A Reply to the Kalam Cosmological Argument (v 7.4.1)

7/29/2019 A Reply to the Kalam Cosmological Argument (v 7.4.1)

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A Reply to the Kalam Cosmological Argument.

1. Introduction and some terminology .

2. An analysis of the proposed creato r, and the proposed creation account .

2.1. Timelessness.

2.1 .1 . Timelessness and change.

2.1.2 Timelessness, changelessness and quiescence.

2.1.2 .1. A brief analysis.

2.1.2 .2. ome terminology.

2.1.2 .!. Changes and infinity.

2.1.2 .". #iscrete time.

2.1.2 .$. An absolute temporal beginning.

2.1.2 .% & o ontological difference.

2.1.! . Timelessness sans creatio n. 'ore on Craig(s description .

2.1." . 'etrically amorphous time.

2.2. Conclusions based on the analysis of the proposed creator .

!. T h e f irst p remise of the KCA.

!.1. )eginning to e*ist and coming into e*istence . A n alternati+e principle .

!.2. Arguments in support of the first premise.

!.2.1. &othing comes from nothing .

!.2.2. Another alternati+e principle.

!.2.! . Is the uni+erse an unustified e*ception-

!.2.". mpirical e+idence.

4. The econd /remise of the KCA.

".1. 0ilbert(s 0otel.

".2. rim reapers.

".!.Aristoteliand iscrete time , infinite regres s and more grim reapers.

".". rim placers and3or grim signalers.

".".1. /ossibility of a grim placer.

".".2. Compressibility of spacetime.

".".! . Infinitary patch4or5 and binary patch4or5 .

".".". )inary patch4or5 suffices.".".$. Infinite past, undefeated.

".$ . An infinity by successi+e addition-


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".$.1. Tristram handy.

".$.2. 'ethuselah.

".$.! . 6rbits and parity.

".% . cientific cosmology.

".% .1. The 7riedmann89ema:tre 'odel.

".% .2. The )orde uth ;ilen5in Theorem.

".%.!. 6ther arguments based on scientific cosmology .

".% .". Cyclic models and others for an infinite past.

$. Conclusio ns.

%. &otes.

P1. Eer!thing that begins to e"ist has a cause.

P#. The unierse began to e"ist.

C. The unierse has a cause.

The KCA is defended b! some theist philosophers in combination with other arguments intended to

bridge the gap between the conclusion that the unierse has a cause and a conclusion that the cause

of the unierse is a being with certain properties$ in particular a personal agent of great power.

% will call the combination of the KCA with those other arguments$ &KCA'.

%n this essa!$ % will assess the KCA'$ and argue that it proides no support for the conclusion that

there is a powerful personal agent who created the unierse$ both b! challenging the premises of the

KCA itself$ and the creation account proposed in usual ersions of the KCA'.

b. % will focus mostl! on illiam *ane Craig+s ersion of the KCA'$ but % will also assess some

alternatie arguments.

c. % will use the word ,-argument+ to denote (depending on conte"t) either formal arguments (i.e.$

premises and conclusion)$ or the arguments (in the sense of -arguing a case+) gien in defense of

said premises these usages are common and shouldn+t cause confusion$ gien conte"t.

d. % will call the parts of this essa! -sections+ and -subsections+$ without using /sub0subsections/ or

similar terms. Conte"t and some lins between different parts of this essa! should preent

ambiguit!.

e. 2! ,incoherent, % mean that a claim is either meaningless$ or meaningful but contradictor!.

2. An analysis of the proposed creator, and the proposed creation account.


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According to illiam *ane Craig$ the creator proposed b! theKCA'is a personal being who is

timeless without creation$ and temporal with creation.

2ut that raises 3uestions lie: -hat does the word -timeless+ mean$ in this conte"t4, ,%s such claim

coherent4, -%s it compatible with the premises of the KCA4,$ etc.

%n this section % will assess some of those issues$ and generall! Craig+s creation account.

2.1. Timelessness.

The word -timeless+ is not a word collo3uiall! used$ in the releant sense.5 1 6

7et$ Craig does not seem to proide a clear definition$ which leaes the matter of the meaning of the

claim that 8od is timeless without creation but temporal with creation$ obscure at best.

%n order to tr! to understand what Craig means b! -timeless+$ or at least to appro"imate the concept$

one potential approach would be to loo at a list of entities that Craig calls &timeless and at a list of

entities that he does not call &timeless 0 and much better !et$ entities that he clearl! wouldcategori9e as nottimeless 0$ and tr! to grasp the meaning of the term -timeless+ from that.

ow$ entities that are not called &timeless b! Craig are eas! to find. ;oreoer$ he claims that 8od

is temporal with creation$ and gien his argumentation$ it seems clear that his position is that$ sa!$

horses$ planets$ humans$ etc.$ are not timeless.

till$ we ma! understand his e"ample as impl!ing that if &numbers e"ist were true ?

as an ontological claim 0$ then a number would be an e"ample of a timeless entit!.

@oweer$ that e"ample alone does not suffice to grasp the meaning of the word in Craig+s usage.

or does the combination of the e"ample of a number and the er! different e"ample of 8od.

>till$ perhaps we ma! add to the list some e"amples of entities ? or alleged entities ? called

&timeless b! some other philosophers. ;a!be Craig and those other philosophers are all using the

word -timeless+ in the same sense.

%f so$ on the list of timeless entities ? or candidates to timeless entities$ if the! were entities and

e"isted 0$ we would hae$ sa!$ the number $ the set of natural numbers$ the proposition that water

is H2O, etc.


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e3uialent to not standing in temporal relationships$ een if the meaning is not the same. That does

not seem to help much in m! iew$ but it+s something. ;oreoer$ there is another wa! of at least

approaching Craig+s concept of timelessness$ namel! considering some of the conse3uences of

timelessness according to Craig$ which one ma! deduce from some of his statements.

>o$ based on that$ and een though what Craig means b! -timeless+ remains obscure$ % will proceed

to anal!9e some of his claims.

2.1.1. Timelessness and change.

Craig claims that in his timeless state$ 8od is changeless$ or unchanging. @oweer$ Craig also

claims that 8od can change and changed and ceased to be timeless. 5 r B 6

2ut how can we mae sense of those claims4

e can understand the idea that an obect < remains changelessfor a while and then changes. That

means that < remains unchanged as time goes by$ during some period$ and after that period ends$ o$ the claim of changelessness is also er! obscure.

;oreoer$ in the conte"t of his defense of the KCA$ Craig claims that instantaneous changes are

impossible$ and that eer! eentDchange has a finite$ non09ero duration. 5 r 6

>o$ let+s consider the changein 8od from being timeless to being temporal. That is surel! a change$

in the usual sense of the word -change+ 0 which is Craig+s usage 0$ and so it follows from Craig+s

claims that it has a finite$ non09ero duration$ sa! d F.

Thus$ there is a temporal interal of non09ero duration d that ends at the first temporal state of the

world$ namel! the first state at which 8od is temporal. That entails there was a temporal interal of

non09ero duration d beforethere was time. 2ut that is absurd.

Craig actuall! addressed this obection or an essentiall! similar one on his website5 r G 6$ and

contended that:

a. hen he defines what &eent means5 r 6$ in the conte"t of his defense of the KCA$ he+s

tr!ing to rule out instantaneous changes$ and in that technical sense of -eent+,$ an!thing that

is instantaneous would not count as an eent.

b. The creation of the unierse b! 8od or$ for that matter$ 8od+s changing from timeless to

temporal$ would not 3ualif! as an eent in that sense$ since it+s instantaneous.

c. hen he said that 8od changed and ceased to be timeless$ he was using the word -change+

in a different sense from the sense in which he was using that word in the conte"t of the


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Kalam Cosmological Argument. Hurthermore$ when he said that 8od changed$ in that conte"t$

he merel! meant that 8od+s properties at his timeless state are different from his properties at

his first temporal state. 5 r G 6

d. %n an! case$ an! problem can be resoled simpl! b! stipulating$ in the conte"t of the

defense of the KCA$ that one is taling about changes of e3ual$ non09ero and arbitrar!

duration$ so the alleged contradiction can be resoled simpl! b! a clarification of one+s terms.

5 r G 6

@oweer$ all four claims a0d. aboe are mistaen$ for the following reasons:

a. Craig defined,-eent+ to mean -an! change+$ and then claimedthat becausean! change

taes time$ then under that definition$ there cannot be an! instantaneous eents$ which is

another wa! of sa!ing that becausean! change taes time$ there cannot be an! instantaneous

changes.@oweer$ it+s notthe case that an!thing instantaneous would not count as an ,-eent+ in that

sense of -eent+ ifthat instantaneous thing were a change. An! change$ instantaneous or not$

would be an eent$ b! definition. Iather$ in the conte"t of that defense of the KCA$ Craig

claims that any change takes time5 r 6$ and from that and the definition of ,-eent+ as ,an!

change+ 0 rather than from the definition of -eent+ alone ? he concludesthat there are no

instantaneous eents.

%n that conte"t$ Craig does not define -change+. Iather$ he uses ,-change+ in the usual sense$

and defines -eent+, in terms of -change+,.

