc ie nt AG … a llgoo d CT… c r e a tor A 1 E ! x(x ∈ Person ∧ x ∈ OS ∧ x ∈ OM ∧ x ∈ AG ∧ x ∈ CT) T he f ollow i ng the or y is c onc e r ne d w ith G od a s a n omni sc ie nt ( OS) be in g. T he othe r a ttr ibute s, pe r sona l ity, omn i pote nc e ( OM) , a llgoodne ss ( AG) a nd be ing a c r e a tor ( CT) w i ll be tr e a te d o nly in sof a r a s the y c ontr ibu te to or c omple me nt t he ma n y a spe c ts of o mni s c ie nc e . I n this r e spe c t the r e la ti ons of

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G od’ s k now le dge to his w il l a nd pow e r a nd the r e la ti ons of hi s k now le d ge to him a s a c a use of c re a tion a r e of spe c ia l impor ta nc e . T 1 g ∈ Person ∧ g ∈ OS ∧ g ∈ OM ∧ g ∈ AG ∧ g ∈ CT A 1, D 2

13.21 Definitions of Omniscience and of Omnipotence D 3 g ∈ OS ↔ ∀p(gKp → p) ∧ ∀p[(p ε T(g) ∨ p ε T(LM) ∨ p ε T(CR)) → gKp] ∧ ∀p(gKp → gKp) ∧ ∀p(gKp → ¬(∃t)gKtp) Just if ic a tion of the de f in ie ns of D 3 ( omn isc ie nc e ) ( 1) ∀p(gKp → p) . A ss ume : ¬∀p(gKp → p) . T he n ∃p(gKp ∧ ¬p) , i. e . the r e is a sta te of a f f a ir s suc h tha t G od kn ow s tha t i t obta in s b ut it doe s not ob ta in. T his is inc ons is te nt w ith the c onc e pt of ( str ong) k now le d ge c f . the di sc uss ion in c ha pte r 1. 3 a n d a ls o i nc onsi ste nt w i t h a pe r f e c t be ing. T he r e f or e ∀p(gKp → p) ( 2) ∀p(p ε T(g) → gKp). A ssu me ¬∀p(p ε T(g) → gKp). T he n ∃p(p ε T(g) ∧ ¬ gKp), i. e . the r e is a sta te of a f f a ir s a b out G o d hi mse lf a l thou gh G o d ha s no know le dge a bo ut i t. T his i s inc o nsi ste nt w ith t he c onc e pt of omn isc ie nc e a nd in ge ne r a l w ith the c onc e pt of a pe r f e c t be ing. T he r e f or e ( 2) holds. ( 3) ∀p(p ε T(LM) → gKp). A ss ume : ¬∀p(p ε T(LM) → gKp). T he n ∃p(p ε T(LM) ∧ ¬gKp), i. e . some the or e ms of logic or ma the ma tic s G od w ou ld not know . Sinc e th is hol ds a lso f or ma n, f or logic ia ns a nd ma t he ma t ic ia ns, G o d’ s know le dge w ou ld n ot dif f e r e sse nt ia ll y f r om t ha t of hu ma ns. But th is se e ms to be a bs ur d, e spe c ia lly if w e th ink of G od a s t he c r e a tor of ma n. T he r e f or e ( 3) must hol d. ( 4) ∀p(p ε T(CR) → gKp). A ssu me ¬∀p(p ε T(CR) → gKp). T he n ∃p(p ε T(CR) ∧ ¬gKp), i. e . some tr ue pr op os itio ns a bou t ( his ow n) c r e a tion G od w ould no t know . A ga in t his h old s f or ma n: so me ( in f a c t ma ny) tr ue pr opost it ions a b out the un ive r se huma ns do n ot k now . Bu t if G o d is the c r e a tor of the unive r se w e ca nnot a ssu me tha t he ha s a huma n a nd f a llib le know le dge c onc e r ning t he unive r se . ( 5) ∀p(gKp → l gKp). A ssu me ¬∀p(gKp → l gKp). T he n i t f ol low s tha t (∃p)(gKp ∧ m¬gKp), i. e . f or some sta te s of a f f a ir s p, G od k now s tha t p b ut possi bly d oe s not k now tha t p. N ow this c ombina t ion – t o know i n f a c t th a t p but poss ibl y not to kno w it – is imp oss i ble f or G od; a lthough i t is ve r y of te n

15 6

the c a se w ith ma n: in a l l c a se s in w h ic h w e le a r n so me thi ng ne w in t he sc ie nc e s w e c a n sa y tha t w e in f a c t kno w it now but ( sinc e w e did’ n t kn ow i t be f or e ) w e possibly do n ot k now it. ( 6) ∀p(gKp → ¬(∃t)gKtp) . A ss ume ¬∀p(gKp → ¬(∃t)gKtp) . T he n it w ou ld hold tha t (∃p)(gKp ∧ (∃t)gKtp) , i. e . G od’ s know i ng w ou ld be a t a c e r ta in time ; but w h ic h ti me , w e c a n a sk. E spe c ia ll y if w e a ssume w ith the Spe c ia l a n d G e ne r a l T he or y of Re la ti vit y tha t spa c e time be lo ngs to t his w or l d ( unive r se ) a nd is bou nd to this f inite u nive r se . T hu s if G od doe s n ot be lo ng to thi s w or ld ( unive r se ) – a lthoug h w e a ssume tha t he ha s c r e a te d it – the n he a nd his know le dge ( a nd his w il l) m ust be out sid e time ; i. e . w e c a nnot a ttr i bute a t ime -inde x to his a c tivi ty ( kn ow in g a nd w i llin g) . T o ma ke t his a r gu me nt mor e tr a nspa r e nt r e me mbe r tha t a lr e a dy o n our e a r th ( a s a r e f e r e nc e sys te m) w e dist ingu ish L ondo n - ti me f r om T okyo - t ime . Mor e ove r ti me doe s not “ f lo w e qua bly” ( N e w ton, Pr inc i pia , Sc h oli um ) e ve r yw he r e but r uns f a s te r or mor e slow l y de pe nd ing o n the ve l oc ity of the r e f e r e nc e syste m ( or of the r e spe c tive a tom ic or bi olo gic a l c loc k, a s in a ni ma ls or hu ma n i ndiv idua l s) . T hus e ve r y r e f e r e nc e syste m ( syste m of sta r s, si m ila r or la r ge r tha n our pla ne ta r y sy ste m w it h the sun) ha s its own time; the r e f or e the c onc e pt of sim ulta ne i ty is r e la t ive to the d ista nc e a nd to the ve loc ity. Mor e ove r : For a n obse r ve r tr a ve lling w ith l igh t ve loc i ty ( in va c uum) t ime doe s n ot pa ss a w a y. A ll thi s s how s c le a r ly t he a bsur d ity of a t tr ibut ing a t ime of a ny suc h r e f e r e nc e syste ms of thi s w or ld to ( the a c tion s of ) G od. ( Cf . c h. 3 of this book) . D 3. 1 g ∈ SK ↔ ∀p(gKp → p) D 3. 2 g ∈ CK ↔ ∀p[(p ε T(g) ∨ p ε T(LM) ∨ p ε T(CR)) → gKp] D 3. 3 g ∈ NK ↔ ∀p(gKp → l gKp) D 3. 4 g ∈ TK ↔ ∀p(gKp → ¬(∃t)gKtp) D 3. 5 g ∈ OS ↔ g ∈ SK ∧ g ∈ CK ∧ g ∈ NK ∧ g ∈ TK T(g) … the sta te s of a f f a ir s ( the or e ms) a bout G o d SK … sound kn ow le dge CK … c omple te kno w le dge LM … logic s a nd ma t he ma tic s NK … ne c e ssa r y know le dge CR … c r e a tio n ( a nd c r e a tur e s) TK … te nse le ss kno w le dge D 4 g ∈ OM ↔ ∀p(gWp → gKp) ∧ ∀p[gCWp ↔ Cons(p) ∧ Cons({p} ∪ Tg’s Essence) ∧

