Logic and the Free Will Problem

8/13/2019 Logic and the Free Will Problem

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Logic and the ree Will Problem

The best way to get an intuitive grip on the problem of free willand determinism is to think of time as a garden of forking paths.That is, to think of the alternatives that one considers in delibera-tion as being incidents that are included in alternative futures,and to think of alternative futures diagrammatically, in the waysuggested by a path or a river or a road that literally forks:

If Jane is trying to decide whether to tell all or to continue her lifeof deception, she is in a situation strongly analogous to that ofsom eone who is hesitating between forks in a road. That is whythis sort of diagram is so suggestive. Let us see how the idea oftime as a garden of forking paths helps us to understand theproblem of free will and determinism.To say that one has free will is to say that when one decidesamong forks in the road of time (or, more prosaically, when onedecides w hat to do ), one is at least sometimes able to take morethan one of the forks. Thus, Jane, who is deciding betw een a forkthat leads to telling all and a fork that leads to a life of continueddeception, has free will (on this particular occasion) if she is ableto tell all and is also able to continue living a life of deception . Onehas free will if sometimes more than one of the forks in the roadof time are open toone. One lacks free will if on every occasion


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78 Social Theory and Practice

about whether to leave, one of the alternative futures he iscontem plating leaving is, in point of fact, not open to him, andhe thu s lacks free will in the matter of staying or leaving.It is a common opinion that free will is required by morality.Let us examine this cotnmon opinion from the perspective that isprovided by looking at time as a garden of forking p aths. W hile itis obviously falsefor about six independent reasonsthat thewhole of morality consists in making judgments of the form, Youshould not have donex, we can at least illustrate certain importantfeatures of the relation between free will and morality byexamining the relation between the concept of free will and thecontent of such judgments. To say that you shouldn 't have doneX is to say that you should have done som ething else instead. Tosay that you should have done som ething else instead is to say thatyou ould have done something else. (If this were not true, onecould say, I concede that you were unable to do x instead of whatyou did. I nevertheless maintain that you should not have d onewhat you did, but should have done x instead. ) To say that youcould have done something else is to say that you have free will.To make a moral judgm ent about a person's act is to evaluate histaking one oftheforks in the road of time relatively to one or m oreof the forks that were also open to him. (Note that if John makesa cho ice by taking one of the forks in what is literally a road, onecannot blame him for taking the fork he did if all of the othe r forkswere blocked.) A moral evaluation of what someone has donerequires two or more alternative possibilities of action for thatperson , jus t as surely asacontest requires two or m ore contestants.

Let us now see w hat help the conception of time as a garden off o r k i n g p a t h s g i v e s u s in u n d e r s t a n d i n g d e t e r m i n i s m .Determinism is the thesis that it is true at every moment that theway things then are determines a unique future, that only one ofthe alternative futures that may exist relative to a given m oment is


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Logic and the Free Will P roblem 79

sheaf of possible futures (like this)

what we really confront is something like this

Here the dotted lines represent futures that are not physicallypossible continuations of the present, and the single solid linerepresents the future that the laws of nature permit.It has seemed obvious to most people who have not beenexposed (I sometimes think that subjected would be a betterw ord) to ph ilos op hy that free w il l and de term inism areincom patible. It is almost impossible to get beginning students ofphilosophy to take seriously the idea that free w ill and determ inismare com patible. Indeed, people who have not been exposed tophilosophy usually understand the word determinism (if theyknow the word at all) to stand for the thesis that there is no freewill. One might think that the incom patibility of free w ill anddeterminism deserves to seem obviousbecause it is obvious. Tosay that we have free will is to say that more than one future issometimes open to us. To affirm determinism is to say that everyfuture that confronts us but one is physically im possible. Andsurely a physically impossible future ca n't be open to one, can it?If we know that a S tarTrek sort of future is physically impossib le(becau se, say, the warp drive that figures essentially in suchfutures is physically impossible), then we know that a Star Trekfuture is not open to us or to our descendants.

People who are convinced by this sort of reasoning are called


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compatibilist can be expected to reply to the line of reasoning Ihave jus t presented in some such way as follows, Yes, a future,in order to be open to one, does need to be physically possible. Itc a n ' t , f o r e x a m p l e , c o n t a i n f a s t e r - t h a n - l i g h t t r a v e l i ffaster-than-light travel is physically impossible. But we mustdistinguish between a future's being physically possible and itshaving a physically possible connection with the pr esen t futurcis physically possible if it is permitted by the laws of nature . Afuture has a physically possible connection with the present if itcould be 'joined' to the present without any violation of the lawsof nature. A physically possible future that does not have aphysically possible connection with the present is one that, giventhe present state of things, would have to be 'inaugurated' by anevent that violated the laws of naturc, but in which, thereafter,events proceed in accordance with the laws. De tenninism indeedsays that of all the physically possible futures, one and only onehas a physically possible connection with the presentone andonly one could be joined to the prcsent without a violation of thelaws of nature. My position is that some futures that could not bejoined to the prcsent without a violation of the laws of nature are,nevertheless, open to us.