The obection here is that the changein 8od from his timeless state to his first temporal state

would be$ well$ a change$ and as such$ b! Craig+s own claims$ it would hae a finite$ non09ero

duration$ resulting in a contradiction.

b. As before$ since -eent+ means -an! change+ in the sense in which Craig uses the term

-eent+, in the conte"t of his defense of the KCA$ 8od+s becoming temporal does 3ualif! as an

eent$ since that is clearl! a change in 8od. %f said change in 8od were instantaneous and had

no finite$ non09ero duration$ then that would contradict Craigsclaimthat an! change taes

time$ and has a finite$ non09ero duration.

c. %f b! sa!ing that 8od changed and ceased to be timeless$ Craig had merel! meant that

8od+s properties at his timeless state are different from the properties 8od has at his first

temporal state$ then for that matter Craig might as well had said that 8od changed and ceased

to be temporal$ becoming timeless. 2ut clearl!$ in conte"t$ that would be a er! different

claim.

>o$ considering conte"t$ one can ascertain that Craig did notmerel! mean that 8od has

different properties at those two states.


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;oreoer$ we can tell that when he said that 8od changed$ Craig meant that...8od changed$

using the word -change+, in the usual sense of that word in English.

The usual sense of -change+ is also the wa! in which Craig used -change+ in the conte"t of the

defense of the KCA as well5 r 6$ since he defined -eent+ in terms of change$ but gae no

definition of -change+ or made an! suggestion that he was using -change+ in a non0standard$

technical fashion.

d. >tipulating that one is going to tal about those eents in particular does not change the fact

that the claimthat an! change taes time and has a finite$ non09ero duration$ plus the claim

that 8od changed from a timeless state to a first temporal state$ entails a contradiction. The

contradiction still follows from Craig+s claims.

%n m! assessment$ Craig+s contradictor! claims plus the fact that in his repl! to the obection

mentioned aboe he misunderstood the claims he had made earlier$ onl! compound the problem ofthe obscurit! of his creation account$ raising serious doubts about his own understanding of the

position he+s defending$ and of the coherence of said position.

>till$ we ma! consider whether there is a wa! out for a defender of a position similar to Craig+s.

%f there were a wa! out of this particular difficult!$ it would re3uire den!ing that an! change taes a

positie amount of time$ since time before time maes no sense$ and 8od clearl! changes$ on

Craig+s description or similar ones$ from a state at which he+s timeless$ to a state at which he is not

timeless.

@oweer$ den!ing that an! change taes a positie amount of time would raise another difficult!$

namel! that instantaneous changes seem to be a problem under a theor! of time that maintains that

time is discrete$ which is the ind of theor! defended b! Craig and usuall! espoused b! defenders

of the KCA'.

;ore precisel!$ if time is dense$ and ? for instance ? there are two temporal interals AJ5a$ b) and

2J5b$ c)$ then the temporal distance between A and 2 is 9ero. %f P obtains all through A$ and P

obtains all through 2$ there is a sense in which it maes sense to sa! that the change from P+s

obtaining to P+s not obtaining is instantaneous. 7et$ if time is discrete$ this option is not aailable$

and it+s hard to see how one can mae sense of instantaneous changes in discrete time.

2ut let+s consider other difficulties$ independent from the preious obection.

2.1.2. Timelessness, changelessness and quiescence.

According to Craig$ the unierse cannot hae e"isted in an &absolutel! 3uiescent state$ lie 8od+s

? alleged ? initial timeless state. 5 r 6

@oweer$ as in the case of changelessness$ that raises the 3uestion of how we can mae sense of

such a claim5 # 6. Lsuall!$ we would understand that a 3uiescent obect is one that is at rest as time

goes by$ but gien Craig+s claim of timelessness$ the claim of 3uiescence is pu99ling.


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%n the rest of this subsection$% will continue to anal!9e that claim$ as well as the claim of

changelessness in the conte"t of his creation account.

2.1.2.1. A brief analysis.

*et+s consider first two scenarios$ ordering states of the world causall!.

cenario a?

First state of the world:

Timeless state >. The onl! obect that e"ists is


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some uF$ and that there are times arbitraril! close to 9ero$ but not an initial moment. @oweer$

Craig+s position entails that such open interal is impossiblebecause it would be an actual infinit!$

so this obection would fail.

%n the following subsections$ % will anal!9e this matter in greater detail.

2.1.2.2. ome terminology and assumptions for the rest ofsubsectio n 2.1.!.

1.% will use use bold$ italic$ uppercase letters (e.g.$J,K$ etc.) to denote finite temporal interals$

and bold italic lowercase letters (e.g.$ t, u$ etc.) to denote temporal instants. % will also number them

(e.g.$ t(1), t(2)$ etc.).

2. hen % tal of temporal interals or instants$ %+m taling about actual features of the world ?

whateer those happen to be 0$ not about mathematical models.

!. hen % spea of temporal interals$ %+m assuming those interals are of finite duration$ though

not necessaril! of e3ual duration.".2! ,M, % mean -earlier than+$ in the usual$ temporal sense of -earlier+,. Hor instance$JMKmeans

thatJ andK do not oerlap in an! interal of non09ero duration$ andJhappens earlier thanK.

$. @hen I pro+e lemmas, unless other4ise stated, I(m assuming any parts of Craig(s position,

as required.%n other words$ those lemmas are statements that follow from Craig+s position. % will

e"plain wh! that is his position when such e"planation is needed.

2.1.2.!. Changes and infinity.

9emma 1?%nfinitel! man! actual changes in the world are impossible$ regardless of whether

their duration is e3ual.

Proof:

This can easil! be seen in Craig+s defense of the KCA. Hor e"ample$ he claims that an infinite

temporal regress is an actual infinit!. 5 r N 6%n conte"t$ Craig is taling about changes of e3ual

temporal length$ but clearl!$ his claim that the! constitute an actual infinit! in the sense of

cardinalit! does not depend on their length$ and he claims that such infinities are impossible.

2.1.2.". #iscrete time

#efinition: A temporal interalJhas propert! O if and onl! if there is some positie integer

(J)$ such thatJdoes not hae more than (J)temporal subinterals different from each

other. E3uialentl!$Jhas propert! O if and onl! if it is not the case that there are more actual

different temporal subinterals ofJ than an! natural number.

9emma 2?%f there are temporal interals$ then eer! temporal interalJhas propert! O.

Proof:

*et+s assume there is a temporal interalJthat does not hae propert! O.

2! lemma 1$ there are onl! finitel! man! actual changes that happen in the world duringJ. >o$ let

m #be a natural number greater than the number of actual changes during B.


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>inceJdoes not hae propert! O$ there is some natural number r 2D mE (for instance)$ such that

J actuall! has r different temporal subinterals$J(1),J(2), J(3).., J(r).

*et us consider the following changes$ for in 1$...$r01Q

5E? od changes from not 5no4ing thatJ(k)is past to 5no4ing thatJ(k)is past.

75E? od changes from not 5no4ing thatJ(k)is present to 5no4ing thatJ(k)is present.

ote that those are actual changes in the world$ more precisel! in the mind of 8od. 8ien that the

interals are different from each other$ there are at least r1 m distinct changes$ contradicting the

assumption. That proes lemma #$ under the assumption that 8od e"ists$ which is clearl! Craig+s

position.

9emma !? %f there are temporal interals$ eer! such interal J is diided in finitel! man!

ordered temporal interals$ each of which has no actual proper subinterals.

Proof:*et n(J) be the total number of actual temporal subinterals of each subinteralJ;b! lemma 2. n(J)

is finite for allJ.

Then$ gien some interalK$ if n(K)J1$ we+re through$ sinceKhas no proper subinterals.

>uppose that lemma = is true for an!J such that n(J) R n$ for some n 1$ and letKbe such that

n(K)Jn.

Then$ letK(1)be a proper subinteral ofK. Then$ b! h!pothesis$ the lemma applies both toK(1)

and to an! part ofKbefore and afterK(1). Then$ b! induction$ the lemma is proed.

9emma "? %f there are temporal instants$ then for eer! two instants tand usuch that t M u$

there is some nonnegatie integer (t, u)$ such that there are no more than (t, u) instants

between t and u.

Proof:

>imilar to the proof of lemma #$ with the re3uired changes to address instants instead of interals.

9emma $: Either there are temporal interals that do not hae actual diisions (i.e.$ no actual

proper subinterals)$ or there are instants.

Proof:


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Proof: *et+s assume there are infinitel! man! past interals K(n)F, for all natural numbers n.

*et+s consider the eents

nE? od changes from not 5no4ing thatK(n)is past to 5no4ing thatK(n)is past.

0nE? od changes from not 5no4ing thatK(n)is present to 5no4ing thatK(n)is

present.

Then$ there are infinitel! man! actual past changes$ contradictinglemma 1.

That proes that if there are temporal interals$ there are finitel! man! past ones$ assuming that 8od

e"ists ? which is Craig+s position 0$ and other parts of his position.

>ince each such interal is diided in finitel! man! subinterals each of which has no proper

subinterals b! preious lemmas$ then it follows that if there are temporal interals$ then there are

finitel! man! past interals with no proper subdiisions$ and a first such interal K().

%f there is some other interalJ such that begins earlier thanJ thanK()$ then b! lemma =we candiideJin interals that are not further diided$ and one of them would be earlier than K()$ a

contradiction.

2! a similar procedure$ we can construct a second one$ and so on$ and the total number up to the

present time must be finite b! lemma 1$ since otherwise we could construct an infinite se3uence of

temporal changes.

That proes lemma G.

9emma


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that 8od nows that there are at least n past instants.