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Cons({p} ∪ Tg’s Commands)] Cons(p) … p is c onsis te nt Cons({p} ∪ Tg’s Essence) … p is c onsi ste nt w i th the t he or e ms of G od’ s e sse nc e Cons({p} ∪ Tg’s Commands) … p is c onsi ste nt w i th the t he or e ms of G od’ s c omma nd s CW … c a n w ill CC … c a n c a use , c a n ma ke , c a n br ing a bout P … pe r mits ( doe s n ot pr e ve nt) Lg … logic Math … ma the ma t ic s U … unive r se OC … othe r c r e a tur e s NC … nor ma ti ve a nd volit ive c onsi ste nt G … good T he w ill of G od is unde r sto od i n suc h a w a y tha t h is w ill is a l w a ys f ulf ille d, i. e . ne ve r f a ils. T his is e xpr e ss e d in the f ir st pa r t of the de f init ion D 4 of omn ipote nc e : ∀p(gWp → gKp) f r o m w hic h it f oll ow s w ith the he lp of gKp → p ( D 3. 1) t ha t ∀p(gWp → p) . O bse r v e how e ve r tha t e xpr e ss ion s li ke “ G od w ill s tha t ma n o be ys hi s te n c om ma nd me nts” a r e not f or mu la te d in a c or r e c t w a y sinc e by the a bove pr i nc iple : if G od w il ls t ha t, the n ma n w il l a lw a y s obe y his te n c om ma nd me nts ; but t his i s not the c a se , a s w e know . T he r e f or e, if G od’ s w i ll is a p plie d to hu ma n a c tio ns of f r e e w ill the c or r e c t f or mula t ion is tha t G od w i ll s tha t ma n should (ought to) obe y hi s te n c o mma nd me nt s, sinc e G od doe s n ot d e str oy the f r e e do m of ma n. T hi s is f or mu la te d i n D 1 3 a nd a lso in D 15. O n the ot he r ha nd thi s doe s not hinde r t ha t in s ome c a se s G od w ill s t ha t the h uma n pe r son w il ls s ome th ing a nd in the se c a se s thi s is not a f r ee w ill de c ision bu t ma y be some inc lina ti on ( na tur a l r ight) w h ic h is ge ne tic a lly in bor n or a r e sult of e nvir one me nt c ondi tio ns or of e duc a tion. Just if ic a tion of the de f in ie ns of D 4 ( omn ipote nc e ) ( 1) ∀p(gWp → gKp), i. e . w ha te ve r G od w ill s tha t it ha ppe ns he kn ow s tha t i t ha ppe ns. W e sha ll f ir st e xa m ine the f ollow i ng i mpor ta n t c onse que nc e of it: ∀p(gWp → p) , i. e . w ha te ve r G od w ills tha t it ha ppe ns, is the c a se . A ssume the c ontr a r y: F or so me sta te s of a f f a ir s p , G od w ill s tha t p oc c ur s but p d oe s not oc c ur : ∃p(gWp ∧ ¬p) . I n thi s c a se G od c ould’ nt be a l mi ghty ( omni pote nt) . W e know tha t t his ha ppe ns ve r y of te n w ith hu ma ns : t he y w ill tha t so me thi ng ha ppe ns b ut i t doe s no t ha ppe n, i. e . the ir w ill is no t ( a lw a ys) f ulf ille d. B ut thi s is i mpos sib le f or a n omnip ote nt be i ng.

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I n or de r to j ust if y ( 1) now a ssu me t h e c ontr a r y: F or so me s ta te s of a f f a ir s w hic h o bta in by G od’ s w i ll it w ou ld hol d tha t G od w ou ld not kn ow t ha t the y obta in. T hi s is c o mple te l y im pos sib le f or a pe r f e c t be ing; suc h a c a se w ould e ve n be a lmo st imp oss ible f or ma n: tha t he br in gs some thin g a bou t w i th h is w ill bu t w oul d not know t ha t it is t he c a se . T he r e f or e ( 1) must hol d. ( 2) ∀p[gCWp → Cons(p)], i. e . if G od c a n w ill ( or c a n c a use ) t ha t p , the n p mus t be c on sis te nt; or : W ha te ve r G od c a n w ill ( c a n c a use ) is c o nsi ste nt. A ssu me the c ontr a r y: the n G o d’ s w i ll a n d G od’ s pow e r w ou ld be inc on sis te nt w hic h is i mpos sib le f or a ne ce ssa r y be ing. O bse r ve tha t “ G od c a n w i ll tha t p ” a n d “ G od c a n c a use tha t p” a r e e qui va le nt pr ovide d tha t p be lon gs to the sta te s of a f f a ir s of c r e a tion or to pos sib le a lte r na tive s ( of c r e a tion) c o mpa ti ble w i t h G od’ s e sse nc e a nd Co m ma nds. T he sa me hold s f or “ G od w ill s tha t p ” a nd “ G od c a use s tha t p” . But in ge ne r a l only gCCp → gCWp a n d gCp → gWp hold u nive r sa l ly; sinc e G od c a n w il l some t hing of hi mse lf ( hi s goo dne ss or his e xi ste nc e ) but he c a nnot c a u se it ( se e D 5 be low ) . ( 3) ∀p[gCWp → Cons({p} ∪ Tg’s Essence)], i. e . w ha te ve r G od c a n w ill ( c a n c a use ) is c onsis te nt w ith h is e sse nc e or w ith h is na tur e . A ss um ing t he c ontr a r y w oul d me a n tha t his w i ll or his pow e r ( w hic h be lon g to hi s e sse nc e ) is inc ons iste n t ( inc om pa tib le ) w ith hi s e sse nc e w hic h is impo ssi ble . ( 4) ∀p[gCWp → Cons({p} ∪ Tg’s Commands)], . i. e . w ha te ve r G od c a n w ill ( c a n c a use ) is c onsiste nt w ith his Co m ma nds ( to w a r ds ma n) . A ss um ing t he c ontr a r y w ou ld me a n t ha t h is w il l or po w e r w ould be i nc ons iste n t i n t he se nse tha t it w o uld be c ontr a r y to hi s c om ma n ds w hic h e xpr e ss a lr e a dy his w ill a nd pow e r tow a r ds ma n. A 2 ∀p(gWp → gCWp)

W ha te ve r G od w ill s he c a n w il l; the o p posi te doe s not ho ld be c a use his pow e r ( w ha t he c a n w ill) e xc ee ds his a c tua l ( f a c tua l) w illing.

A 3 ∀p(gCp → gCCp)

W ha te ve r G od c a use s he c a n c a use ; the oppos ite doe s no t hol d, be c a use his pow e r ( w ha t he c a n c a use ) e xc e e ds his a c tua l ( f a c tua l) c a using.