T w o p h i l o s o p h i c a l p r o b l e m s f a c e t h e d e f e n d e r s o fcom patibilism. The easier is to provide a clear statement of whichfutures that do not have a physically possible connection with thepresent arc open to an agent. The morc difficult is to make itseem at least plausible that futurcs that arc in this sense open to anagent really deserve to be so described.

An exam ple ofasolution to these problems m ay m ake the naturcof the problem clearer. Th e solution I shall briefly describe wouldalmost certainly be regarded by all present-day compatibilists asdefective, although it has a respectable history. I cho ose it not tosuggest that compatibilists can't do better, but simply because it


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not break the bonds of gravitation, for even if one managed toinduce some people to choose not to be subject to the force ofgravity, their choice would not be effective. Therefore (thecompatibilist concludes), it is entirely appropriate to speak of afuture as open if it is a futurc that would be brought about by acho ice. And if someone protests when you punish him for notchoosing a futurc that was in this sense open to him, on the groundthat it was determined by events that occun-ed before h is birth thathe not make the choice that would have inaugurated that future,you can tell him that his punishment will not be less effective inmodifying his behavior (and the behavior of those wh o witness thispunishment) onthataccount.

What I have tried to do so far is to give a brief and intuitiveaccount of free will and determinism, and of the two majorapproaches to the problem, the approaches taken by theincom patibilist and the compatibilist. W hat I want to do in thesequel is to look at one aspect of the problem in some deta il. I amafraid it must be rather technical detail, for there comes a point inthe discussion of a philosophical problem at which one can go nofurther w ithout going into technical detail. I am going to presentan argument for the incompatibility of frce will and de terminism,and defend this argument against an objection that manyphilosophers have found cogent

Let 'N ' be an operator that exprcsses wh atever sort of necessityit is that is opposed to free will. It seems plausible to suppose thatthe following two inference-rules governing 'N' arc valid:( a ) D p \~ p (where n ' has its standard sense)

Dq \-Nq.Now let *S 'be a sentence that gives a complete description of the


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Logic and the Free Will Problem 83

And from this consequence of determinism, it follows, by elemen-tary modal and sentential logic, that

D(S=> ( L3T ) ) . From this it follows by (a) that 'N(S3(L=)T)) .Now it would seem that both the laws of nature and statementsabout the pastand certainly the remote pastshould be ac-counted necessary in the sense expressed by *N'. We have,therefore *NS'and 'NL',andthen,by twoapplicationsof (p),'NT'.That is, if determinism is true, then any truth whatever is neces-sary in a sense that is opposed to our having free will aboutwhether it is true. If the argument that has led to this conditionalis valid, then determinism is incompatible with free will.

Is the argument valid? Since no one (I think) would want todispute (a), this question reduces to the question whether (p) isvalid. And that is a very good question indeed.

In an important and much-cited article, Michael Slote hasattempted to cast doubt on the validity of (p).^ Slote suggests thatanyone who accepts (p) probably accepts it only because heaccepts these two rules:

Agglomeration Np, N I- N (p^)Closure Np |-N^, providedqis derivable fromp.

He says:Anyonewho assumes the validity ofarguingfrom 'Np' and 'N (> Z q)*to *N^'


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operator will have the properties of aggl


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Logic and the Free Will Problem 85

made a serious and sustained effort to construct a cou nterexam pleto (p) w ill com e to share my conviction that (p) is valid, or, if notto share it, then at least to see how someone could have thisconviction quite independently of his convictions about thevalidity of any other rules of inference.I will remark in passing that I am inclined to think thatAgglomeration and Closure are valid. Consider the set of worldsW such that the actual world belongs to W and a non-actual world

belongs to W if and only if someone has, or once had, a choiceabou t whether that world is actual. It seems to me plausible tosuppose that W is such that, for any p .pand n o one h as, or ever had, any choice about whether p Iis true {sc. in the actual world) if and only if p is true in everymember of W. That is to say. there is a certain set of worlds(containing the actual world) such that for every p,' 'N p' ' is true ifand only if p is true in every member of that set. More generally,for every w orld w, there is a set of w orlds W (containingw suchthat for every p,*^Np is true in w if and only if p is true in everymem ber of W. Th is means that *N* is what we might call a classical necessity operator and not what Slote calls a selectivenecessity operator. I leave as an exercise the trivial proof thatAgglomeration and Closure hold for all classical necessityoperators.