>o$ if n$ then the states T() and T(n) are actuall! different from each other. Also$ since each T(n)

corresponds to a single instant$ it has no proper temporal subdiisions.

%f there are no instants$ then there are interals with no proper subinterals b! lemma . >o$ let T(n)

be the state of the world atK(n)$ for all past interals with no proper temporal subinterals$ and

taingK(n) MK(n!1).

Then$ for n$ at T() 8od nows thatK(n)is past and that there are at least n past interals with no

proper subinterals$ whereas at T(n)$ it is not the case that 8od nows thatK(n)is past and it is not

the case that 8od nows that there are at least n past interals with no proper subinterals. >o$ if

n$ then the states of the world T() and T(n) are different from each other.

Also$ since each T(n) corresponds to a single interal with no proper subinterals$ there are no

actual temporal diisions in each state T(n).This establishes lemma S.

2.1.!.%. &o ontological difference

*et+s consider now the following two scenarios$ ordering the states in terms of causal priorit!.

cenario 1?


Timeless state >.

The onl! obect is 8od$ which e"ists timelessl! at > and without a cause of his e"istence.

Second state of the world:

Hirst temporal state T(F).

8od e"ists temporall!$ and the unierse5 B 6 e"ists. The change from the first to the second state

of the world$ including the creation of the unierse and 8od+s own change from timeless to

temporal$ taes place because 8od intends to bring it about.

hird state of the world:

>econd temporal state T(1). The obects are 8od$ the unierse$ and perhaps some other

obects.

cenario 2?


Hirst temporal state T(F).

The onl! obect is 8od$ who e"ists temporall! at T(F) and without a cause.


>econd temporal state T(1).

8od e"ists temporall!$ and the unierse e"ists. The change from the first to the second state of

the world$ including the creation of the unierse$ taes place because 8od intends to bring it


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about.

hird state of the world:

Third temporal state T(#). The obects are 8od$ the unierse$ and the same other obects as in

scenario 1(if an!)$ with the same causes.

%t appears that een though the word -timeless+ is used in the first scenario$ the first causal state in

scenario 1is ontologicall! no different lie the first temporal and causal state T(F) in scenario #. %n

other words$ it seems those aren+t reall! two scenarios$ but one scenario with two different labels.

This is so because:

i. %n both cases$ what we hae is a first state of the world changinginto the ne"t$ then the

ne"t$ and so on.

ii. %n both cases$ 8od e"ists without a cause of his e"istence at the first state of the world.

iii. %n both cases$ the unierse e"ists at the second state of the world$ and e"ists because 8odintends to bring it about$ and so on.

i. 8enerall!$ one is not able to find a distinction on those states b! inspection of the

description$ other than the difference in the words that are used.

Also$ sa!ing that the difference between the two scenarios is that one state ? namel!$ state > in

scenario 1 ? is timeless and changeless and the other ? namel!$ T(F) in scenario # ? is temporal and

changing$ or that in one of them there at least one tensed fact$ whereas in the other one there are no

tensed facts$ etc.$ would fail to address the obection$ since that would ust amount to denyingthat

there is no ontological difference$ without e"plaining howor whythat is so$ which is a burden on

the defender of the KCA '$ since it seems intuitiel! er! plausible that the states are ontologicall!

identical ust b! looing at the description of those states$ regardless of the word -timeless+.

%n particular$ one can tell that despite the claim that the first state in scenario 1is said to be timeless$

it is notchangeless. %n fact$ -both+ states are not changeless$ and for the same reason$ namel! that

ust as 8od changes from his first to his second state in scenario #$ he does so in scenario 1.

>o$ it seems it remains the case that there is an entit! ? i.e.$ 8od ? that e"ists at a first state of the

world and without a cause of his e"istence$ changes to a second state$ then to a third one$ etc.$

regardless of whether the first state of that entit! is called "timeless.

Thus$ ifthe concept of timelessness is coherent and entails changelessness$ then scenario 1is

improperl! described as timeless$ since the first state is not changeless$ and hence not timeless. %t

appears$ then$ that scenario 1is ust scenario #$ plus a false claim of timelessness.

*et+s consider now potential obections$ claiming ontological differences between scenario 1and

scenario #.

"b#ection 1$#n ontological differencebetweenscenario $andscenario 2is that temporal

states of %od mustchange as time goes by, whereas the timeless state S in scenario 1could


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ha&e remained unchanged'

(n other words, if %od e!ists at temporal state )*+ as in scenario #?, then necessarily,

there will be a second temporal state )$+, and necessarily, %od will change from )*+ to

)$+' On the other hand, if %od e!ists in a timeless state S )as in scenario 1+, then it is

%ossible, gi&en that first timeless state S of %od, that %od ne&er changes'

The problem with that obection is that it follows from an! creation h!potheses posited b!

defenders of the KCA '? i'e', gi&en what %ods first state actuallywould ha&e been, based on the

implications of their claims $ that it is im%ossiblethat 8od neer changes gien thatparticularfirst

allegedl! timeless state >$ which shows bothscenario 1and scenario #are indistinguishable in that

regard as well$ as the following reasoning shows (as usual$ the states of the world are ordered

causall!):

cenario !?First state of the world:

Timeless state >. The onl! obect is 8od$ who e"ists timelessl! at > and without a cause.


Temporal state T(F). 8od e"ists temporall!$ and the unierse e"ists temporall!. The change

from the first to the second state of the world$ including the creation of the unierse and 8od+s

own change from timeless to temporal$ taes place because 8od intends to bring it about.

cenario "?


Timeless state >,. The onl! obect is 8od$ which e"ists timelessl! at >, and without a cause.

There are no temporal states of the world.

%n scenario =$ if 8od does not intend at the allegedly timeless state & to change$ then at T(F) 8od

-ust found himself altered.

%n other words$ if 8od+s intent to change does not e"ist at the allegedly timeless state &$ then the

change is notsomething brought about because 8od intends to bring it about$ but something that

happenedto %od$ be!ond his intent.

That is so because the change under consideration is a change in 8od+s state$ andfrom the causally

first state >' %n other words$ it+s a changefrom S to T(F)'

>o$ if 8od does not intend at Sto bring about the change$ then said change cannot hae been caused

b! 8od+s intent at T(F) or at an! later state of the world$ gien that > is causally prior to T(F) and to

an! other state.

@oweer$ that contradicts the h!pothesis that the change in scenario =happens because %od intends

to bring it about$ rather than being something that happens to 8od.

Thus$ at >, 8od intends to bring about the change. @ence$ gien 8od+s state at >in scenario =$ it is


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impossiblethat 8od does not change$ since 8od can,t fail to bring about what he intends to bring

about.

;oreoer$ ust as in scenario =it is impossible that 8od does not change$ the same is true and for

the same reasons in scenario 1. Also$ the state > in scenario =is different from the state >, in

scenario B$ in which 8od does not change$ and so he does not intend to change.

>o$ if the concept of timelessness is coherent and state >, inscenario Bis a timeless state$ thenthat

state is ontologicall! different from an! initial state of the actual world posited b! defenders of the

KCA'$ which ? despite claims of timelessness ? remains ontologicall! indistinguishable from a

first temporal state$ as far as one can tell.

At this point$ someone might suggest that$ in scenario =$ 8od e"ercised his libertarian free will at

T(F) to bring about the change$ but at S$ it is not the case that he intends to change.

@oweer$ leaing aside issues about the coherence of libertarian free will$ that is impossible for thesame reasons % gae aboe$ namel! that since the change under consideration is 8od+s changefrom

S to )*+$ it was not decided at T(F) or later$ due to the causal priorit! of >.

Thus$ as shown aboe$ at S8od intends to change$ andgi&en S$ necessaril! 8od changes.

%f that conclusion is incompatible with 8od+s haing libertarian free will at >$ then that would not

bloc the conclusion % proed aboe ? since the argument goes through ust as well 0$ so that would

onl! mean that Craig+s description is incompatible with 8od+s haing libertarian free will at >$

creating a new problem for Craig+s account$ rather than resoling one.

$ the

point remains thatgi&en S$ necessaril! 8od changes$ and so obection 1 fails.

"b#ection 2.#n ontological differencebetweenscenario $andscenario 2is that gi&en the

first temporal state of %od in scenario 2, it is not only necessary but causally necessary that

the state changes, whereas gi&en timeless state S in scenario 1$ it is necessary that %od

changes, but not causally necessary'

Actuall!$ een if sometimes a state of affairs can determine but not causall! determine following

states$ this is not the case of the state > and 8od+s being in a different state later$ since gi&en S$ it is

necessar! and causally necessar! that 8od changes.

The reason for that is that the change in 8od from the timeless state > to the first temporal state T(F)

is a changefrom the causally first state of the world, and brought about by %od. >o$ gien that what

causes 8od to change from the first state > is that 8od intends to change$ and nothing at T(F) or

generall! later than > could hae caused a changefrom S$ then 8od intends to change at S$ and that

is causall! sufficient to bring about that %od changes'

"b#ection 3..hile its true that there is no ontological difference betweenscenario 1and

scenario 2, the initial state in both scenarios is timeless, not temporal' he scenario


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improperly described isscenario 2,rather thanscenario $'

Assuming for the sae of the argument that the first state of 8od is somehow is properl! called

-timeless+ in scenario 1for some reason$ then it seems that the same is true of the first state of the

uni&ersein the following scenario$ understanding that metaph!sical time begins with the unierse.

cenario $?