D 5 gCp ↔ p ε T(CR) ∧ gWp G od c a use s tha t p if f p be longs to t he th e or e ms of his c r e a tion a nd G od w ill s tha t p. D 5. 1 gCCp ↔ ¬(p ε T(g)) ∧ ¬(p ε T(LM)) ∧ gCWp

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O bse r ve tha t ‘ G od c a n c a use tha t p’ ( gCCp ) i mpl ie s via D 5. 1 a n d D 4 t ha t p mus t be c onsis te nt i tse lf a nd c ons iste nt w it h ( the the or e ms of ) G od’ s e s se nc e a nd G od’ s c omma nds ( c f . T 106)

D 6 g ∈ AG ↔ g ∈ NC ∧ ∀p(gWp → p e G) D 6. 1 g ∈ NC ↔ ∀p[(p ε Tg’s Will w.r.t. man) → gPp] D 7 g ∈ CT ↔ ∀p[(p ε T(CR) ∧ gCCp) → gCp] D 8 p ε T(g) ↔ (p ε Tg’s Essence ∨ p ε Tg’s Relation to CR) D 9 p ε T(LM) ↔ (p ε T(Lg) ∨ p ε T(Math)) D 10 p ε T(CR) ↔ (p ε T(U) ∨ p ε T(OC)) D 11 p ε Tg’s Essence ↔ (l gKp ∧ l gWp ∧ gKl p) D 12 p ε Tg’s Relation to CR ↔ p ε Tg’s Knowledge about CR ∨ p ε Tg’s Will about CR D 12. 1 p ε Tg’s Knowledge about CR ↔ [gK(p ε T(CR)) ∧ gKp ∧ l gKp ∧ gK¬l p] D 12. 2 p ε Tg’s Will about CR ↔ [(gWp ∧ ¬l gWp ∧ gW¬l p) ∨ (p ε Tg’s Will w.r.t. man)] D 13 p ε Tg’s Commands ↔ ∀x∈ H(gW(xSWp) ∧ gW(xSAp)) D 14 gPp ↔ ¬gW¬p D 15 p ε Tg’s Will w.r.t. man ↔ ∀x∈ H[gW(xWp) ∨ gW(xAp) ∨ gW(xSWp) ∨ gW(xSAp)] SW … shoul d ( ought t o) w ill t ha t SA … s houl d ( ought t o) a c t ( in suc h a w a y) that T 2 g ∈ Person T 1 T 3 (∃p)gKp ∧ (∃p)gWp T 1, D 1

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13.22 God’s Knowledge T 4 g ∈ OS T 1 T 5 ∀p(gKp → p) T 4, D 3 W ha te ve r G od know s is tr ue ( is the c a se ) T 6 g ∈ SK T 5, D 3. 1 G od ha s sound k now le d ge T 7 ∀p[(p ε T(g) ∨ p ε T(LM) ∨ p ε T(CR)) → gKp] T 4, D 3

I f p is a the or e m a bout G od or a the or e m a bout l ogic or ma the ma tic s or a the or e m a bout c r e a tion the n G o d know s tha t p

T 8 g ∈ CK T 4, D 3. 2 G od ha s c omple te kn ow le dge T 9 ∀p(p ε T(g) → gKp) T 7 G od know s e ve r yth ing a bou t hi mse lf T 10 ∀p(p ε Tg’s Essence → gKp) T 9, D 8 G od know s e ve r yth ing a bou t his e sse nc e T 11 ∀p(p ε Tg’s Relation to CR → gKp) T9, D8 G od know s e ve r yth ing a bou t his r e la ti on to his c r e a tion T 12 ∀p[p ε Tg’s Essence → (l gKp ∧ l gWp ∧ gKl p)] D 11

W ha te ve r be longs to G od’ s e sse nc e , G od ne c e ssa r ily know s a nd ne c e ssa r ily w ill s a nd of it G od know s th a t it is ne c e ssa r ily the c a se .

T 13 ∀p[(l gKp ∧ l gWp ∧ gKl p) → p ε Tg’s Essence] D 11 T 14 ∀p(p ε T(LM) → gKp) T 7 T 15 ∀p(p ε T(Lg) → gKp) T 14, D 9 G od know s a l l the or e ms of L og ic T 16 ∀p(p ε T(Math) → gKp) T 14, D 9 G od know s a l l the or e ms of Ma the ma tic s T 17 ∀p(p ε T(CR) → gKp) T 7 G od know s a l l the or e ms ( tr ut hs) a bout c r e a tion a nd c r e a tur e s T 18 ∀p(p ε T(U) → gKp) T 7, D 10 G od know s a l l the or e ms a bou t the unive r se T 19 ∀p(p ε T(OC) → gKp) T 7, D 10 G od know s a l l the or e ms a bou t othe r c r e a tur e s T 20 ∀p(gKp → l gKp) T 1, D 3 W ha te ve r G od know s he ne c e ssa r ily kno w s

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T 21 g ∈ NK T 20, D 3. 3 G od ha s ne c e ssa r y know le dge T 22 ∀p(gKp → ¬(∃t)gKtp) T 1, D 3 W ha te ve r G od know s he doe s not kn ow a t some ti me T 23 g ∈ TK T 22, D 3. 4 G od ha s te nse le ss kn ow le dge D 16 x ∈ LO ↔ ∀p(p ε T(Lg) → xKp) LO … log ic a lly o mni sc ie nt T 24 g ∈ LO T 15, D 16 G od is log ic a lly o mni sc ie nt A 4 ∀p[p├ q → (gKp ├ gKq)] p ├ q me a ns tha t p → q is a the or e m G od know s a l l the logic a l c onse q ue nc e s of w ha t he know s T 25 ∀p[(p ├ q ∧ gKp) → gKq] A 4 D 17 x ∈ LI ↔ ∀p[(p├ q ∧ xKp) → xKq] LI … logic a ll y ( or de duc tive ly i nf a llib le ) T 26 g ∈ LI D 17, T 25 G od is log ic a lly ( or de duc tive ly) inf a ll ib le A 5 ∀p[(p ε Tg’s Essence ∨ p ε T(LM)) → p is timeless] T he or e ms a bout G o d’ s e sse nc e a nd the or e ms of logic a nd ma the ma tic s a r e time le ss ( a r e not bound to the ti me of this w or ld ( uni ve r se ) ) T 27 ∀p(p ε Tg’s essence → p is timeless) A 5 T 28 ∀p(p ε T(LM) → p is timeless) A 5 T 29 ∀p[gK(p ε Tg’s Essence) → gK(p is timeless)] T 27, A 4 T 30 ∀p[gK(p ε T(LM) → gK(p is timeless)] T 28, A 4

13.23 God’s Knowledge of the Universe D 18 p ε T(U) ↔ p ε T-Law(U) ∨ p ε T-State(U) ∨ p ε Init(U) ∨ p ε T-Const(U) ∨ p ε Event(U)

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p ε T-Law(U) … p be lon gs to the la w - th e or e ms or la w sta te me nts of the unive r se U p ε T-State(U) … p be longs to t he the or e ms de sc r ibi ng a sta te of the unive r se U or of a pa r t of it p ε T-Init(U) … p be lon gs to the the or e ms de sr c ibi ng a n init ia l c ondi tio n of the unive r se or a pa r t of it p ε T-Event(U) … p be longs t o the the or e ms de sc r ibin g a n e ve nt ( or pr oc e ss) of the unive r se U p ε Const(U) … p be long s the the or e ms a bout the va lue of a na tur a l c onsta nt of the uni ve r se U D 19 p ε T-State(U) ↔ (∃t,∃f)pt,f

w he r e pt,f de sc r ibe s a ( ph ysic a l) sys te m be longi ng to U a t t ime t r e la tive to a r e f e re nc e f r a me f

D 20 p ε T-Event(U) ↔ ∃S1(t1f) ∃S2(t2f) S1, S2 ε State(U) ∧ p(S1,S2) w he r e p(S1,S2) de sc r ibe s the tr a nsitio n f r om sta te S1 to sta te S2 D 21 p ε T-Init(U) ↔ ∃S1(t1f) ∃S2(t2f) S1, S2 ε State(U) ∧ p(C(S1,S2))

w he r e p(C(S1,S2)) de sc r ibe s S1 a s a c ausa l c ond i tio n, toge t he r w ith a la w , f or S2

