Against Middle Knowledge

7/27/2019 Against Middle Knowledge

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226 PETER VA N INWAGENit is or once was within H is power so to arrange (or so once to have arranged)matters that they be false-that there are exactly 80,966hairs o n Toms head, forexample, or that the re is a physical universe. Th ere is, thirdly and finally, God sscientin media or middle knowledge, which comprises those m etaphysically con-tingent tru ths such th at i t is nor (and never has been) within Gods power so toarrange or so to have arran ged matters th at they be false. Many p hilosophers andtheologians would insist that this third class of propositions is empty. Molina,however, insisted th at it contains propositions of the type nowadays called tru ecounterfactuals of freedom.I shall assume that there is such a thing as middle knowledge only i f thereare true co unterfactuals of freedom-or, as I shall so me time s say, only i f thereare such things as m iddle facts.*A counterfactual of freedom is a wou ldc on-ditional that says of a certain agent that tha t agent would freely have performeda certain act in certain circumstances that d o not in fact obtain. For example:

I f Curley had been offered a bribe of $20,000 at noon last Friday to permit thedestruction of O ld North Church, he would freely have accepted i tis a counterfactual of freedom, provided that Curley was not in fact offered abribe of the kind specified at noon last Friday. An d if this proposition is tnw, i tis a middle fact. ( I f , that is, facts are tru e propo sitions.Those who wish to distin-guish between facts and t r u e propositions may substitute whatever phrase theyt h i n k is appropriate for is.)My purpose in this essay is to argue that there is no middle knowledgebecause there are no middle facts. ( I f there are no middle facts, then, obviously,the proposition that Go d does not have middle knowledge does not entail thatG od is not omniscient. If something is not there to be k n o w n , then even an om-niscient being will not know it. If all counterfactuals of freedom are false-orlack truth-values-then an omn iscient being will know that, but know ing of eachcounterfactual of freedom that i t is false or truth-valueless doe s not const i tutemiddle knowledge.)I will argue that all counterfactuals of freedom ar e false.3 My ar gum entproceeds from two premises that I believe to be true but will not defend. Thefirst is that David Lewiss semantics for cou nterfactual cond itionals is the correctsemantics for counterfactual conditionals.4 Th e second is incom patibilism, thethesis that free will is incompatible with determinism . Anyon e who rejects eitherof these premises may regard my argument as having a conditional conclusion:Iflewiss semantics is correct and if free will is incompatible with determinism,then all counterfactuals of freedo m are false. (A s regards the second of thesepremises, it should be pointed ou t that the defenders of middle knowledge havealways assum ed tha t free will is incom patible with determinism -or th at , as theysometim es put it, a l ibertarian account of free will is ~ o r r e c t . ~t would, I sup-pose, be a par t of what most peop le who use the ter m me an by m iddle knowl-edg e that th e existence of middle knowledge entails that free will is incompat-ible with determinism . I much prefer to say that if free will and determ inism arecompatible-and if determinism is tru e and if people do sometimes act freeiy-


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AGAINST MIDDLE KNOWLEDGE 227then there w ill, of necessity, be tr ue coun terfactuals of freedom an d a n omnis-cient being would, of necessity, have middle knowledge.)Here, briefly, is Lewiss seman tics for cou nterfa ctual cond itiona ls (I use h iswell-known symbol for the counterfactual-conditional connective):

p [)3 4 is true if and only if either p is impossible or some world in which pand q are both true is closer to actuality than any world in which p is true andq is false.

(The second disjunct of the definiens is sometimes informally sta ted like this: qis tru e in a ll the closest p-worlds.) In the sequel, I shall ignore the first disjunctof the definiens; I shall always assume tha t the antecedent of whatever cou nter-factual we may be considering is possible. T he above coun terfactu al of freedomis then true in just the following case:Som e world in which Ciirley was offered a b ribe of $20,000 at noon last Fririnyto perm it the destruction of Old North Church an d Crirley free ly accepted th ebribe are both true is closer to actuality than any world in which Ciirley wasoffered CI bribe of $20,000 at noon Inst Friday to permit the d estnictio n of OldNorth Church is true and Ciirley freely accepted the bribe is false.