The unierse e"ists without a cause of its e"istence. othing else e"ists ? there ma! or ma!

not be some things in the unierse$ but nothing be!ond the unierse.


The unierse has changed and e"ists in its second state. othing else e"ists.

ust as 8od e"ists without a cause in scenario1$scenario #$and scenario =$ the unierse5 B 6 e"ists

without a cause in scenario . And ust as 8od changes from the first to the second state of theworld in scenario 1$ scenario #$ andscenario =$ the unierse so changes in scenario .

After that$ 8od in those scenarios continues to change from one state of the world to the ne"t$ and

the same is true of the unierse in scenario .

Also$ when the unierse changes from its first state to its second state$ there is no preious change$

and no period during which the unierse remains unchanged. 2ut that is e'actlywhat happens in the

case of 8od in scenario 1.

8ien the aboe$ there seems to be no sense of "/uiescent or "changeless in which the uni&erse

would fail to be /uiescent or changeless inscenario 0, but %od wouldnt fail to be so inscenario$'

>o$ there seems to be no ontological difference that would ustif! den!ing that the first state of 8od

is temporal in scenario1$ but wouldn+t ustif! den!ing that the first state of the unierse is temporal

in scenario .

>omeone might suggest that in scenario1and scenario #$ the change from the first to the second

state of the world$ including the creation of the unierse and 8od+s own change from timeless to

temporal$ taes place because 8od intends to bring it about$ whereas in scenario $the cause of the

change is not specified.

@oweer$ that would be unrelated to the issue of changelessness$ 3uiescence$ etc.$ and in an! case$

we ma! as well further specif! the scenario and add that$ in scenario $ the change from the first to

the second state of the unierse is brought about b! the unierse+s conditions at its first state

(including$ of course$ an! particles if there are an!$ etc.$ and generall! the unierse+s causal powers

andDor causal powers of the particles$ etc.)$ regardless of whether we put that in terms of substances

and causal powers and liabilities$ or in terms of substances and laws$ or in some other wa!.

Thus$ the unierse$ which has certain conditions in its first state$ brings about the change to its

second state$ ust as 8od and his intent at the first state brings about the change in scenario1.


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e ma! also stipulate if we so choose ? though we don+t need to ? that the change indeterministic

in scenario $ so that gien the first state of the unierse$ there is more than one possible second

state$ but onl! one actuall! obtains or we ma! alternatiel! mae it deterministic$ etc.

%n an! case$ that would not mae an! difference in terms of changelessness or 3uiescence.

2.1.". Timelessness sans creation. 'ore on Craig(s description.

%n this subsection$ % will address a more elaborate description of 8od+s alleged timelessness sans

creation$ which Craig gies in one of his articles5 r U 6.

%n that article too$ he claims that sans creation$ 8od is changeless.

@oweer$ as % argued aboe$that claim would be false. ;ore precisel!$ in the account of creation

that Craig gies$ 8od is not changeless$ but changes ust as he or the unierse would change in

scenarios in which there is no allegedl! timeless state of affairs.

%n addition$ Craig claims that 8od is immobile. @ow can one mae sense of such a claim4%t maes sense$ of course$ to sa! that an obect remains immobile for a while$ so as time goes b!$ the

obect does not moe with respect to some frame of reference. 2ut here the claim does not seem to

be about spatial moement$ so plausibl! the claim is e3uialent to the claim of changelessness$

which has the shortcomings alread! addressed.

Else$ Craig would hae to e"plain what he means.

That aside$ Craig gies an argument in support of the iew that in his changeless state$ 8od is also

timeless. A first and decisie problem is that$ as argued aboe$ the state in 3uestion ? i.e.$ the first

state of 8od ? would notbe changeless. 2ut let+s consider Craig+s argument in greater detail:

@e claims that there is a possible world ? sa!$ , 0 in which 8od refrains from creating an!thing$

and claims that in that case$ the state in 3uestion can be plausibl! and coherentl! conceied of as

&timeless.

Then$ he argues that similarl!$ the first state of 8od in the actual world is timeless$ since there is no

intrinsic difference between the first state at the actual world and the first state at , Craig also

claims that the initial segments of the actual world T and the other world , would be identical.

%t+s still not clear to me what Craig means b! ,-timeless+ 0 if an!thing 0$ but leaing that aside$ the

claim that there is no intrinsic difference between the two states isfalse$ at least in an! releant

sense of -intrinsic+$ as the following argument shows:

*et > be the first state of the actual world T$ according to Craig+s description. Then$ 8od e"ists at

>$ and nothing else e"ists at >. *et >, be the onl! state of the world ,$ at which 8od e"ists alone.

Then$gi&en>$ necessarily%od changes$ as the anal!sis of scenario = aboeshows.

,$ it+s not the case that 8od necessaril! changes$ is sufficient to establish that the states


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are not intrinsicall! identical$ as Craig claims.

>imilar considerations appl! to causal necessit!$ also as argued aboe.

As for the claim that the initial segments would be identical$ it is also false$ since an! initial

segment of T on Craig+s account would contain the first state >$ which is a state at which 8od and

onl! 8od e"ists$ and such thatgi&ensuch state >$ necessarily 8od changes$ whereas that is not true

of an! initial segment of ,.

>o$ if one assumes Craig+s account of creation$ then gien an! initial segment of the actual world$

necessaril! change occurs. hether which changes occur are determined b! such initial state is

another matter$ but there is no need to discuss it in this conte"t$ since the obections succeed either

wa!.

%n light of the fact that gien an! initial segment of the actual world assuming Craig+s account of

creation$ change necessaril! follows$ whereas it+s not the case that gien an! initial segment of ,$change necessaril! follows$ we ought to conclude that Craig+s claim is not true$ and the initial

segments are not identical.

Alternatiel!$ and to mae the point shorter$ an! initial segment of T contains > but not >,$

whereas an! initial segment of T, contains >, but not >. @ence$ the!+re not identical.

>imilar considerations can be made with regard to casual necessit!$ also as arguedearlier.

*et+s consider now two potential obections:

"b#ection $ The difference between > and >, described aboe is not intrinsic, whereas the

difference between T(F) inscenario 2and > inscenario $orscenario is intrinsic.

That obection claims that there is a difference between T(F) and >$ but does not e"plain how there

is that difference$ or what ind of difference that would be$ or wh! it would be intrinsic. >a!ing that

> is intrinsicall! lie >, does not seem to address the problem$ because b! the descriptions$ > seems

indistinguishable from T(F)$ but releantl! different from >, 0 een assuming >, is coherent$ which is

not clear$ either (e.g.$ how can we mae sense of a person who does not change at all$ not een in

his states of mind4 %t seems he wouldn+t een thin$ feel$ or do an!thing$ not een in his mind if so$

how can he be conscious4 2ut *et+s let that pass).

"b#ection $ %ods state of mind at S resembles more %ods state of mind at S1 than it

resembles the state of mind that %od would ha&e at an initial temporal state, li3e the state

)*+ presented inscenario 2'

*eaing aside that it+s not at all clear that it+s coherent to posit an! state of mind ? or an! person$ for

that matter ? in a purportedl! timeless changeless state lie >,$ obection maes a claim of a

difference without an! e"planation as to how the state of mind of 8od in > and T(F) would be

different$ and further$ different in a sense that is connected to the issue of time.

8ien that > and the first state at T(F) in scenario #appear not to be different at all$ based on the


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descriptions ? as argued aboe 0$ there appears to be no good reason to accept this obection$ either$

at least until a defender of a KCA' can e"plain that difference coherentl!.

2.1.$ 'etrically amorphous time.

hile Craig reects >winburne and Padgett+s account of undifferentiated time before creation 5rU6$

he contends that a ariant of it would be compatible with 8od+s creation.

>o$ someone might tr! to combine the KCA with an account lie that$ instead of timelessness.

@oweer. the account in 3uestion is obscure as well$ and those defending it would hae the burden

of e"plaining what the! mean. 2ut moreoer$ for that matter$ if the account is coherent$ the! would

hae to e"plain wh! 8od would be the onl! or most plausible candidate for e"isting in this ind of

amorphous time$ rather than some weird 3uantum thing$ or space$ or something along those lines.

2.2. Conclusions based on the analysis of the proposed creator.

2ased on the anal!sis so far$ in m! assessment one ought to reect the KCA'as defended b! Craig$or releantl! similar ersions$ since:

a.%t+s not clear that the idea of a timeless agent is coherent.

b.Een if a timeless agent is coherent$ it+s not clear that the idea of an agent that is timeless

sans creation but temporal with creation is coherent.

c.There are strong reasons to thin that the creator proposed b! Craig actuall! would be an

entit! that begins to e"ist but has no cause of his e"istence$ contradicting premise 1 of the

KCA.

d.%f the creator proposed b! Craig for some reason can be properl! called -timeless+ sans

creation$ but temporal with it ? which seems &eryimplausible gien the preious subsections

0$ it seems that plausibl!$ the same would appl! to the unierse if it had a first state$ which on

its own would bloc the KCA$ as argued earlier.

%t might be suggested that$ perhaps$ some ersions of the KCA' defended b! other philosophers

fare better.

@oweer$ as long as the! claim that there is a personal creator that is timeless sans creation and

temporal with creation$ or mae an! similar claims$ it seems that the same problems will liel!

arise$ and such claim seems to be a e! part of the KCA'$ at least in all usual ariants.