T 31 ∀p[(p ε T-Law(U) ∨ p ε T-State(U) ∨ p ε T-Init(U) ∨ p ε T-Const(U) ∨ p

ε T-Event(U)) → gKp] T 18, D 18 G od kno w s a ll the t he or e ms a bou t t he la w s, sta te s, in it ia l c ond iti ons, c onsta nt s a nd e ve nts of the unive r se

T 32 ∀p(p ε T-Law(U) → gKp) T 18, D 18 T 33 ∀p(p ε T-State(U) → gKp) T 18, D 18 T 34 ∀p(p ε T-Init(U) → gKp) T 18, D 18 T 35 ∀p(p ε T-Const(U) → gKp) T 18, D 18 T 36 ∀p(p ε T-Event(U) → gKp) T 18, D 18 A 6 ∀p[(p ε T-Law(U) ∨ p ε T-Const(U)) → (∀t∀s)pt,s]

L a w s of N a tur e ( of the unive r se ) a nd Con sta nt s of N a tur e ( of the unive r se ) hold a lw a ys a nd e ve r yw he r e viz . a r e spa c e - time inva r ia nt ( ‘ s’ sta nds f or t he spa c e c ondit ions) . W e ha ve to a dd he r e c r itic a lly: A c c or ding to our kn ow le dge t oda y. T he que sti on w he the r so me c onsta n t s of na tur e c ha nge ve r y slow ly ha s be e n se ve r e ly te ste d by e x pe r ime n ts w ithi n the la st de c a de s. So f a r no vi ola tio n of the ir c onsta nc y w a s disc ove r e d ( w i thin the r e spe c ti ve d e gr e e of a c c ur ac y) . I f some f unda me nta l c on sta nt s like α or G w o ul d c ha nge the n a l so la w s of na tur e

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w ould n ot be c omp le te ly t ime - tr a ns la tio n - inva r ia nt, si nc e suc h c onsta nt s e nte r f unda me nta l la w s of na t ur e . ( Cf . Mi tte ls ta e dt/W e in ga r tne r ( 2005, L N t) c h. 8. 2) .

T 37 ∀p(p ε T-Law(U) → (∀t,∀s) pt,s) A 6 T 38 ∀p(p ε T-Const(U) → (∀t,∀s) pt,s) A 6 T 39 ∀p[gK(p ε T-Law(U)) → gK((∀t, ∀s)pt,s)] A 4, T 37 T 40 ∀p[gK(p ε T-Const(U)) → gK((∀t, ∀s)pt,s)] A 4, T 38 T 41 ∀p[p ε T-State(U) → (∃t,∃f)pt,f ε T-State(U)] D 19 T 42 ∀p[p ε T-Event(U) → ∃S1(t1f) ∃S2(t2f) S1, S2 ε State(U) ∧ p(S1,S2) D 20 T 43 ∀p[p ε T-Init(U) → ∃S1(t1f) ∃S2(t2f) S1, S2 ε State(U) ∧ p(C(S1,S2)) D 21 T 44 ∀p∀t∀f(pt,f ε T-State(U) → gKpt,f) T 33 I nsta nt ia tio n T 45 ∀p∀t1∀t2∀f[p(S1,S2) ε T-Event(U) → gKp(S1,S2)] T 36 I nsta n t ia tio n T 46 ∀p∀t1∀t2∀f[p(C(S1,S2)) ε T-Init(U) → gKp(C(S1,S2))] T 34 I nsta nt ia tio n T 47 (∀t,∀f)[pt,f → p ε T-State(U)] D 19 T 48 ∀S1(t1,f)∀S2(t2,f)[S1,S2 ε State(U) ∧ p(S1,S2) → p ε T-Event(U)] D 20 T 49 ∀S1(t1,f)∀S2(t2,f)[S1,S2 ε State(U) ∧ p(C(S1,S2)) → p ε T-Init(U)] D 21 T 50 (∀t,∀f)[pt,f → gKpt,f] T 47, T 44

G od know s a ny ( si ngula r ) sta te oc c ur r i ng a t ti me t r e la tive t o r e f e r e nc e f r a me f ( of the unive r se ) . For the pr oof of T 50 obse r ve tha t T 41 is e quiva le nt to ∃t∃f[p ε T-State(U) → pt,f ε T-State(U)] w hic h i nsta n tia te s to: p ε T-State(U) → pt,f ε T-State(U). A pply ing uni ve r sa l ins ta ntia t ion s of T 47 a nd T 44 le a ds to T 50

T 51 ∀S1(t1,f)∀S2(t2,f)[S1,S2 ε State(U) ∧ p(S1,S2) → gKp(S1,S2)] T 48, T 36

T 52 ∀S1(t1,f)∀S2(t2,f)[S1,S2 ε State(U) ∧ p(C(S1,S2)) → gKp(C(S1,S2))] T 49, T 34

T 53 ∀t ≤ t0∀f[pt≤t0,f → gKpt≤t0,f] T 50 I nsta nt ia tio n w he r e t0 ist the pr e se nt time r e la tive to a r e f e r e nce f r a me f; G od kno w s

a ll pa st a nd pr e se nt sta te s ( of the uni ve r se ) ; viz . G od know s a ll sin gula r tr uths c onc e r nin g pa st a nd pr e se nt ti me ( in thi s w or ld)

T 54 ∀t > t0∀f[pt>t0,f → gKpt>t0,f] T 50 I nsta nt ia tio n G od kn ow s a l l f utur e s ta te s ( of the un ive r se ) ; viz . G od k now s a ll s ingu la r tr uths i n the f utur e

T 55 ∀S1(t1≤t0,f)∀S2(t2≤t0,f)[S1,S2 ε State(U) ∧ p(S1,S2) → gKp(S1,S2)] T 51 I nsta nt ia tio n

G od kn ow s a ll pa st a n d pr e se nt e ve nts ( of the un ive r se ) ; G od k now s a ll singu la r tr uths de sc r ib ing pa st a nd pr e se nt e ve nts

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T 56 ∀S1(t1>t0,f)∀S2(t2>t0,f)[S1,S2 ε State(U) ∧ p(S1,S2) → gKp(S1,S2)] T 51 I nsta nt ia tio n

G od kno w s a ll f u tur e e ve nts ( of the unive r se ) ; v iz . G od know s a ll singu la r tr uths de sc r ib ing f ut ur e e ve nts

T 57 ∀S1(t1≤t0,f)∀S2(t2≤t0,f)[S1,S2 ε State(U) ∧ p(C(S1,S2)) → gKp(C(S1,S2))] T 52 I nsta nt ia tio n

G od know s a ll pa st a nd pr e se nt i nit ia l c ondit ions ( of the un ive r se ) ; viz . G od know s a ll s ing ula r tr uth s de sc r ibing pa st a nd pr e se nt ini tia l c ondit ions

T 58 ∀S1(t1>t0,f)∀S2(t2>t0,f)[S1,S2 ε State(U) ∧ p(C(S1,S2)) → gKp(C(S1,S2))] T 52 I nsta nt ia tio n

G od kn ow s a ll f u tur e in itia l c ond iti ons ( of the u nive r se ) ; v iz . G od know s a ll singu la r tr uths de sc r ib ing f ut ur e initia l c ondit ions

T 59 ∀p[¬p ε T(g) ∨ ¬p ε T(LM) ∨ ¬p ε T(CR)) → gK¬p] T 7, ¬p/p G od kn ow s w ha t i s n ot ( t he c a se ) ; w h a t is not the c a se a bou t h imse lf , w ha t is not the c a se a bout L ogic s a nd Ma the ma t ic s a nd w ha t is n ot the c a se a bout c r e a tion