Is there a world having this property? I n attempting t o answer this question, wemust remind ourselves what incom patibilism actually implies abou t free actions.We must remind ourselves what the proposition that a certain action is free ac-tually implies i f free will is incompatible with determinism. Let us examine thecase of t h e thief and the poor-box that I discussed in An Essay on Free Will:[A hardened thief] is in the act of lifting the lid of the poor-box in a littlecountry church. He sneers and curses when he sees what a patheticallysmall su m it contains. Still, business is business: he reaches for the money.Suddenly there flashes before his minds eye a picture of the face of hisdying mother and he remembers the promise he made to her by her dea th-bed always to be honest a nd upright. Th is is not th e first occasion on whichhe has had such a vision while performing som e mean act of theft, buthe has always disregarded it . This time, however, he does not disregard it .Instead, he thinks the matter over carefully and decides not to take themoney. Acting on this decision, he leaves the church em pty-handed. (VanInwag en, pp. 127-28)

We assume th at this was a free act and t ha t free will is incompatible w ith d eter-minism. Wh at does this imply? It implies that if G od had caused the world torevert to exactly the sta te in which i t was just before the thief m ade the decisionnot to steal the money (an d had then allowed the world to go forw ard again),the thief might well have stolen the money this time. If, moreover, there werea large number of occasions on which Go d caused the world to revert to exactlythe state it was in just before th e thief m ade t he decision not to ste al the money,a suitably placed observer of all these replayings would find that sometimesthe thief stole the money and sometimes he did not! In other words, if t is the


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228 PETER VAN INWAGENmom ent at w hich the thief m ad e his decision, there are physically possible worlds(worlds in which the laws of nature are the actual laws) of two kinds: W orldswhose histories ar e identical with the history of the actual world up to t in whichthe thief stole the money (n o dou bt th ere a re infinitely many such worlds if ther eare any at all); and worlds whose histories are identical with th e history of theactual world up to t i n which the thief did not steal the money (the ac tual world,at least, is such a world, and no dou bt there are infinitely many o the rs). If therear e no worlds of the former kind, the thiefs act (leaving the church empty-handed) was dete rm ined by the past and the laws of natu re, and-if free will isincompatible with determinism-that act was therefore not free.Now suppose tha t at the moment the thief was abou t to decide whether tosteal the money, he was alarmed by some noise a nd fled the church withou t m ak-ing a decision. What (free) decision would he have made if the noise had notoccurred (and if nothing else had prevented his making the decision)? In th eactua l world-proper nam e &-the thief freely decided not to steal the money;ou r question conc erns some very close world w in which a sudden noise fright-ened him a nd sent him run nin g. We want to know wh ether the cou nterfactualconditional I f things had been at t exactly os they were in a at t, the thief wouldhave freely decided not to steal th e money is true or false in the world w-or wemight ask the sam e question abou t I f things had been at t exactly as they were ina nt t, the thief woirld h ~ i v ereely decided to steal the mone y. (These two proposi-tions are contraries: in any given world,either on e is true and one false, or theyreboth false.) Does the thief freely decide not to steal [freely decide to steal] themoney in all the worlds closest to w in which things were a t t exactly as theywere in a at t? If he freely decides not to steal in every mem ber of t his class ofworlds, then the fo rmer p roposition is true in w; i f he freely decides to steal inevery member of this class of worlds, the la tter proposition is true in w; f hefreely decides not to steal in som e of them and freely decides to steal in othe rs,then both propositions are false in w.It would seem that a is one of the worlds in this class-one of the worldsclosest to w in which things w ere just a s they were in a at t. (We could certainlyso choose w tha t a is one of th e w orlds closest to w in which things were just asthey w ere in a a t t. L et us suppose that we have done so.) It follows that Ifthingshad been at t exactly as they were in a at t, the thief would have freely decided tosteal the money is false in w. But what abo ut its contrary, the p roposition t hathe would have freely decided not to steal the money? Could that pro position bet rue in w? ha t proposition will be tru e in w only if every world whose historyis identical with the history of a up to t and in which the thief freely decides tosteal the money is more distant from w than a is.