%n an! case$ an! defender of the KCA' ought to e"plain what the! mean when the! sa! that the

creator is timeless without creation and temporal with it$ or b! an! alternatie but also obscure

claims the! mae etc.$ and in particular$ e"plain how it+s not the case that 8od begins to e"ist in

their model of creation.

All that said$ % will address the premises of the KCA and the arguments offered in support of them

in the rest of the essa!$ and % will raise a number of obections that do not depend on an! of the

preious ones.


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!. The first premise of the KCA.

The first premise of the KCA states:

P1. Eer!thing that begins to e"ist has a cause.

%n this section$ % will assess first the meaning of the first premise$and then arguments gien in

support of it.

!.1. )eginning to e*ist and coming into e*istence. An alternati+e principle.

%n his defense of the KCA$ illiam *ane Craig assumes an understanding of -begins to e"ist+5 r S 6

which % will call ,C0begins0to0e"ist,$ and which can be stated as follows:

An entit! V C0begins to e"ist at t if and onl! if the following conditions obtain:

C456i' 7 e!ists at t, and its a tensed fact that 7 e!ists at t'

C456ii' here are no states of the world at which 7 e!ists timelessly'

C456iii' 5ither there is no t1 8 t such that 7 e!ists at t1, or any t1 8 t at which 7 e!isted isseparated from t by an inter&al of positi&e duration'

%n that definition$ V ranges oer entities$ and t oer instants or interals of finite$ non09ero duration.

*et+s briefl! anal!9e the conditions:

C456i' 7 e!ists at t, and its a tensed fact that 7 e!ists at t'

The re3uirement that V,s e"istence at t be a tensed fact$ in particular$ rules out that an! obects begin

to e"ist if a tenseless theor! of time is true.

%t seems odd to me that Craig would include tense in the definition of /begins to e"ist/$ but he

argues that$ under a tenseless theor! of time$ a unierse with a first eent did not begin to e"ist ust

as a meter stic does not begin to e"ist ust because it has a first centimeter. 5 r S 6

That argument sounds odd to me as well$ since while a meter stic does not begin to e!istin irtue

of haing a first centimeter$ that,s not releant$ since haing a first centimeter is aspatial$ not a

temporalclaim$ while ,begins to e"ist, 0 at least$ in this conte"t ? is clearl! a claim about time$ not

space.

%n fact$ the stic in 3uestion ma! properl! be said to hae a beginning in spacebecause it has a first

centimeter 0 at least if there is no demand for an arbitraril! precise spatial beginning 0$ as long as

we ? e"plicitl! or b! conte"t ? pic a direction in space to sa! which centimeter is first and which

last$ or which endpoint is the spatial beginning and which one is the spatial end.

2ut similarl!$ een if a tenseless theor! of time is true$ the stic does hae a beginning in timeif

there is$ for instance$ afirst year at which it e!ists at least if there is no demand for an arbitraril!

precise temporal beginning$ and a fu99! beginning will do 0$ and in the case of time$ we needn,t

specificall! pic the direction$ since the direction from past to future is alread! implicit in our

language.

That does not appear to be a difficult! for a temporal beginning of e"istence under a timeless theor!


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of time. %ntuitiel!$ to sa! that the stic begins to e"ist seems to be the same as to sa! that the stic

has a temporal beginning$ or a beginning in time$ and then it follows that the stic does begin to

e"ist$ regardless of whether a tenseless theor! of time is true.

C456ii' here are no states of the world at which 7 e!ists timelessly'

This is an een odder condition$ since the term -timeless+ is e"tremel! odd on its own$ to sa! the

least. %t+s not clear that it+s een being used coherentl! b! Craig$ as % argued earlier. 2ut %,e alread!

addressed the matter of timelessness$ so % will go no further on this point$ and assume from now on

and for the sae of the argument that the concept of C0begins0to0e"istis a coherent concept.

C456iii' 5ither there is no t1 8 t such that 7 e!ists at t1, or any t1 8 t at which 7 e!isted is

separated from t by an inter&al'

This condition$ together with the fact that t ranges oer instants or interals of positie finite

duration$ entails that if there is a finite open interal (F$t6 at the beginning of the unierse$ then theunierse began to e"ist. %t+s a debatable matter whether that respects our usual terminolog!$ gien

that it+s arguable whether the metric of time is intrinsic. 2ut % will no go further on this$ either$ and

will grant for the sae of the argument that the metric is intrinsic.

%n addition to giing that definition$ Craig understands ,begins to e"ist, and ,comes into being, as

semanticall! identical. %n fact$ he actuall! defines ,begins to e"ist, to mean the same as ,coming into

being,$ and then defines /comes into being/. 5 r S 6

% don,t thin that that captures the meaning of ,comes into being, or ,comes into e"istence,.

The idea of coming into e"istence ? or coming into being % see no semantic difference between the

two e"pressions ? seems to impl! a changein the state of the world$ plausibl! from a state at some

time t, at which some entit! V does not e"ist$ to a later state at a time t t,$ at which V does e"ist.

8ranted$ someone might sa! that the idea of coming into e"istence does not re3uire that the

preious state of the world at which V does not e"ist be temporal, and a causall! prior state suffices$

een if it+s a timeless state. Hor the reasons % e"plained earlier$ there are serious 3uestions about the

coherence of a timeless state that is causall! prior to a first temporal state. e ma! assume here for

the sae of the argument that it is coherent in order to assess the first premise and some ariants$ but

it remains the case that % cannot mae an! sense of such a state$ so it+s hard for me to mae an!

intuitie assessment on that.

>till$ in an! case$ we ma! *et+s leae the issue of the coherence of a timeless cause of a first

temporal state and define temporallycoming into e"istence$ or coming into e"istence in time, as

follows:

An entit! V temporally comes into e!istence or into being at t if and onl! if the following

conditions obtain:

TC%E0i: V e"ists at t.


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TC%E0ii: There is a time t, R t such that V does not e"ist at t,.

TC%E0iii: There is no time t,, such that V e"ists at t,,$ and t, R t,, R t.

%n this conte"t$ V is also an! entit!$ and t an! instant or an! temporal interal of positie duration.

8ien those definitions$ *et+s consider another potential principles$ as an alternatie to premise 1.

P1,: Eer!thing that temporall! comes into e"istence has a cause of its e"istence.

% do not claim that the principle is true. %t ma! well be challenged. @oweer$ % offer it in order to

compare it with the principle offered in premise 1 of the KCA$ since % find P1, to be a lot more

intuitiel! plausible$ at least if one assumes that there might be a beginning of time ? a matter % will

consider in the ne"t subsection.

!.2. Arguments in support of the first premise.

%n this section$ % will consider arguments in support of the first premise gien b! illiam *ane

Craig in his defenses of the Kalam Cosmological Argument =r1>.!.2.1. &othing comes from nothing.

Craig maintains that the principle that nothing comes from nothing is intuitie and supports the first

premise. %n this conte"t$ he points out that obects don,t ust pop into e"istence without a cause$ and

proides e"amples b! considering h!pothetical scenarios in which certain obects come into

e"istence without a cause$ and pointing out that those scenarios are counterintuitie.

@oweer$ the e"amples he proides as obiousl! counterintuitie are all e"amples of obects

temporall! coming into e!istence without a cause$ in the sense in which % defined ,temporall! com es

into e"istence, earlier.

%t is true that those scenarios are alsoe"amples of obects that would begin to e"ist without a cause$

and een C0begin0to0e"istwithout a cause if a tensed theor! of time is true.

@oweer$ it ma! er! well be that the feature that maes it intuitie that those obects probabl!

hae causes is that the! temporall! come into e"istence$ not that the! begin to e"ist ? or ma!be it+s

some other feature.

o$ after considering that$premise 1,still loos intuitie5 6$ but premise 1 does not.

>o$ on intuitie grounds$ one ma! reect premise 1.


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%ncidentall!$ the defender of the KCA is appealing to intuitions in support of premise 1$ and then

arguing that time has a beginning as a means of supporting premise #. 2ut if time has a beginning$

then premise 1 becomes counterintuiti&e' >o$ if the appeal to intuitions in the conte"t of the KCA is

acceptable ? as the defender of the KCA maintains 0$ then the KCA ought to be reected ? at least$

going b! m! intuitions.

%ncidentall!$ also$ een Craig+s e"amples ? lie$ sa!$ a horse coming into e"istence without a cause

? are counterintuitie as e"amples of what might actually happen. % do not see an! good reason to

thin it+smetaphysically impossible for an! of that to happen. At least$ if conceiabilit! is a guide to

metaph!sical possibilit!$ the! seems conceiable. The reason that those eents do not actually

happen ma! er! well hae to do with the causal structure of the actualworld$ but not with what+s

metaph!sicall! possible. >till$ the other considerations %+m giing are enough to reect the KCA on

intuitie grounds$ regardless of the issue of metaph!sical possibilit!.!.2.2. Another alternati+e principle.

After further considering m! intuitions on the matter b! contemplating more scenarios (but which

don+t inole a beginning of time)$ it also seems intuitiel! plausible to me$ after reflection$ that for

eer! obect < that e"ists at some time t$ there is some time u R t$ and some obect L at u which is a

cause of


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lie option.