I am therefore inclined to think that *N'is ,as Slote puts it, bothagglom erative and closed under logical implication because I aminclined to think that the following two operators are equiva lent:p and no one has, or ever had, any choice about whether pThe proposition that p is true in the actual world and in allnon-actual worlds such that someone has, or once had, a choice


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while the statement that *N' is a classical necessity operator entailsthe validity of (p), the validity of (p) does not entail that *N' is aclassical necessity operator. ) I should still accept (p) becausemy conviction that (p) is valid rests on what I believe have learnedby attempting to construct counterexamples to (p) and not on mybelief that the two sentences displayed above are equivalent or onmy belief that the Choice Necessity operator isaclassical necessityoperator. (My belief that there are peop le does not rest on mybeliefor on my tacit assumption that there are peop le in Tibet,despite the fact that I do believe, and with great conviction, thatthere arc people in Tibet, and know that the proposition that thereare people in Tibet entails the proposition that therc arc peo ple. Ifsomething convinced me that there were, after all, no people inTibet, I should still believe that there were people.)

I have implied that it is at least very difficult to find acoun terexam ple to (p). I will now say this explicitly, and while Iam atit make explicit an important qualification: it is at least verydifficult to find a counterexample to (p) that can be seen to be acounterexam ple independently of the question w hether free will iscom patible with detenn inism . Of course if free will is com patiblewith de terminism , it is easy to findacoun terexam ple to (p ); in factwe have already done so. If free will is com patible w ithdetenninism, then one or the other of the two applications of (p)in the argument for incompatibilism displayed above must havetak en us from truth to falsity. Bu t, of co ur se , pu tati vecoun terexam ples to (p) that work only if com patibilism is trueare of no intercst in a dispute about the truth of compatibilism.W hat would be of intercst would be a putative counterexam ple to(p) that could be evaluated independently of the question wh etherfrce will and determinism were compatible.

My allegiance to (p), thercfore, is quite independent of w hateveropinions I may hold about Agglomeration and Closure, and an


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Logic and the Free W ill Problem 87

Agglomeration or Closure since the invalidity of (p) entails thateither Agg lomeration or Closure is invalid.) Does Slote sayanything that one might apply directly to (p)? Only this. Hedisplays various plausible instances of alethic necessity forwhich (p) failsfor example, non-accidentality, irresistibleimpulse , and com pulsion. These certainly seem to be in somesense types of necessity, and Slote shows convincingly that (p)is not valid if N is interpreted as exprcssing any of them. Butwhat is the point of this procedure? I concede that it might serveto undermine an allegiance to (p) that was based on a belief thatall necessity operators were classical, or was based on anunexamined analogy between Choice Necessity and standardlogical or metaphysical (or even physical) necessity. But I do n otknow of anyone whose allegiance to (p)does rest on so infirm afoundation. I know that mine do esn 't, and I suspect that Ginet andLam b and Wiggins would say the same.

I am m oreover, puzzled that Slote should bother discussing theserelatively unintercsting selective necessity operators when it iseasy to find selective necessity operators that seem to be far morcrelevant to the problem of free will and determ inism. Considerthis one , for examp le:p and no one is, or ever has been, such that if he w ere to choose tobring it about that it is (or was) false that p, then it would be (orwould have been) false thatp .Th e rule (p) fails for this operator. Moreover, this opera tor is ofspecial intercst in discussions of the free will problem becauseadherents of the popular view that xcan do A is equivalent to If x w ere to choose to do A,x would do A would, presumably,say that it was equivalent to our Choice Necessity operator:

p and no one ha s, or ever had, any choice about


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are,as so many com patibilitists allege, a certain sort of disguisedcond itional, then any a rgument for the incompatibility of free w illand determ inism is either invalid or else has false prem ises. It isobviou s that if the Equivalence Th esis is coiTect, then canstatements are disguised conditionals of that type. It is obviousthat if our argument is invalid it is only because (p) is invalid. Itis therefore not surprising that, if the Equivalence T hesis scorrect,then (p) is invalid. So much the worse for the Equivalence Thesis,I say. It is obvious that (p) is valid (or so it seems to me); it is notobv ious that the Equ ivalence Thesis holds. If two propositions areincompatible and one seems obviously true and the other does notseem obviously true, then, all other things being equal, one shouldaccept the obvious m ember of the pair if one accepts either.

I am, therefore, unmoved by the fact the (p) fails if 'N' isinterpreted as expressing the were to choose operator. But whythen should I be moved by the fact that (p) fails if 'N ' is interpretedas expressing the operators ( it is no accident thatp and so on)that Slote calls our attention to? I do not think that the were tochoose operator expresses Choice Necessity. But it is certainlytm e that many philosophers hav e thought that it does, or have heldview s that entail that it does. Therefore, there is an intimate andimportant connection, at least in the minds of many philosophers,between the were to choose operator and the prob lem of free willand determinism. The operators that Slote displays, however, aremuch less intimately connected with the problem of free will anddetemiinism, and the fact that (P) fails for these operators isconsequently even less troubling to the incompatibilist than thefact that (p) fails for the were to choose operator.