Le t p be such a world-a world whose history is ident ical with th e his-tory of a p to t and in which the thief freely decides to s teal the m oney. Le tus recapitulate what we know about ways in which the three worlds are re-lated to one anothe r: their histories are identical up to the moment at which thethief is distracted from his deliberations by the noise; thereafter, a and p divergefrom w. A brief mom ent later, at t, the thief freely decides (in a ) not t o steal the


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AGAINST MIDDLE KNOW LEDGE 229money, and freely decides (in p) to steal the money and a an d p accordinglydiverge.D oe s it follow from these things we have stipulated th at a s closer to wthan p is? Well, what a re th e relevant conside rations? If ct is closer t o w than pis, this must be du e to what go es on in the two worlds after r. How should one goabout m aking judgme nts abo ut the distances between these worlds and evalu-ating these judgments?There are various ways to think about this sort of question. Suppose wefollow David Lewis and th ink about th e distances between worlds in terms oftheir overall similarities and differences. Suppose we identify o ur qu estion w iththe question whether a s more similar to w than p is. It is hard to discern anyfactor that could be relevant to answering this question oth er tha n the rangesof particular fact that hold in the t hre e worlds. Th e laws of nat ure a re the sa mein all thre e worlds, these laws are indeterm inistic, and th e case of the thief as wehave imagined it implies tha t no miracle (n o largemiracle, no small miracle,no miracle in eithe r the usual sense of the word or in Lewiss special technicalsense ) is involved in the divergence of a nd p.Is there any thing abou t the way things go in p from which we are obligedto infer that p is more unlike w than the actual world is? It would not seem so ,if only because we have not said very much about p, In fact, J3 is not really aparticular world at all but a n arbitrarily chosen object. We have picked out pby means of an indefinite description: a world that is identical with a p to 1,and in which the thief freely decides to steal.There no do ub t exists a vast infinityof worlds that satisfy this description and nevertheless differ radically from oneanother. An d w hat i t seems most reasonable to believe about this vast infinity ofworlds is this: som e of them are less like w than a s, some of th em are more likew than a s,and some of them are neither m ore nor less like w than a s. All th eworlds that satisfy ou r indefinite description are, after all, indeterministic, andanything that is consistent with their common indeterministic laws and theircommon state at the m omen t of their collective divergence from th e actual worldwill hap pen in one or ano ther of them given sufficient time-including recon-verging with w.2We are not obliged to look at the concept of distance between possibleworlds as Lewis does-in term s of overall similarity amo ng worlds. I myself pre-fer to thin k of the p-worlds that are closest to w s those worlds in which p istrue that could be obtained from w by making the smallest possible changesin w. I assume tha t we are able to distinguish between a change an d its conse-quences, and between th e magnitude of a change and th e mag nitu de of its con-sequences.) A momen ts reflection will show th at th e class of p-worlds tha t canbe obtained from w by the smallest possible changes in w and the class of p-worlds tha t are most similar to w need not be the same-for some of the worldsin the f orm er class might, throughout t he e ntire f utur e, diverge radically from w,and thu s not belong to th e latter. (The minimal changes in w hat secure the t r uthof p might be miracles, replacements of the entire past of w by other entirepasts, or indeterministic swerves of som e of the in habitan ts of w.O r some of