>till$ een the acceptance of P1, is tentatie$ since it+s not clear that our intuitions are so reliable in

cases inoling all of time$ a small dense unierse$ etc.5 6$ and leaing aside the issue of

metaph!sical necessit!.


24/62

present0da! models$ therewereotherstates of the unierse that are be!ond the descriptie

capabilities of current scientific understanding.

;oreoer$ while it ma! be that if some scientists assess that our uni&ersebegan to e"ist$ in some

limited sense of -unierse+$ that would not entail an assumption that timehad a beginning$ and so

the! might loo for causes earlier in time ? for instance.

%n the end$ readers will mae their own intuitie assessments of course$ but % don+t thin m!

intuitie assessments with regard to premise 1 and premise 1, are unusual. %n an! case$ % inite

readers to assess the matter b! their own intuitions: As % see it$ premise 1 is intuitie under the

assumption that time does nothae a beginning$ and er! counterintuitie under the assumption that

time does hae a beginning. Premise 1, is intuitie either wa!.

That said$ there are difficulties with appeals to our intuitions about time and space in conte"ts such

as the purported beginning of time$ such as:a. There ma! be significant differences between the intuitions of different people. There ma!

well een be differences between their pretheoretical intuitions. >o$ perhaps$ and at least on

some the issues under discussion$ there ma! not be one single human normal pretheoretical

intuition on a matter.

b. The intuitions of a person on some of these matters ma! well change oer time$ as that

person learns more about ph!sics$ cosmolog!$ philosoph!$ etc.$ and sometimes it+s difficult to

figure out what a person+s pretheoretical intuitions are.

c. There seems to be no particularl! good reason to thin that pretheoretical intuitions are

more reliable than intuitions deeloped later ? let alone more than the intuitions of specialists$

lie cosmologists.

d. %n an! case$ and plausibl! more importantl!$ modern ph!sics shows that in unfamiliar

enironments lie something er! small or massie$ things are -weird+$ and our intuitions

about time$ space and related matters do not seem to wor well. 2ut the unierse a long time

ago was both er! small and massie.


25/62

least$ it seems perfectl! conceiable that obects temporall! come into e"istence without a cause$ so

if conceiabilit! is a good guide to metaph!sical possibilit!$ then that gies us a reason to thin that

premise 1, is not metaph!sicall! necessar!$ either.


26/62

and een leaing aside the problems with the concept of the agent that the! propose.

". The econd /remise of the KCA.

The second premise of the KCA states:

P#. The unierse began to e"ist.

%n addition to the 3uestion of the meaning of -begins to e"ist+$ an important issue is the meaning of

-unierse+,.

Craig stipulates that in the second premise of the KCA$ the unierse is the whole of material realit!.

5 B 6 5r1 16

hile it+s not clear what -material+ means$ assuming it+s coherent and precise enough in the conte"t

of the KCA$ it+s clear enough that at least the &whole of material realit! contains the (or a)

multierse if there is a multierse$ and contains an! uni&ersesolder than ourunierse$ using here

the word -unierse+, in a sense in which it+s sometimes used in astronom! and cosmolog!$ butwhich is more restrictie than the sense in which the word -unierse+, is used in the second premise

of the KCA.

@ence$ arguments showing that the unierse$ in that more restrictie sense of the word -unierse+$

began to e"ist$ would fail to proide support for the second premise of the KCA.

% will come bac on this point later$ when % assess Craig+s arguments allegedl! based on science.

2ut first % will address other arguments$ made b! Craig$ Pruss$ Koons and aters.

".1. 0ilbert(s 0otel

The first argument % will consider is the -@ilbert @otel+ argument$ defended b! Craig intended to

show that an actual infinit! is metaph!sicall! impossible. 2ased on that conclusion$ Craig argues

5 r 126 that an infinite past is metaph!sicall! impossible$ since it would be an actual infinit!.5 N 6

According to Craig$ the -@ilbert @otel+ argument shows that an actual infinit! is counterintuitie$

and based on that$ he claims that an actual infinit! is plausibl! metaph!sicall! impossible ?

apparentl!$ according to Craig$ it+s counterintuitie from the perspectie of some intuitions of

metaph!sical possibilit!.

>o$ let+s assess the argument:

The @ilbert @otel is a hotel with a denumerable number of rooms$5 U 6 and Craig maintains that it+s

the actual application of the concept of infinit! to the real world$ rather than the consideration of

abstract sets$ what brings the counterintuitieness of an infinit! to one+s attention.


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o$ is it true that there are no more guests after a new guest arries$ in the first scenario4

%n the sense of cardinalit!$ it+s true.

%n the senses considered in 1.b and 1.c$ it+s false.


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ow$ Craig also sa!s that it+s counterintuitie that the new guest is accommodated een if all

the rooms were full.


29/62


30/62

-fewer+. The preious considerations suffice.

7ifth scenario?

This time$ all of the guests in all rooms e"cept for Y1$ Y#$ and Y= leae$ and een though the

number of guests that left is the same as the number of guests that left in scenario =$ the

number of remaining guests is onl! =.

Craig seems to beliee that such argumentation is a powerful argument against the

metaph!sical possibilit! of the @otel$ and as a result allegedl! against the metaph!sical

possibilit! of actual infinities. 2ut an! alleged counterintuitienesswith regard to the

numbers disappears ones one considers what the words mean$ and basic math.

Hor that matter$ the set of odd natural numbers and the set of natural numbers hae the same

cardinalit!$ but if is the set of natural numbers$ AJXodd natural numbersQ5 S 6$ and

2JX$ then A is an infinite set$ whereas 2 is the empt! set. That is not a problem at all.As for other features of the @otel itself$ ifan! of them is a problem for the metaphysical

possibilityof the @otel ? and % see no good reason to beliee so$ as e"plained earlier the

metaphysical possibilityof it does not seem in an! wa! counterintuitie to me$ at least as long

as the people inoled are not human or similar to human in powers$ etc. 0$ then there seems

to be no good reason to thin that that is a problem for actual infinities in general$ or in

particular ? for e"ample 0$ for infinitel! man! gala"ies$ planets$ stars$ etc.

8ien the preious considerations$ the conclusion is that the -@ilbert @otel+ argument fails to

proide an! eidence against the metaph!sical possibilit! or een the e"istence of actual infinities.

That said$ % would lie to also comment on a particular claim he maes. Wespite the fact that Craig

distinguishes between three t!pes of possibilit! in this conte"t (and impossibilit!$ and necessit!) 0

namel!$ strict logical possibilit!$ strict logical possibilit! augmented b! the meaning of terms within

the scope of modal operators$ and metaph!sical possibilit! ?$ and he maes it clear that his claim is

that actual infinities are metaph!sicall! impossible$ he does claim that there is a contradiction$

apparentl! in subtracting e3ual 3uantifies from e3ual 3uantities and hae different numbers in the

end.

%n particular$ he gies the e"ample that the set of een numbers E has an identical number of

elements as the set A of natural numbers greater than four$ and !et if we subtract E from the set of

natural numbers $ we get an infinite set$ but if we subtract A from $ we get a set with onl! =

elements.

>o$ allegedl!$ it would be contradictor! that identical numbers from an identical number and we did

not get the same number.

2ut there is no contradiction$ because A and E (and ) hae an identical number of elements in the

sense that there is a biection between them. 2ut there is no contradiction in sa!ing that there is a


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biection between A and E (andDor between each of them and $ for that matter)$ but there is no

biection between XA and XE. %n fact$ not onl! is that not contradictor!$ but it+s clearl! true.

or is an! of that counterintuitie$ for that matter.

>o$ in short$ there is nothing to the &@ilbert @otel argument that Craig defends.

".2. rim reapers.

The -grim reapers+ argument (or 8I argument) has different forms$ and it might be gien in support

of the h!pothesis that actual infinities are impossible$ andDor that infinite temporal regress is

impossible$ andDor that time is necessaril! discrete$ among others.

%n this subsection$ % will focus on one of Ale"ander Pruss+s ersions of the argument. =r1!>

The argument is as follows:

/russ? =r 1 !>

/1. %f there could be a bacwards infinite se3uence of eents$ @ilbert+s @otel would bepossible.

#. If Hilberts Hotel were possible, the GR Paradox could happen.

3. The GR Paradox cannot happen.

. Therefore, there cannot be a bac!wards infinite se"uence of e#ents.$

2riefl!$ the 8I Parado" is as follows:

Hred is alie at tF? which is 11.FF am in Pruss+s scenario 0$ and then$ there is a grim reaper

(sa!$ 8In)$ set to ill Hred at tnJ(tF'(1Dn) seconds)$ if Hred is alie$ and to do nothing if Hred

is dead. Hred cannot surie a grim reaper attac.

The reasoning used in defense of premise # is that if the @otel were possible$ it would be possible to

mae one reaper in each room (8In

in room Yn)$ and the staff could program it to act at tnJ(t

F'(1Dn)

seconds).

>o$ what to mae of the argument4

Hirst$ let+s mirror the reasoning$ and mae an argument against infinitel! man!gala!ies$ for

e"ample$ b! maing one grim reaper per gala"!.

>hould we then conclude that infinitel! man! gala"ies are not possible4

% do not thin so. %n fact$ there are h!pothetical scenarios that hae infinitel! man! gala"ies and are

consistent.