T 60 ∀p[¬p ε T-Law(U) ∨ ¬p ε T-State(U) ∨ ¬p ε T-Init(U) ∨ ¬p ε T-const(U) ∨ ¬p ε T-Event(U)) → gK¬p] T 31, ¬p/p

G od know s w ha t is no t ( the c a se ) c onc e r ning the un ive r se ; w ha t is n ot the c a se a bout la w s, w ha t is not the c a se a bout s ta te s, w ha t i s no t the c a se a bout ini tia l c ondi tio ns, w ha t i s n ot the c a s e a bout c ons ta nts of na tur e , w ha t is not the c a se a bout e ve nts

D 22 Mut-K(x) ↔ ∃t1∃t2(t1≠t2 ∧ xKt1p ∧ xKt2¬p) Mut-K(x) … the know le d ge of x is muta ble D 22. 1 ¬Mut-K(x) ↔ ∀t1∀t2[(t1≠t2 → ¬(xKt1p ∧ xKt2¬p)] ¬Mut-K(x) … the know le dge of x is im muta b le ( i. e . doe s not c ha nge ) T 61 ∀p[gKp → ¬Mut-K(g)] T 22, D 22. 1 G od’ s know le dge is im mu ta ble T 62 ∀p(p → ¬gK¬p) T 5, ¬p/p, Con tr a pos iti on T 63 ∀p(gKp → ¬gK¬p) T 62, T 5 T 64 ∀p(gK¬p → ¬gKp) T 63 T 65 ∀p(¬gKp ∨ ¬gK¬p) T 63

O bse r ve tha t ∀p(gKp ∨ gK¬p) d oe s n ot f ol low f r o m T 5 or T 6 3. T hi s the sis im plie s toge t he r w ith w ith T 5 t he the sis ∀p(gKp ↔ p) . T he la tte r

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is a l so use d in the lite r a tur e a s a de f in it i on of om nisc ie nc e . A l tho ugh w e think t ha t thi s str ong t he sis i s a possib le the sis ( or de f init ion) of omni sc ie nc e if the unive r sa l qua nt if ie r i n “ f or a ll sta te s of a f f a ir s p : if p the n G od know s tha t p” is ta ke n w ith r e spe c tive c a re , w e pr opose d a w e a ke r but a t t he sa me ti me muc h mor e de ta ille d de f ini tion of omni sc ie nc e ; i ts r e s pe c tive t he sis w hic h r e pla c e s ∀p(p → gKp) is T 7. Cf . the pr oble m s disc us se d in se c tio n 11. 46 a bove .

13.24 God’s Knowledge and Will T 66 ∀p(gWp → gKp) T 1, D 4 W ha te ve r G od w ills ( tha t i t is the c a se ) he know s ( tha t it i s the c a se ) T 67 ∀p(gWp → ¬gK¬p) T 66, T 63 T 68 ∀p(¬gKp → ¬gWp) T 66 T 69 ∀p(gK¬p → ¬gWp) T 67 T 70 ∀p(gWp → p) T 5, T 66 W ha te ve r G od w ills i s the c a se ; or G od’ s w ill is a lw a y s f ulf il le d T 71 ∀p(p → ¬gW¬p) T 70, ¬p/p, Co ntr a pos. T 72 ∀p(gWp → ¬gW¬p) T 70, T 71 T 73 ∀p(p → gPp) D 14, T 71

E ve r ythin g w h ic h oc c ur s ( w h ic h i s a f a c t) is pe r mit te d ( no t pr e ve nte d) by G od; i. e . G o d doe s not w il l tha t it doe s not oc c ur ( c f . T 71)

T 74 ∀p(gKp → ¬gW¬p) T 5, T 71 T 75 ∀p(gKp → gPp) T 5, T 73

W ha te ve r G od know s to be t he c a se ( i. e. w ha t is a f a c t) G od pe r mit s ( or doe s not pr e ve nt) to be the c a se

T 76 ∀p[(p ε Tg’s Will w.r.t. man) → gPp] T 1, D 6. 1 T 77 ∀p[(p ε Tg’s Commands) → (p ε Tg’s Will w.r.t. man)] D 13, D 15 T 78 ∀p(p ε Tg’s Commands → gPp) T 76, T 77

E ve r ythin g t ha t be lo ngs to ( t he the or e ms of ) G od’ s c o mma n ds is pe r mitte d ( no t pr e ve nte d) by G od

T 79 ∀p(p ε Tg’s Commands → ¬gW¬p) T 78, D 14 T 80 ∀p(¬p ε Tg’s Commands → ¬gWp) T 79, ¬p/p

I f ¬p be long s to G od’ s c om ma nds the n it is no t t he c a se tha t G o d w ill s tha t p

T 81 ∀p(¬p ε Tg’s Will w.r.t. man → gP¬p) T 76, ¬p/p T 82 ∀p(gCp → gWp) D 5

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T 83 ∀p(gCCp → gCWp) D 5. 1 O bse r ve tha t the oppos ite im plic a t i ons o f T 82 a nd T 83 do not hold ; sinc e G od( ne c e ssa r ily or by hi s ow n na t ur e ) w ill s ( a nd c a n w il l) h is o w n e xiste nc e a nd his goo dne ss bu t he doe s not ( a nd c a nnot) c a use it. A s a f ir st c a use he is only r e la te d to h is c r e a tion a nd c r e a tur e s but w ith hi s w il l h e is r e la te d to b oth, t o hi mse lf a n d to his c r e a tion a nd c r e a tur e s. I n my book o n e vi l ( 200 3, E D K ) I u se d t he t w o de f ini tio ns gWp ↔ gCp a nd gCWp ↔ gCCp. F or the r e a sons give n a bove the y a r e too str ong; o nly the impl ic a tion s e xpr e sse d in T 82 a nd T 83 a r e c or re c t. H ow e ve r f or the de r iva tion of t he or e ms in my boo k on e vil ( 2003, E D K ) I use d in f a c t only T 8 2 a nd T 83 a n d not the opp osi t e impl ic a tion s. T hus n o the or e m w hic h is too s tr ong w a s in f a c t de r ive d i n ( 2003, E D K )

T 84 ∀p(gCp → gCWp) D 5, A 2 T 85 ∀p(¬gWp → ¬gCp) T 82 T 86 ∀p(¬gCWp → ¬gCCp) T 83 T 87 ∀p(¬gCWp → ¬gCp) T 84 T 88 ∀p[(p ε T(CR) ∧ gWp → (¬(p ε T(g)) ∧ ¬(p ε T(LM)))] A 3, D 5, D 5. 1 T 89 ∀p[gCp → [Cons(p) ∧ Cons({p} ∪ Tg’s Essence) ∧ Cons({p} ∪ Tg’s Commands)]] T 84, D 4

W ha te ve r G od c a use s ( T 89) a nd w h a te ve r G od c a n c a use ( T 90) is c onsis te nt a nd c onsis te nt w i th his e sse nc e a nd his c omma nds. O n the othe r ha nd if a ny sta te of a f f a ir s is inc onsis te nt i n itse lf or inc ons iste n t w ith G od’ s e sse nc e or c om ma nds he c a nnot c a use i t ( a nd doe s not c a use it) .