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230 PETER VAN INWAGENthem might be of one of the se types and some of the ot he r two. However we un-derstand the idea of a change, some worlds produced by the smallest changesin w that a re sufficient to secure the tru th o f p will not be amo ng the worlds thatare-over all-most simila r to w.)Suppose, then, that we look at distance am ong possible w orlds as a functionof size of change. Does i t follow from any of the stipulations we have madeabout p and w that p is farthe r from w than the actual world is? It would notseem so. A ce rta in event-the noise that frightens the thief-occurs in w but notin cx and p, and thereafter t he latter two worlds (still coinciding) diverge fromw; bit late r, at r, the thief makes one decision in a nd ano ther in p, and thosetwo worlds diverge. To change w into a, herefore, what is required is the noiseplus the und etermined course of the thiefs deliberations taking on e fork in theroad; to change w into p, what is required is the noise plus the undeterminedcourse of the thiefs deliberations taking the o ther fork. Th e noise, so to speak,cancels out. Can the fact that the undetermined course of the thiefs delibera-tions went on e way in the actual world and the oth er in p have the consequencethat the actual world could be got from w by a smaller change than any thatwould suffice to produce p?Remember that i f , on a vast number of occasions,God miraculously caused the universe to revert to the precise state it was i n justbefore t, and then allowed things to proceed without f urt he r miracles, on someof these occa sions the thief would refrain from stealing the money and on someof them he would steal the mon ey.Given th at this is the case,it is very hard indeedto see why an yone would say tha t a larger change in w is required to produce thestate of affairs the thiefdecides to steal than is required to produce the state ofaffairs the thief decides not to steal.

I t would therefore seem that whether we understand q is true in al l thep-worlds closest to w sq is true in all the p-worlds that are, over all, the most similar to w

or asq is tru e in all the worlds that can be got from w by the sma llest changes thatsuffice for the truth of p,

i t is not the case that the thief freely decides to refrain from stealing in all theworlds closest to w in which his deliberations about whethe r to steal are un in-terrupted by the noise. On either interpretation, therefore, the counterfactualconditionalIf the thiefs deliberations about whether to steal had not been interrupted bythe noise, he would freely have decided not to steal

is false in w. We have already seen that If the thiefs deliberations aboutwhether to steal had not been interrupted by the noise, he would freely havedecided to steal is false in w.) Bu t the arguments that have led us to th is conclu-sion in no way depend on the particulars of the case we have imagined. If these


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AGAINST MIDDLE KNOWLEDGE 231argum ents are sound, then there are no middle facts (no true counterfactuals offreedom) and hence no middle knowledge.We should note that this conclusion depends on no features of free actsoth er than the fact that they are undetermined (a consequence of incom patibi-lism). Argum ents that differ from the above in no important way show that thereare no facts abo ut what the outco me of any non-actual course of events wouldhave been if its outcome would have been undeterm ined. Consider, for example,a contraption that has th e following design. It is a little box on t he o uter surfaceof which there are a butto n and two lights, a red light and a green light. If some-one presses the button, one or the oth er (never both) of the lights will light. An dsuppose tha t it is genuinely und eterm ined which light will light on any partic ularoccasion on which the button is pressed. (Perhaps the outcome of pressing thebutton depends on individual qua ntum events.) Suppose tha t no on e pressed thebutton at noon. If someone had, which of the lights would have lit? I f o u r argu-ments concerning the thief are correct, similar argum ents will show that we cansay only that one or the o ther would have lit; we canno t say tha t th e green lightwould have l i t , because it is false that the green light would have lit; we cannotsay that the red light would have lit , because i t is false that the red light wouldhave l i t . (Of course i t is also false that the g reen light would not have l i t , and falsethat the red light would not have lit.) G od , being omniscien t, knows all thesethings, knows th at i t is tru e that o ne light or the o ther would have lit,an d knowsthat al l t h e oth er propositions I have mentioned are false. But He do es not knowwhich light would have li t because no such thing is there to be know n.Go d might, however, know-He would i f i t were true-that i f the buttonhad been pressed at noon, the green light would prubobly have lit. And such athing could easily be true . (Suppose tha t there is a magical, truly indeterministiccoin-a fair coin such tha t i f it is tossed it is truly undetermined whether i t willfall head s or tails. G od c ann ot know whether, i f you had tossed the magicalcoin once at noon-you didnt-it would have fallen tails, for, again , no suchthing is there to be known. Nor does He know that if you had tossed i t five timesat noo n, it would have fallen tails at least once, for in some of the closest worldsin which you tossed it five times at noon, it fell heads every time. But He canand does know that i f you had tossed it five times a t noon,it would probably havefallen tails at least once. He know s this because i t is true. It is tru e becau se, inmost of the closest worlds in which you tossed the coin five times a t noon, i t felltails at least once (in 96.875 percent of them, to be exact).13Depending on thedetails of the design of th e red-green device, the prob ability of th e red lightslighting i f the bu tton is pressed may be 0.5o r 0.25or 0.3333 . .or any other num-ber between 0 an d 1.A nd whatever the prob ability of the red lights lighting maybe (conditional on the buttons being pressed), God will know what i t is, for thisthing, this probability, is there to be known.No ma tter how probable it may be-short of certainty-that the red lightwould light if the button were pressed, Go d does not know w hether th at lightwould have lit if the button had been pressed on som e occasion when i t was notp r e s ~ e d . ~ven if the probability of r ed is 0.9999999, it will still be t ru e th at if