Hor e"ample$ there seems to be no contradiction in a scenario with infinitel! man! gala"ies but in

which time is relatie and in which no entit! has the power to send information from one gala"! to

another faster than the speed of light. %n such a scenario$ there seems to be no wa! to derie the

parado"$ since in such a scenario$ no one would be able to mae reapers who can chec on Hred lie

that.


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8ranted$ someone might tr! to derie the parado" in some other wa!$ but that can be bloced b!

conditions on the causal structure of the h!pothetical scenario ? or world if one accepts tal of

possible worlds.

;oreoer$ there are scientific$ non0contradictor! models inoling infinitel! man! gala"ies. There

seems to be no contradiction in adding the stipulation that no entit! has the power to send

information from one gala"! to another faster than the speed of light ? which ma! be a problem for

theism$ but not for the scenario+s immunit! to the 8I parado".

>o$ if infinitel! man! gala"ies are possible$ then clearl! it+s not possible that a contradiction obtains.

And there is no good reason to beliee the!+re not possible.

8ranted$ someone might posit a ariant in which the infinitel! man! reapers are in the same place$

or the!+re spaceless unembodied entities that send signals to one another$ etc.

2ut the e! point in this reasoning is that this would not be a problem for the possibilit! ofinfinitel! man!gala!ies$ but for the problem of infinitel! man! reapers with certain powersin a

certain scenario.

This seems to wor againstpremise #in Pruss+s argument as well$ because it seems it is not the case

that if @ilbert+s @otel were possible$ then a contradictor! 8I scenario would be possible. Iather$ if

@ilbert+s @otel were (or is) possible$ there would be (or there are) possible worldsDscenarios at

which it e"ists$ and then no contradiction would arise (or arises) in an! of them$ plausibl! because

of the causal structure of each of the worldsDscenarios$ which would ar! (or aries) from one

possible scenario to another possible scenario.

This seems to bloc the argument forpremise #$ as well as an argument directl! from an infinite

past to a contradictor! 8I scenario.

%f an infinite regress of past eents is possible$ then no parado" arises in those possible scenarios$

and what blocs the formation of the parado" plausibl! aries from scenario to scenario.

At this point$ someone might raise the following obection:

"(f its metaphysically impossible for there to be infinitely many gala!ies, then that e!plains why a

contradictory %9 scenario in&ol&ing infinitely many %9 one per gala!y would be pre&ented'

4ut if it were metaphysically possible for infinitely many gala!ies to e!ist, then a contradictory %9

argument would seem to be possible' 5lse, what would pre&ent the formation of a contradictory %9

scenario, in a possible world or scenario with infinitely many gala!ies1

@oweer$ % will argue that the obection is misguided$ on the following grounds:

a. The 3uestion -what would preent the formation of a contradictor! 8I scenario in a

possible world or scenario with infinitel! man! gala"ies4+ ma! be interpreted as:

a.1.A 3uestion about a general necessaril! true principle that somehow would in some

sense -preent+ the formation of the 8I scenario.


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%n that case$ one ma! point to the necessaril! true principle that contradictions are

impossible in particular$ one does not need a further principle that actual infinities are

impossible$ or that infinitel! man! gala"ies are impossible.

a.2.A causal 3uestion$ namel!$ , what would causall! preent a 8I scenario from

coming to be$ in a possible scenario with infinitel! man! gala"ies4,

%n that case$ the answer is that itdepends on the specific possible scenario or world in

/uestion'

%f the scenario is complete ? lie possible worlds$ if one accepts tal of possible worlds

? or at least sufficientl! specified$ then in different possible scenarios (or worlds)$ there

are different causal structures of the scenarioDworld$ and in some cases$ different things

would fail if some entit! or entities attempted to bring about the contradictor! 8I

scenario$ or if each of them attempted to perform a single tas that together would be acontradiction$ etc.

b. The 3uestion raised in the obectionma! be mirrored b! a similar 3uestion$ in repl! to the

suggestion ? made b! the person arguing against actual infinities$ or at least against infinitel!

man! gala"ies ? that an e"planation as to wh! a contradictor! 8I scenario inoling

infinitel! man! gala"ies wouldn+t happen is that actual infinities ? or at least infinitel! man!

gala"ies ? are metaph!sicall! impossible.

The mirror 3uestion would be: -hat would preent the formation of infinitel! man! gala"ies

? not one at a time$ of course$ but in bloc so to spea ? in a possible scenario in which there

are finitel! man! obects4,

Then$ we ma! consider options:

b.1.%f the person positing the metaph!sical impossibilit! of actual infinities$ or at least

of infinitel! man! gala"ies$ responds that what would preent the formation of infinitel!

man! gala"ies in a possible scenario in which there aren+t infinitel! man! obects is that

actual infinities ? or at least infinitel! man! gala"ies ? are metaph!sicall! impossible$

then that would not seem an! stronger than a repl! to the original 3uestion in the

obection that says that 4hat 4ould pre+ent the formation of a contradictory R

scenario in a possible 4orld or scenario 4ith infinitely many gala*ies is that

contradictions are not possible.

;ore precisel!$ there is of course a clear difference between the two replies: we do

now contradictions are impossible$ but we do not now that infinities are$ or that

infinitel! man! gala"ies are.

@oweer$ and leaing that aside$ the two replies are similar in that$ in both cases$ the

person answering the 3uestion is appealing to a principle the! hold is necessaril! true ?


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in one case$ the impossibilit! of contradictions in the other$ the 5alleged6 impossibilit!

of an actual infinit!$ or of infinitel! man! gala"ies 0$ as an answer to a 3uestion as to

what would preent the formation of a certain scenario from a preiousl! gien

scenario.

This of course generali9es to other replies to the mirror questionthat are based on

some 5allegedl!6 necessaril! true principle$ as an answer to the 3uestion -hat would

preent the formation of infinitel! man! gala"ies ? not one at a time$ of course$ but in

bloc so to spea ? in a possible scenario in which there are finitel! man! obects4,

>uch replies are also appeals to some 5allegedl!6 metaph!sicall! true principle as

e"plaining what blocs such a formation$ and as such the! seem no stronger than the

appeal to the metaph!sicall! true principle that contradictions are impossible as a repl!

to the 3uestion of wh! a contradictor! 8I scenario would not be formed in a possiblescenario in which there are infinitel! man! gala"ies$ if infinitel! man! gala"ies were

possible.

b.2. %f the person positing the metaph!sical impossibilit! of actual infinities$ or at least

of infinitel! man! gala"ies$ gies a causal answer as to what would preent the

formation of infinitel! man! gala"ies in a possible scenario in which there are finitel!

man! obects$ then that does not seem to be an! better than the causal reply abo+e.

To be more precise$ % thin pointa.aboe suffices to show that theobectionis misguided$ butb.is

a wa! of showing that the person arguing against an actual infinit! is at least in no better position.

".!. Aristoteliandiscrete time, infinite regress and more grim reapers.

Pruss also distinguishes between the following two t!pes of discrete time:

1. Time is rigidl! discrete if there necessaril! is a minimum temporal unit.

#. Time is discrete in an Aristotelian sense if there are in fact finitel! man! moments of time

between an! two gien times in the finite past$ but each interal can be subdiided infinitel!

man! times.=r1!>5r1B6

Then$ he gies an argument against infinite regress if time is discrete in an Aristotelian sense.

The reasoning is basicall! as follows: if there were an infinite se3uence of past eents W(0n)$ for all

natural n$ such that W(0n) precedes W(0m) if nm$ then W(0n) could cause something at time tF'1Dn

for some tF$ contradicting the h!pothesis that time is discrete in an Aristotelian sense. According to

Pruss$ there is no reason to rule out all of those happening together.

2ut the difficult! seems to be the same as in thepreious case. %n fact$ what Pruss seems to be

doing is going from the finite to the infinite case$ including in the infinite case scenario some entit!

or entities with the causal power to bring about all of those things at time tF'1Dn$ and who e"ercise

such powers successfull!. 2utthatspreciselynotwhat happens in a consistent scenario in which


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time is discrete in an Aristotelian sense$ and in which there is infinite temporal regress. Hor that

matter$ one might mae an argument against infinitel! man! gala"ies if time is discrete in the

Aristotelian sense ? programming one reaper per gala"! 0$ but that fails as the argument aboefails.

At this point$ someone might as 3uestions lie.

a. hat would preent that scenario from happening$ if an infinite temporal regress is

possible4

b.hat would preent that scenario from happening$ if infinitel! man! rooms$ or gala"ies$

are possible4

%f the 3uestion is about some general metaph!sical principle$ we now that contradictor! states

cannot come to e"ist. %f it+s a causal 3uestion$ we ma! properl! as$ in the case of a specific

h!pothetical phenomena @$ what would causall! preent @ from happening.

2ut if the h!pothetical scenario is sufficientl! determined ? lie a possible world$ presumabl! 0$then different possible scenarios hae different causal structures.

>o$ essentiall!$ the repl! to this ind of obections is along the same lines as the repl! to the

obectionin the immediatel! preious subsection.

".". rim placers and3or grim signalers.

%n this subsection$ % will address a ariant of the argument from grim reapers$ defended b! Iobert

Koons5 r 1 6.


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seems no less intuitiel! clear to me that it+s possible that no agent e"ists$ so if % were to accept that

criterion$ that alone would mae Koons+s premise no stronger than an intuitie assessment that there

is no necessar! being.

%n an! case$ *et+s grant h!pothesis 1 for the sae of the argument.

".".2. Compressibility of spacetime.