T 90 ∀p[gCCp → [Cons(p) ∧ Cons({p} ∪ Tg’s Essence) ∧ Cons({p} ∪ Tg’s Commands)]] T 83, D 4

13.25 God’s Knowledge and Will in Relation to Moral Evil D 23 p e ME ↔ [p e E ∧ ¬Cons({p} ∪ Tg’s Commands )]

p is a mor a l e vil if f p is a n e vil a nd p is inc ons i ste n t w ith the t he or e ms of G od’ s c omma nd s

D 23. 1 p e E ↔ p is some la c k, de f e c t, a bse nc e, pr iva tion or de f ic it of some pa r tic ula r good w h ic h e ithe r oug ht t o be pr e se nt in a subje c t or

or ga nis m or is a c c e pta ble to be a bse nt in or de r to a c hie ve a nothe r hi ghe r good

D 24 ¬Cons({p} ∪ Tg’s Commands ) ↔ (∀x∈H)(gWxSW¬p ∧ gWxSA¬p)

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T 91 ∀p[p e ME → ¬Cons({p} ∪ Tg’s Commands )] D 23 T 92 ∀p[¬p ε Tg’s Will w.r.t. man ↔ ∀x∈H[gW(xW¬p) ∨ gW(xA¬p) ∨ gW(xSW¬p) ∨ gW(xSA¬p)]] D 15, ¬p/p T 93 ∀p[¬Cons({p} ∪ Tg’s Commands ) → ¬p ε Tg’s Will w.r.t. man] D 24, T 92 T 94 ∀p[p e ME → ¬p ε Tg’s Will w.r.t. man] D 23, T 93 T 95 ∀p[¬p ε Tg’s Will w.r.t. man → ¬(p ε Tg’s Will w.r.t. man)]

I ndir e c t Pr oof : A ssu me the c on tr a r y: ¬p ε Tg’s Will w.r.t. man ∧ p ε Tg’s Will w.r.t. man. T he n ¬p a nd p be lon g to the the or e ms of G od’ s w ill w . r . t. ma n, suc h tha t G od’ s w il l is i n c onsis te nt w hic h is i mpo ssi ble . T he r e f or e T 95.

T 96 ∀p[p e ME → ¬(p ε Tg’s Will w.r.t. man)] T 94, T 95 T 97 ∀p(p e ME → gP¬p) T 94, T 76 T 98 ∀p(p e ME → ¬gWp) T 97, D 1 4 T 99 ∀p(p e ME → ¬gCp) T 98, T 85 T 100 ∀p[(p ∧ p e ME) → (¬gWp ∧ ¬gW¬p)] T 98, T 71

I f p is a m or a l e vi l tha t oc c ur s, t he n ne i the r G od w il ls tha t p oc c ur s nor G od w ill s tha t p doe s no t oc c ur ( othe r w ise it w ould no t oc c ur )

T 101 ∀p(p → ¬gC¬p) T 71, T 85, ¬p/p T 1 02 ∀p[(p ∧ p e ME) → (¬gCp ∧ ¬gC¬p)] T 99, T 101 I f p is a mor a l e vil a nd p oc c ur s the n ne ithe r G od c a use s tha t p oc c ur s nor G od c a use s tha t p doe s not oc c ur . T 103 ∀p[(p ∧ p e ME) → p ε T(CR)]

I ndir e c t Pr oof : A ss ume (p ∧ p e ME) ∧ ¬(p ε T(CR)). T he n p ε T(g) or p ε T(LM). Bu t it i s imp oss ible tha t p ε T(g) ( i. e . tha t G od c ommits a mor a l e vil) , i. e . ¬(p ε T(g)). T he n p ε T(LM). But thi s i s a ls o i mpo ssi ble be c a use the s ta te of a f f a ir s of a n oc c ur in g m or a l e vi l c a nno t be a the or e m of logic s a nd ma the ma t ic s ( se e de f ini tion s D 3. 2 a nd D 7) . T he onl y possi bil ity le f t i s the n tha t p ε T(CR), i. e . tha t p be longs to the the or e ms a bout c r e a tion or c r e a tur e s ( viz . ma n) . O r in othe r w or ds: Mor a l e vil tha t oc c ur s be longs to t his w or ld ( be c a use it is c a use d by inha bi ta ns of th is w or ld) .

T 104 ∀p[(p ∧ p e ME) → gKp] T 103, T 17 T 105 ∀p[(p ∧ p e ME) → (gKp ∧ ¬gWp ∧ ¬gW¬p)] T 104, T 100

I f p is a m or a l e vi l a nd if p oc c ur s th e n G od know s t ha t p oc c ur s b ut ne ithe r G od w i lls t ha t p oc c ur s nor G od w ills tha t p doe s n ot oc c ur . T ha t m e a ns tha t G od doe s n ot e nga ge h is w ill in m or a l e vil tha t oc c ur s ( e xc e pt

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in the se nse of pe r mitta nc e ) . I n othe r wor ds: the c a se of oc c ur ing mor a l e vil sh ow s tha t w ith r e s pe c t to the se s t a te s of a f f a ir s G od’ s know le d ge e xc e e ds G od’ s w ill.

T 106 ∀p[gCWp → Cons({p} ∪ Tg’s Commands) ] T 1, D 4 I f G od c a n w ill p the n p is c onsis te nt w it h ( the the or e ms of ) his c omma nd s. T 107 ∀p(p e ME → ¬gCWp) T 106, T 91 I f p is a mor a l e vil the n G od c a nnot w ill tha t p oc c ur s ( c f . T 98) . T 108 ∀p(p e ME → ¬gCCp) I f p is a mor a l e vil the n G od c a nnot c a use tha t p oc c ur s ( c f. T 99) T 109 ∀p[(p ∧ p e ME) → (gKp ∧ ¬gCWp ∧ ¬gCCp)] T 104, T 107, T 108

I f p is a mor a l e ma il a nd if p oc c ur s, the n G od know s tha t p oc c ur s but ne ithe r G od c a n w ill tha t p oc c ur s nor G od c a n c a use tha t p oc c ur s. I n othe r w or ds the c a se of oc c ur ing mor a l e vil show s tha t w i th r e spe c t to the se sta te s of a f f a ir s G od’ s know le dge e xc e e ds G od’ s pow e r .

T 110 ∀p[(p ∧ p e ME) → (gKp ∧ ¬gCp ∧ ¬gC¬p)] T 102, T 104 A 7 ∃p(p ∧ p e ME) T he r e is mor a l e vil ( w hic h oc c ur s) T 111 ∃p(p ∧ ¬gWp) A 7, T 98 T 112 ¬(∀p)(p → gWp) T 111 G od doe s not w i ll e ve r ythi ng tha t i s the c a se T 113 ¬(∀p)(p → gCp) T 99, A 7

G od doe s not c a use e ve r yt hin g tha t is th e c a se ; f or e xa mple G od doe s n ot c a use mor a l e vil of f r e e d ec isions of ma n

T 114 ¬(∀p)(p → gCWp) A 7, T 107 G od c a nno t w ill e ve r yth ing tha t is the c a se ; f or e xa m ple G od c a nno t w il l ( a nd c a nnot c a use ) mor a l e vil

T 115 ¬(∀p)(p → gCCp) A 7, T 108 G od c a nnot c a use e ve r ything tha t i s the c a se D 25 x ∈ AW ↔ ∀p(xWp ∨ xW¬p) x is a llw ill ing if f f or a ll sta te s of a f f a ir s p: x w ills tha t p or x w ill s tha t ¬p D 25. 1 x ∈ AC ↔ ∀p(xCp ∨ xC¬p)

x is a llc a usi ng if f f or a ll sta te s of a f f a ir s p: x c a use s tha t p or x c a use s tha t ¬p