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232 PETER VA N INWAGENthe button had be en pressed, the red light might not have lit, and this propositionis equivalent to the denial of the proposition th at, f the button had been pressed,the red light would have lit. As L ewis has pointed ou t (1973, p. 2) , the wouldand might conditional connectives are interdefinable:

p D-) q =df -(p c+ 4 )p c+ =df -(pD-, -4 ) .Th e second of these schemata suggests ano the r sort of argu me nt for the nonex-istence of true counterfactuals of freedom, a very simple argumen t ind eed . Le tus suppose tha t if Curley had been offered a certain bribe (which a building con-tractor in Ch elsea was seriously considering offering him , but , in the end , didnot), he would freely have acce pted it. I will argue th at if free will is incom patibl ewith determinism , then the falsity of this counterfactual of freedom follows fromits truth. A ssume

(1) Free w ill is incompatible with determinisman d

(2 ) Curley was offered the bribe D-, Curley freely accepted t he bribe.Premise (2 ) entails

(3 ) Curley was offered the bribe C-+ Curley was able not to accept thebribe.Premise (1) and proposition (3 ) together entail

(4 ) Curley was offe red the bribe O+ - Curley accepted the bribe.By the second D-)/W chem a above, proposition (4) entails( 5 ) - (Curley was offered the bribe D-) Curley accepted the bribe),an d ( 5 ) entails- (Curley was offered the bribe D-, Curley freely accepted the bribe ),which is the denia l of (2), the counterfactual of freedom w ith which we started .It is obvious that a parallel argument could be constructed with respect to anycounterfactual of freedom.I wish finally to consider two minor but interesting points a bou t counter-factuals of freedom.1.Alvin Plantinga has presented a very pretty little argu me nt for the con-clusion that th ere are true co unterfactuals of freedom (Pla ntin ga, p. 177). Sup-pose (he argu es) that Curley was offered a bribe of $20,000and accepted it .Then ,surely, it is evident th at if he had been off ered a bribe of $35,000 on the sameoccasion to secure the same service, he would have taken it? Bu t then th ere is atleast one true coun terfactual of freedom.O ne m ight wonder, however, how we know t ha t Curley would have freelyaccepted the larger bribe. For all anyone but G od knows, Curley was able to re-