Another assumption of Koons+s argument ? though this one is an assumption for a reductio ma!

be stated as follows:

#. %f there is some obect A with an intrinsic propert! O in a region I of finite duration e in a

possible world $ then:

a. There is a function f from the parts of I to the parts of some region I, of some

possible world ,$ such that f is topolog!0presering and compresses time and space b!

half. Hor instance$ if the duration of I is e$ the duration of I, is eD#b. There is a counterpart A, of A and a counterpart O, of O$ such that A, intrinsicall! has

propert! O, in I,.

@!pothesis # is used for a reductioagainst temporal densit!. Koons argues that h!pothesis #. is

reasonable under the assumption that time is dense.

%f there is an intrinsic metric of time$ it+s not clear to me that no properties are incompressible$ no

processes re3uire at least some amount of time$ etc.

2ut *et+s grant h!pothesis #as well$ for the sae of the argument.

".".!. Infinitary patch4or5 and binary patch4or5.

A e! principle of Koons+s argument is what he calls &infinitar! patchwor 5 r 1 6 (or %P)$ and

which can be stated as follows: 51F6

*et+s suppose the following conditions obtain:

%P(1): + nQ is a countable series of possible worlds$ and-I

nQ$ is a countable series of

regions of those worlds$ such that for all n$ Inis a region of

n.

%P(#): f is a function from- into the class5%%6 of spatio0temporal regions of some world $

such that f preseres the metric and topological structure of each of the In$ and such that$ if

nZm$ then f(In) does not oerlap f(I

m).

Then$ there is a possible world +$ and an isomorphism g from the spatio0temporal regions of to

the spatio0temporal regions of +$ such that the following obtains:

%P(C): The part of nwithin I

nis e"actl! lie the part of + within g(f(I

n). 5 r 1 6.

Koons also proposes binar! patchwor$ which is the binar! counterpart of infinitar! patchwor. %nother words$ in the case of binar! patchwor$ onl! two regions are patched.


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@ere$ two e! 3uestions are:

i.>hould we accept both principles4

ii.%f we do$ does Koons+s conclusion follow4

*et+s address iifirst.

As Koons points out when he considers what he calls &The Ama9ing [anishing Particle$ his

argument re3uires that each grim placer ? or grim signaler$ as he renames them ? hae the power to

send a signal to a successor$ and the power to receie a signal from a predecessor.

%n particular$ een though the placers or signalers hae onl! powers intrinsic to each interal$ the!

hae the power to send a signal beyond their own interal.

ithout that power$ the argument would fail$ as the following scenario shows:

1. There is a se3uence of temporal interals %nJ(t

n'1$t

n6Q$ for all natural numbers n.

#. Each interal %nhas length d\#0n

=. Wuring interal %n$ or at least during the last portion of it$ there is a Hred particle at the

designated position d\#0n meters from the designated plane P. There is no other Hred particle

during interal %n

B. Wuring interal %n$ there is a grim placer Yn$ 8P

n.

That+s not contradictor!$ and is consistent with Koons+s premises$ as long as the powers do not

inoled sending signals beyond the interal in which the!+re e"ercised.

%f the scenarios to be patched were lie that$ there would be no contradiction.

>o$ a e! assumption in Koons+s argument is that the powers of the grim placers of signalers$ een

if intrinsic to each spatio0temporal region in the sense defined b! Koons$ include powers to act

beyond such spatio0temporal region.

ow$ Koons sa!s that there is no action at a distance$ since the interals ma! be contiguous$ lie in

the preious e"ample %nJ(t

n'1$t

n6.

@oweer$ it seems that wouldn+tbe enough$ as the following e"ample shows:

*et+s sa! that grim signalerYn$ or 8>n$ e"ists in %

nJ(t

n'1$t

n6$ whose length d\#0n

*et+s further stipulate that 8>n

has the power to send signals that persist within %n$ but not be!ond

her interal. At an! time in %n01

$ it is not the case that the signal sent b! 8>npersists$ so there is

nothing that 8>n01

$ who onl! acts in %n01

J(tn$ t

n016 might detect.

That is$ of course$ unless %n01 has the power to detect signals that e"ist at e"actl! tn or earlier$ but the

problem is that the use of infinitar! patchwor does not entail that %n01

e&en e!istsat tn$ or earlier.


38/62

>o$ Koons+s argument re3uires that each grim signaler has a power that$ while intrinsic to her

interal$ inoles sending a signal that willpersist for some time ? een if a er! small time$ and

een if the amount of time ma! ar! from possible world to possible world ? into a temporall! later

interal.

7et$ een that would not be enough.

o$ Koons+s argument uses not onl! that each grim signaler has the intrinsic power in her interal to

send a signal that endures for at least some time into the ne"t interal$ but also that she e"ercises

that power successfull!$ and that the successful e"ercise of that power is a matter intrinsic to herown spatio0temporal region$ e&en if it in&ol&es the persistence of her signal in another spatio6

temporal region'

%n fact$ Koons+s argument assumes at leastthe following conditions:

a. hen appl!ing binar! or infinitar! patchwor$ one ma!stipulate that the powers intrinsic

to a spatio0temporal region I11

whose temporal component is an interal %1inole powers to

send signals that e"ist in a region I#whose temporal component is an interal %

#that does not

oerlap with %1and %

#is later than %

1$ proided that the temporal distance between %

1and %

#is

9ero (lie (a$ b6 and (b$ c6$ or 5a$ b) and 5b$ c)).

b. ;oreoer$ when appl!ing binar! or infinitar! patchwor$ one ma! stipulate that the matter

of whether an e"ercise of such powers is successful is also a matter intrinsic only to the

inter&al at which they were e!ercised, een in cases in which the stipulation described in

condition a. aboe is also made.

Conditions a.and b.would impl! that when both the stipulations described in a.and b. are made$

the matter of whether a signal ? whether the signal is a Hred particle or something else ? e"ists at

some time in a spatio0temporal region I#

is a matter intrinsic to a spatio6temporal region I1

that is

dis-oint from I#'

@oweer$ under that er! weird notion of intrinsicalit!$ there is no good reason to accept either of

the patchwor principles. >uch principles are e!tremelycounterintuitie upon reflection$ and after

Koons+s conditions are anal!9ed as aboe$ and there is no reason to reect our intuitions on the

matter and come to beliee that the principles are true.".".". )inary patch4or5 suffices.


39/62

*et+s grant in this subsection for the sae of the argument that the principles of infinitar! and binar!

patchwor are true ? including conditio ns a. and b.$ een though as % e"plained in the preious

subsection$ there seems to be no good reason to beliee that the! are true.

8ien the ind of powers and dispositions that Koons patches ? as seen in the preious sections 0$

infinitar! patchwor is not re3uired to conclude that temporal densit! is metaph!sicall! impossible.

%n fact$ binar! patchwor suffices to establish that for eer! two non0oerlapping temporal interals

%1and %

#$ the temporal distance between them is non09ero. 2ut that rules out temporal densit!$

because if time were dense$ the temporal distance between some temporal interals lie (a$ b6 and

(b$ c6$ or between 5a$ b) and 5b$ c) would be 9ero.

>o$ let+s proe from binar! patchwor that there are no temporal interals such that the temporal

distance between them is 9ero:

*et+s stipulate the following conditions:

A: There are two temporal interals (a$ b6 and (b$ c6$ in world 1. %n (a$ b6$ there is one entit!

E11 with the power and disposition to send a signal of t!pe T1into (b$ c6.

)?%n 1$ E11 e"ercises her power successfull!.

C? %n another world #$ there are also interals (a$ b6 and (b$ c6$ and there is no signal of t!pe

T1in an! of those two temporal interals$ and no entit! receiing or sending an! signals.

#?All of the powers and dispositions in those interals are intrinsic to those interals$ and

whether the e"ercise of powers is successful is also a matter intrinsic to the interals in whichthe powers are e"ercised.

e ma! pic the spatial interals to coer all of space at those times$ or some other stipulation of

our choosing there are man! options. % will leae the spatial condition aside to simplif!$ but nothing

hinges on that.

Also$ we ma! pic temporal interals that are open into the future and closed into the past instead of

open into the past and closed into the future. That maes no releant difference$ either.

>o$ b! binar! patchwor$ we patch interal (a$ b6 from 1 and interal (b$ c6 from #into some

world =.

%n =there is no signal of t!pe T1 at an! time in (b$ c6$ since there is no such signal in # and = is

an e"act duplicate of # in interal (b$ c6.

>imilarl!$ in = there is in (a$ b6 one entit! E11 with the power and disposition to send a signal of

t!pe T1into (b$ c6$ and who e!ercises her power successfully in . as well. 2ut gien that the power

was e"ercisedsuccessfully$ there is a signal of t!pe T1 at least at some time in (b$ c6 in =.

That is a contradiction.

A potential obection would be that een if there is no signal of t!pe T1at an! time in (b$ c6 in #

and een if = is an e"act duplicate of # in interal (b$ c6$ it is possible that there are signals of


40/62

such t!pe in (b$ c6 in =$ and that the condition of e"act duplication should not be understood as

ruling out other entities. 2ut such an obection would seem to use the e"pression -e"act duplication+

in a wa! that does not seem to resemble the meaning of the words$ and there appears to be no good

reason to accept a modified principle based on the usage of -e"act duplication+ sugg

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A Reply to the Kalam Cosmological Argument (v 7.4.1)

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