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T 116 ¬(∀p)(gWp ∨ gW¬p) G od is not a ll w il lin g A 7, T 100: ∃p(¬gWp ∧ ¬gW¬p) T 117 ¬(∀p)(gCp ∨ gC¬p) G od is not a llc a u sing A 7, T 102: ∃p(¬gCp ∧ ¬gC¬p) T 118 g ∈ OS ∧ g ∈ OM ∧ ¬g ∈ AW ∧ ¬g ∈ AC T 1, T 116, T 117, D 25, D 25. 1 G od is om nisc ie n t a nd a lmi ghty b ut ne it he r a llw illi ng nor a llc a usi ng T 119 ∃p(gKp ∧ ¬gWp ∧ ¬gW¬p) T 105, A 7

For so me sta te s of a f f a ir s it ho lds : G o d know s the m, bu t ne i the r G od w ill s tha t the y oc c ur nor w il ls t ha t the y do not oc c ur . I n othe r w or ds : For some p, G od know s tha t p a nd pe r mi ts t ha t p but doe s no t w ill t ha t p ( se e D 14)

T 120 ¬(∀p)[gKp → (gWp ∨ gW¬p)] T 119 N ot e ve r ythin g w hic h is k now n by G o d is sub je c t to his w i ll i n the se nse tha t it i s e ithe r w ille d to oc c ur or w ille d not to oc c ur . But ob se r ve tha t it holds : E ve r yth ing is e it he r w ille d or pe r mit te d by G od:

T 121 ∀p[p → (gWp ∨ gPp)] T 73 E ve r ythin g w ha t is t he c a se is e ithe r w ille d or pe r mit te d ( not pr e ve nte d) by G od

T 122 ∀p[gKp → (gWp ∨ gPp)] T 5, T 121 E ve r ythin g w hic h is kno w n to be the c a se by G od is e ithe r w ille d or pe r mitte d ( no t pr e ve nte d by hi m)

T 123 ∃p(gKp ∧ ¬gWp) T 119 T 124 ¬(∀p)(gKp → gWp) T 123 N ot e ve r ythin g w hic h is kn ow n by G od i s a lso w ille d b y him T 125 ∃p(gKp ∧ ¬gCp ∧ ¬gC¬p) T 110, A 7

For so me sta te s of a f f a ir s it ho lds : G o d know s the m, bu t ne i the r G od c a use s the m to oc c ur nor c a use s the m no t to oc c ur

T 126 ¬(∀p)[gKp → (gCp ∨ gC¬p)] T 125 N ot e ve r ythin g know n by G o d is sub je c t to his c a usa tion T 127 ¬(∀p)[gKp → gCp] T 125 N ot e ve r ythin g w hic h is kn ow n by G od i s c a use d by G od T 128 ∃p(gKp ∧ ¬gCWp) T 109, A 7 T 129 ∃p(gKp ∧ ¬gCCp) T 109, A 7 T 130 ¬(∀p)(gKp → gCWp) T 128 N ot e ve r ythin g w hic h is kn ow n by G od c a n be w ille d by him

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T 131 ¬(∀p)(gKp → gCCp) T 129 N ot e ve r ything w h ic h is know n by G od c a n be c a use d by him. O bse r ve tha t t his i s no t a w e a kne ss of pow e r bu t a s ign of pe r f e c t ion : he c a nnot c a use mor a l e vil

T 132 ∀p[(p ∧ p e ME) → gPp] T 100, D 14 I f mor a l e vil ( in f a c t) oc c ur s the n G od p e r mits ( doe s not pr e ve nt) i t; s inc e he c r e a te d ma n w ith f r e e w ill a nd is n or ma tive a nd vo lit ive c onsi ste nt ( N C, c f . D 6. 1 a nd D 15) . But ob se r ve t ha t f r om T 13 2 it d oe s not f o llo w tha t G o d pe r mi ts ( d oe s no t pr e ve nt) e ve r y mor a l e v il; i. e . ∀p(p e ME → gPp) is no t a t he or e m. T hu s G o d ma y p r e ve nt so me m or a l e vil in a w a y w hic h doe s not ta ke a w a y f r e e w ill f r om the a c ting huma n pe r son.

T 133 ∀p[p e ME → (¬gWp ∨ l gWp ∨ ¬gW¬l p)] T 98 T 134 ∀p[p e ME → ¬(gWp ∧ ¬l gWp ∧ gW¬l p)] T 133 T 135 ∀p[p e ME → ¬(p ε Tg’s Will about CR)] D 12. 2, T 134, T 96

I f p is a mor a l e vi l, the n i t is n ot t he c a se tha t p be l ongs to the the or e ms of G od’ s w il l a bou t c r e a tion a nd c r e a tur e s. O bse r ve how e ve r t ha t i t doe s not f o llow f r om t ha t, tha t in t his c a se G od w ill s t ha t non-p ; s inc e the n mor a l e vil w ou ld ne ve r oc c ur ( be c a use his w ill i s a lw a ys f ulf il le d) . T he r e f or e if mor a l e vil ( in f a c t) oc c ur s, G od pe r mit s i t ( d oe s n ot pr e ve nt it) , c f . T 132.

13.26 God knows his activities A 8 gOp → gK(gOp) W he r e O is one of the ope ra tions W, CW, C, CC, A, P. T 136 gK(gOp) → gOp T 5 T 137 gOp ↔ gK(gOp) A 8, T 136 G od ha s know le d ge of a ll his a c tivit ie s r e pr e se nte d by W, CW, C, CC, A a nd P. T 138 gWp ↔ gK(gWp) A 8 T 139 gCWp ↔ gK(gCWp) A 8 T 140 gCp ↔ gK(gCp) A 8 T 141 gCCp ↔ gK(gCCp) A 8 T 142 gAp ↔ gK(gAp) A 8 T 143 gPp ↔ gK(gPp) A 8 T 144 gCWp ↔ [Cons(p) ∧ Cons({p} ∪ Tg’s Essence) ∧ Cons({p} ∪ Tg’s Commands)] T 1, D 4

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T 145 gCWp ↔ gK[Cons(p) ∧ Cons({p} ∪ Tg’s Essence) ∧ Cons({p} ∪ Tg’s Commands)] T 139, T 144 G od c a n w ill tha t p ( or ha s pow e r w . r . t. p) if f G od know s tha t p i s

c onsis te nt a nd tha t p is c on sis te nt w i th hi s E sse nc e a nd w ith his Co mma nd s.

T 146 gCCp → gK[Cons(p) ∧ Cons({p} ∪ Tg’s Essence) ∧ Cons({p} ∪ Tg’s Commands)] T 83, T 145

I f G od c a n c a use tha t p ( or ha s the p ow e r to c a use tha t p ) the n G od know s tha t p is c o nsi ste nt a n d p i s c ons iste nt w it h hi s E s se nc e a nd w it h his Co m ma nds.