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AGAINST MIDDLE KNOWLEDGE 233fuse the sm aller bribe b ut w ould have been u nable to refuse th e larger. Well, letus simply ussume that it is tru e tha t he would have been able to refuse the largerbribe. Bu t then-given incompatibilism-we know th at if he had be en offere dthe larger bribe, he might have refused it. And how could we know, how couldeven God know, that what m ight have happened would not have happe ned ? Wecertainly could not know this (for it would not b e tru e) if it might have hap pene dis logically equivalent t o it is false th at it wou ld not have happen ed, as it is onLewiss seman tics. (At t, I am asked to toss the m agical coin once; I immediatelydo so, and it lands heads. D o I know that if, at t, I had been asked to toss ittwice and had immediately done so,it would have landed heads at least once?I do not, for that is not true.)2. If my arguments are correct, they show not only that there are no t ruecounterfactuals of freedom, but tha t there could not be any (for my premises, ifthey are t rue at all, are necessary truths). Do es it follow that counterfactuals offreedom are necessary falsehoods? Th at they are is not a formal consequence ofmy conclusion, since being a counterfacrud of freedom is an accidental propertyof those propositions t hat have it, and it might be th at some coun terfactuals offreedom are only contingently false because they are true in some worlds inwhich they are no t counterfactuals of freedom. Counterfactuals of freedom areonly accidentally counterfactuals of freedom because they are not counterfactu -als of freedom (as I have defined the term) in worlds in which their an tecedentsare tr ue. Proposition (2 ) above, for example, is not a c oun terfa ctua l of freedomi n those worlds in which Curley was offered t he bribe. Might (2 ) be tru e in someof these worlds? It not only might be tr ue in some of these w orlds bu t is t rue insome of them on one version of Lewiss seman tics, the version th at inco rpora testhe assum ption of unweakened centering-that is, the assumption tha t noothe r world is as close to any world as tha t world is to itself. (A nd t hat assump-tion derives a certain degree of plausibility from the normal associations ofwords like closer and distance. In thei r norm al, nonmetapho rical sense, thesewords apply to places, and no oth er place is as close to any place as tha t place isto itself. If we thi nk of closeness amo ng worlds as Lewis does, as a fu nction ofsimilarity, the unweakened centering assum ption can s eem undeniable: if W Iandw2 are distinct worlds, then things must go differently in them-and in tha t case,how could wz e a s similar to w1 as w1 s?16 erhaps, however, the assumption canseem less obvious if we thin k of the d istance from w1 o w z s being given by thesize of th e change in w1 hat would be required to t urn it into WZ;f w1 is inde-terministic, then it may be tha t, in one sense, no change at all is needed to tu rn itinto a world with which it coincides up to some point in time and in which thesame indeterministic laws hold.) On he version of Lewiss semantics th at incor-porates unweakened centering, p C H is a logical consequ ence of p& q, and(2) will therefore be tru e in any world in which Curley is offered the bribe andtakes it. If, however, we reject the unweak ened cen tering assumption-if we ac-cept w eakened centering, if we allow the fo rma l possibility of ot he r worlds th atare as close to a world as that world is to itself-there is no formal or logicalreason to suppose th at there is any counterfactual of freedom that is only contin-


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234 PETER VAN NWAGENgently false. If, moreover, it is indeed possible for some world to be as close tosome other world as the latter is to itself, there would seem to be no reason todoubt the following thesis:For every world w, nd for every would conditionalof freedomp whose antecedent and consequent are both true in w, here is (as-suming incornpatibilism) a world as close to w as w s to itself in which the an-tecedent o fp is true and its consequent is false. And if that is the case, then everywould conditional of freedom is a necessary falsehood.

NOTES1. The brief account of Molinas concept of middle knowledge that is contained in thisparagraph is based on Flint ( IYXX). Flints article may be consulted for citations of Molina an dfor a n overview of th e litera ture on middle knowledge and related topics. Many useful refer-