Notes


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Log ic and the Free W ill Problem 89

This diagram has the following intCTesting feature: if it is viewed from adistance, the viewer will not be able to tell which of the forks is the one thatis continuous with the pas t This may be thought of srepresenting the factthat, from our point of view (which is not that of God or the LaplacianIntelligence), we cannot tell which mem ber of a sheaf of possible futures isthe one tha t is continuous with reality.

3 . Professor Slote, in his comments, contends that the situation has changedsu^iciently in tfie last few years that it is no longer clear that the majorityof Eng lish-speaking ph ilosophers are com patibilists. On reflection, I aminclined to agree with him .4 . This argumen t is discussed in greater detail than is here possib le ocnecessary) in C h ^ t e r HI of my bookAn Essay on Free W ill (Oxford: TheClarendon Press, 1983).5 . Not even the gods can change the past ;onlya Godor, at least, somesort of supernatural beingcould change (OTviolate, set aside, defy, causethings to act in wa ys other than those prescribed b y) the laws of nature .6. Selective Ne cessity and the Free-W ill Problem , The Journal ofPhilosophy, 7 9 (1982); 5-24. Slote's article is a criticism of four defenses

of the incompatibility of free will and determinism: Carl Gin et, M ight WeHave N o Cho ice? in Keith Lehrw, ed..Freedom and Determinism (NewYOTk: Random House, 1966), pp . 87-10 4; Jam es La m b, On a Proof ofIncompatibilism, Philosophical Review8 6 (1977); 20-3 5; David W iggins, Tow ards a Rea sonab le Libertarianism, in Ted Ho nderich, ed..Essays onFreedom of Action(London: Routledge and Kegan Paul. 1973). pp.31-61;my The Incompatibility of Free W ill and DettTminism, PhilosophicalStudies T 1915):185 -99. M y articleisreprinted in Gary W atson,ed FreeWill(New York: Oxford U niversity Pre ss, 1982), pp . 46 -58 .Slote has a certain am ount of trouble with m y article, the argum ent of whichis laid out in a way that is ratha- inconv enient for his purpo ses. But he isperfectly right in thinking that the points he make s are as applicable to myarticle as the othe r three. Because the aigument of Section 3.10 of my boc4c:(see n. 4) is laid out in such a way that Slote's points can be applied to itwithout trivial and annoying adjustments and qualifications. I shall defendthat argum ent rather than the argumen t of The Incompatibility of Free W illand Detenninism.

7. Nor, as Slote repeatedly suggests, does the example of standard alethicmodal logic play any role in my conviction. Or not so far as I can tell.


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Here is a general description of what one experiences when one attemptsto construct a counterexa mp le to (p ). On e substitutes particular declarativesentences for >* and q\ and one devises a case according to wh ich, onehopes, the premises of the resulting argument are true and its conclusionfialse. On careful ex am ination, however, it transpires that (say) one of th e{Semises is false; one adjusts the case to make the premise true andthereupon discovers that one has inadvertently made the other prem ise false;a second adjustment, intended to correct this fault, causes the conclusion tobe true; when this defect is corrected, it turns out that the premise thatoccasioned the original modification of the case is onc e mo re false. As thehours passhours during which one tries many and various pairs of sub-stitutions for '/?*and q and constructs many bizarre scenarios one beginsto recogn ize patterns in the repeated blockings of the TTF case , patternsthat display to one the inevitability of the frustration of every attempt todevise an instance of that case.

9. I shall not invariably be careful ab out distinguishing use and mention orvariables from dum my letters.10. For example. let W b e any possible world. If * N'is interpreted a s ' it is true

in W th at' . (p) is valid and N is not a classical necessity operato r (as is easilyseen from the fact th at/ j could be false and Np true ).11 . The best I know of is due to Thomas McKay. Suppose John has a choiceabou t whether he plays dice, and, in fact does play dice. But no one has acho ice about how the dice fall in a fair gam e. Th e game is fair. John thro wsa six. The proposed counterexample is:

N John throws a sixN (John throw s a six z) John plays dice)..N Joh n plays d ice.

The first prem ise is true for the reason given. The second premise is truebecause the emb edded con ditional is a necessary truth. Th e conclusion isfalse for the reason given .I reply : the first prem ise is false. John could have avoided throw ing a sixby avoiding playing dice. W hat John has no choice about is whether hethrows a six given that he plays dice; thatis.about whether (John plays dice3 John throws a six).

12. I'm n ot sure wh at Slote mean s by alethic. In a draft of this paper, Isuggested neither deontic nor doxastic. but Slote has denied (in con esp on -dence ) that this was what he meant. He did not. how ever, explain w hat he


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Logic and the Free Will Problem

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