T 147 gK(gWp) → gKp T 66, T 138 T 148 gK(gCp) → (gWp ∧ gKp) T 82, T 66, T 140 T 149 p → gK(gPp) T 73, T 143 T 150 gK(gCp) → (gK(gCCp) ∧ gK(gCWp)) A 2, A 3, T 83, T 141

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183

Subject Index actual event, ambiguity of, 127 all, 136 allcausing, 46, 58, 169 allcausing God, 46, 59, 169 allwilling, 46, 59, 169 allwilling God, 48, 59, 169 anthropic principle, 46 A-propositions, 68, 74 arithmetically expressible, 145 atemporal, 107 axiom systems, limitations of, 146 axiomatisable, 135, 144, 148, 150 causal relation, 44, 53, 58, 60, 118 causing and willing, 44, 47 chance, 38, 45 characteristica universalis, 142, 145 closed propositions, 112 coding system, 145 complete knowledge, 126, 143, 149 completeness, 143, 149 consistency, 44, 47, 148 constant, 162 contingency, 100, 102, 105, 131 contingent, 16, 100, 105 contingent status, 105, 131 contribution of imperfect creatures,

56 copula 'is', 153 counterfactuality, 53, 85, 93, 120 counterfactuals, knowledge of, 93,

95, 120 creation, 140, 159 decidable, 136, 143, 147, 151 degrees of freedom, 71 determinably false, 107 determinably true, 107, 110 determinism, 106, 128

discursive knowledge, 73, 81 Divine Liar, 1, 10, 12 dynamical law, 69, 72, 88 elementhood relation, 153 eternity, 31 event, 162 fact, 50, 129 FADW, 120 finitely analytic, 143 foreknowledge, 116, 128 free action or decision of will, 45,

121, 129, 133 future contingency, 101, 105, 108,

110, 123, 131, 141 future contingency, consistency of,

131 future necessity, 101 future probabilistic contingency,

101, 105 future states of affairs, 116, 119,

125, 131, 141, 164 goal, subordinating under, 44 Gödel numbers, 145 God's commands, 159 God's essence, 138, 159 God's knowledge about the

universe, 161 God's knowledge and truth, 113,

137, 160 God's power, 41, 48, 139 God's will, 43, 46, 47, 58 God's will about creation, 159 God's will w.r.t. man, 57, 159 immutable, 81, 83, 164 impossible, 86 impossible, logically, 86 incompatible with laws of nature,

86 indeterminism, 45, 70

184

infinite, 150 infinitely analytic, 143 initial condition, 46, 162 initial state, 46 irreflexivity, 60, 118 irrelevant truths, 67, 73, 136, 151 KCH, 80 knowing and causing, 55, 58, 168 knowing at some time, 26, 35, 76,

82, 110, 124 knowledge, 3, 7, 42, 52, 135, 138 knowledge about creation, 19, 140,

159, 161 knowledge about himself, 19, 138,

170 knowledge about logic and

mathematics, 141 knowledge and belief, 7, 15 knowledge and falsity, 91 knowledge and power, 42, 47, 121 knowledge and truth predicate, 108,

145 knowledge and will, 19, 23, 47, 55,

165 knowledge, change of, 79, 81, 83,

164 known as actual, 115, 122, 125, 128 known in their causes, 115, 117,

120, 128 KT, 4 law, 69, 162 law of entropy, 71 law without law, 71 law-necessity, 108 learning process, 56, 87 logic and mathematics, 142 logic and mathematics, limitations

of, 145

logical and deductive infallibility, 6, 89

logical and deductive omniscience, 5, 89

logical necessity, 99 logically determined, 98 mathematical necessity, 99 mathematisation, 142 microstates, not realised, 88 middle knowledge, 95, 120 moral evil, 166 more geometrico, 142 mutable, 81, 83, 164 natural necessity, 99 natural necessity, conditional, 99,

101, 118 necessarily contingent, 15, 52 necessary cause, 61 necessary knowledge - knowledge

of the necessary, 22, 97, 139 necessary status, 102 necessity and time, 110 non-contradiction, principle of, 86 normative and volitive consistent,

57, 159 normatively inconsistent, 46 not actual, 90 NW, 86 omnipotence, 43, 47, 49, 139 omnipotence, definition of, 43, 156 omnipresent beinig, 125 omniscience and freedom, 53, 62,

116, 129 omniscience and necessity, 2, 15,

19, 115, 118 omniscience, definition of, 155 omnitemporal contingency, 102,

107, 110 operators, 154

185

paradoxes, 136 past and present, 37, 123, 127, 163 past necessity, 100 person, 154 possibility and time, 87, 110 probabilistic contingency, 100, 105 providence, 44, 48, 51 recursive, 136 recursively enumerable, 135, 151 seabattle, 106 singular truths, 67, 69 state, 162 states of affairs, different kinds, 99 states of affairs, not realised, 50, 87 states of affairs, status of, 99, 104,

109, 113 statistical law, 69, 71, 72, 74, 88 sufficient cause, 61 syllogism, 143

Tarski's truth condition, extension of, 11

time as chronological order, 29, 82 time of this world, 26, 32, 82, 125 time, analysis of, 26, 124 time, biological and psychological,

33, 82 transitivity, 53, 59, 118 true justified belief, 2, 13 truth predicate, 103, 107, 109, 145 truth predicate, time index of, 103,

107, 109 truth, reason for, 112 truths, set of, 135, 147, 150 twin paradox, 126 universe, 161 unpreventable necessity, 100 veritees de raison, 142 what is not, 85, 90 what is not, ambiguity of, 90

186

187

Name Index Anscombe, G.E.M., 106 Aristotle, 10, 16, 27, 44, 67, 85ff.,

90, 97, 106, 110, 112, 118, 121 Augustine, 31, 48, 54, 61, 67, 68,

74f. Barrow, J., 46 Batens, D., 86 Baumgartner, H.M., 33 Boethius, 31, 106 Boltzmann, L., 71 Breuer, Th., 127 Cain, J., 145 Casati, G., 72 Castaneda, H.N., 83 Chirikov, B., 72 Chisholm, R., 4 Church, A., 136 Craig, W.L., 54, 95 Damnjanovic, Z., 145 Devalla L., 115 Dobzhansky, Th., 7 Dworkin, R., 115 Eccles, J., 61 Ellis, G.F.R, 27, 119 Feys, R., 16, 108, 114, 153f. Fraenkel, A., 8, 137, 145, 147, 149 Gale, R., 68, 75f. Galles, D., 60 Gettier, E., 2, 14 Gödel, K., 8, 136f., 144ff. Grim, P., 1f., 9f., 13 Hafele, J.C., 126 Hausman, D.M., 93 Hawking, S.W., 27, 119 Hintikka, J., 4ff., 10, 16, 87, 106,

145 Hunt, D.P., 21

Inwagen, P. van, 45 Jammer, M., 27 Keating, R., 126 Kreisel, G., 144f. Kretzmann, N., 79f., 82 Kripke, S., 10, 145 Kutschera, F. von, 83 Leftow, B., 76, 85, 91f. Leibniz, G.W., 142ff., 149 Lenzen, W., 6 Lewis, D., 93 Lukasiewicz, J., 106 Marshall, D., 143 Matthew, 94 Maxwell, J.C., 99 Maynard-Smith, J., 7 Mittelstaedt P., 27f., 46, 53, 61, 69,

71f., 87f., 93, 99, 107, 119, 163 Molina, 95, 120 Moore-Ede, M.C., 33 Myhill, J., 145 Newton, I., 27, 69, 93, 99, 125, 156 Pearl, J., 60 Penzias, A., 33, 124 Pike, N., 54, 63ff. Plantinga, A., 65 Plotinus, 23 Popper, K.R., 61 Prigogine, I., 73 Prior, A.N., 29, 61, 106 Rescher, N., 86, 106, 142 Ruse, M., 119 Schrödinger, E., 71, 99 Schurz, G., 74, 145 Schuster, G., 72 Simmons, K., 13 Spinoza, B., 44, 53 Stump, E., 80 Sulzmann, F.M., 33

188

Takeuti, G., 145 Tarski, A., 10f., 90, 135, 145f. Thomas Aquinas, 3, 6f., 13f., 20f., 23, 28, 31f., 37, 40f., 43, 48, 51, 54, 57, 60f., 73, 76, 89f., 95, 98, 106f., 110, 115ff., 122f., 125, 139f., 146 Tipler, F., 46 Treismann, M., 33 Urquhart, A., 177

v. Neumann, J., 8, 14, 137, 146f. Van Benthem, I., 29 Weinberg, St., 33 Wheeler, A., 70f. William of Ockham, 116 Wilson, R., 33, 124 Wright, G.H. von, 16, 108, 114 Zagzebski, L, 116f. 130ff.