encescanalsobefoundinAdams(lY77).(Imaysaythat I findlittle todisa grcew ith inAdanissclassic essay, and that there is perhaps little i n the present essay that can not be f ound , at leastin embryo, in Adams. This essay is a rather more technical version of w hat I have been sayingin undergraduate lectures in courses on the philosophy of religion for many years. I t is myhope that th e reader who tinds th e general outline of the arguments presented he re old newswill at least find some of the d etails interesting.)2. My business in this essay is with counterfactuals of freedom. I will not address thequestion whether. i f there are true counterfactuals of frcedom, at least homc ol thcrn wouldhave to be items of Gods middle know ledge in Molinas sense. Nor will I address the qucstionwhether my assumption that th ere i s middle knowledge only i f therc ;ire true countcrfactualsof freedom is in fact correct. I t should he no ted, however, that i f God does indeed havc middleknowledge of some truths, i t cannot be that al l of them are true countcrfactuals of freedom.It should also be noted that, i f true counterfactuals of freedom are possible, i t would sccm tobe possible for at least some tru e counterfactuals of freedom to belong to Gods free knowl-edge. As to the first po int: If a true counterfactual of freedom belongs to Godsmiddle knowl-edge, then so does any contingent truth that it entails; for example, the material conditionalwith the same antecedent and consequent. (An d if true counterfactuals of freedom are itemsof Gods middle knowledg e, then no doubt so are certain tr ue cou nterfac tuals of indetermi-nation-such as the counterfactual about the red-green device that will be considered laterin the body of the essay-that are not themselves counterfactuals of freedom.) A s to the lat-ter point: Suppose that in al l the clo sest possible worlds in which Adam is placed in a certaindeterminate set of circumstances, he freely disobeys Go d.T hen it is true that if he were placedin that set of circumstances, he would freely disobey God. But, consistently with this, we cango on to suppose that there is a world that it is within Gods power to actu alize in which A damis not placed in those circumstances and in which i t is false that if he were placed i n thosecircumstances he would freely disobey God.3. My argument for this conclusion will depend on the assum ption that every propositionis either tr ue or false. Without this assumption, my argument would show only that no coun-terfactual of freedom is tru e.B ut this conclusion is sufficient to establish the fu rth er conclusionthat there is no middle knowledge. My argument for the nonexistence of middle knowledgedoes not therefore depend on my assumption that every proposition is tr ue or false.4. My official term for the type of conditional of which Lewiss semantics treats is would cond itional. Officially,I apply the term counterfactual conditional only to wouldconditionals with false antecedents.But I shall not usually spe ak officially.When I am speakinggenerally abo ut would conditionals I shall mostly follow established usage and call themcounterfactual conditionals o r counterfactuals. But I shall in every case apply th e specialterm counterfactual of freedom to a conditional only if it has a false antecede nt.


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AGAINST MIDDLE KNOWLEDGE 2355 . Or, worse, that in the phrase counterfactual of freedom, the word freedom is to beunderstood in its libertarian sense. I keep telling people not to use the word lib ertarian, but

no one listens. There are no libert arian accounts of freedom, or,more exactly,all incompati-bilist accounts of freedom that anyone has actually offered are entirely unsatisfactory. Andthe word freedom does not have a libertarian sense. because the compatibilist and the in-compatibilist use the word in the same sense.6 . It do es not, however, follow tha t f or any given pair of con trary co unte rfactua ls of free-dom, one of them will be true. If the mechanisms underlying human deliberation were, al-though fully determ inistic, sufficiently chaotic-if small, indeed humanly imperceptib le,variations in the conditions under which these mechanisms operated could change the out-come of a deliberation-it might be tha t both members of many such pairs of con trar ies werefalse. Let us supp ose that we are compatibilists an d determinists . Still, if we believe that themechanisms that underlie human deliberation are chaotic, we must admit that th ere are manyworlds in which the proposition Curley was offered a bribe of $20,000 at noon last Friday ropermir rhe destruction of Old Norrh CIirirch is true . And i f we believe that human deliberationis a chaoticprocess, we must admit that, for all we know, the re are two such worlds, both ofthem among t he closest worlds in which Curley was offered the bribe, in one of which he freelyaccepted the bribe and in the other of which he freely refused the bribe.Then it is false that i fCurley had been offered a bribe of $20,000 at noon last Friday to permit the destruction ofOld North Ch urc h, he would freely have accepted it-and false tha t he would freely have re-fused it. And we should generalize this concession: for al l we know, both members of manysuch pairs of con traries are false, owing to t h e extreme sensitivity of the outcome of humandeliberation to imperceptible variations i n the conditions under which that deliberation iscarried out.7. Lewis (IY73).

8. Or, to be pedantic, the probability t ha t this is what the observer would see would ap-proach 1 as the number of replayings increased without limit.9. Here is ano the r way they could both be false in w:suppose tha t for every world in whichthe com mon antece dent of the two counterfactua ls is tru e and he steals, the re is a world closerto w in which the antecedent is true and he does not steal; and that for every world in whichthe common antecedent of the two counterfactuals is true and he does not stea l, there is aworld closer to w in which the antecedent is true and he steals.10. This paragraph contains some allusions to the discussion in Lewis (1979) of the factors

that are relevant to judgments of overall similarity among worlds. Th e reader can follow theargument of th e present essay without understanding the allusions.11. As is w,which is specified as follows: a world tha t coincides with a up to some pointafter the thief has begun his deliberations,in which a noise frightens him away before he canreach a decision, and which is such that a s among the worlds closest to it in which the thiefcompletes his deliberations.12. And even i f we neglect the fact that these worlds are indeterministic, we should notethat there are lots of ways in which the event by which p diverges from a-th e thiefs decidingto steal-might happen. (Th e thief might take a sho rter or longer time to decide to steal; hemight decide to put the money in his left pocket or his right pocket.) If , therefore, the physicalworld is at all chaotic then th e worlds in which the thief decides to s teal might diff er radicallyfrom one ano ther, some being more like w than a s. (Cf. n 6.)13. No do ub t there a re infinitely many possible worlds. If ther e are infinitely many worlds,no dou bt th ere are infinitely many worlds in which the coin is tossed five times an d falls tailsat least once and also infinitely many worlds (an infinity of the sam e cardinality) in which thecoin is tossed five times and falls heads every time. What we are suppo sing is that manyinfinite sets of worlds have a size, a measure, th at is not de term ine d by their cardinality. Setsof possible worlds are thus an alogous to sets of points on a plane, many of which have sizes ormeasures that are not determined by their cardinalities: one set of points may occupy twosquare feet, and a noth er set of the sam e cardinality (the power of the continuum ) may occupyone square foot-or a square light-year or square micron. Inmy view, it is impossible to m ake


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236 PETER VAN INWAGENsense of probabilities without making this assumption. When I say that th e coin falls tai1satleast once in 96.875 percent of th e worlds in which it is tossed five times, I mean that the ratioof the measure of the set of worlds in which the coin falls tails at least once out of the fivetimes it is tossed to the measure of the whole set of worlds in which it is tossed five times is96.875.14 . A se t of points may easily have the sam e area as one of its pro per subsets. No doubt thesame thing may hold, mutatis mutandis, for sets of worlds and th eir measures. The re is, there-fore, at least a forma l possibility th at p D+ q might be false even if the probability of q, givenp, is 1. shall not explore the implic ations of this forma l possibility for the problem of Godsmiddle knowledge.15. See Lewis (1973). pp. 14-15,26-31.16. But se e Lew is (1973). p. 29.

REFERENCESAdams. Rob ert M errihew. 1977. Middle K nowledge and the Problem of E vil. AmericanFlint,Thomas I? 1988. Two Accounts of Providen ce. In Morris.Lewis, David. 1973. Coiinterfactiials. Cambridge,Mass.- 1979. Co unterf actual D ependence and Times Arrow. Noiis 13:455-76.Morris, Th om as V., ed. 1988.Divine an d Hiinian Act ion : Essays i n di e Metiphysics of Theism.Plantinga. Alvin. 1974. Th e Notiire ofNecessity. Oxlord.Van Inwagen, Peter. 1983.An Essay on Free Will. Oxford.

Philosophical Quarterly 14109-17.

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Against Middle Knowledge

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