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Identity through Possible Worlds: Some QuestionsAuthor(s): Roderick M. ChisholmSource: Nos, Vol. 1, No. 1 (Mar., 1967), pp. 1-8Published by: Blackwell PublishingStable URL: http://www.jstor.org/stable/2214708

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IdentityThroughPossibleWorlds:SomeQuestions

RODERICK M. CHISHOLMBROWN UNIVERSITY

It is now easy to see a simple way of avoiding undesirableexistentialgeneralizations in epistemic contexts. Existential generalization with re-spect to a term-say b-is admissible in such contexts if b refers to oneand the same man in all the "possible worlds" we have to consider.1

In an article on Hintikka's Knowledge and Belief, I suggestedthat certain difficult questions come to mind when we consider thethought that an individual in one possible world might be identicalwith an individual in another possible world.2 The present paperis written in response to the editor's invitation to be more ex-plicit about these questions.Let us suppose, then, that the figure of an infinity of possibleworlds makes good sense and let us also suppose, for simplicity ofpresentation, that we have a complete description of this one.We may consider some one of the entities of this world, alter itsdescription slightly. adjust the descriptions of the other entitiesin the world to fit this alteration, and then ask ourselves whetherthe entity in the possible world that we thus arrive at is identicalwith the entity we started with in this world. We start withAdam, say; we alter his description slightly and allow him to livefor 931 years instead of for only 930; we then accomodate our

1JaakkoHintikka,Knowledgeand Belief: An Introductionto the Logic ofthe Two Notions (Ithaca: Cornell University Press, 1962), p. 152.2 "The Logic of Knowing,"Journalof Philosophy, LX (1963), pp. 773-795; see especially pp. 787-795.

1

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2 NOtSdescriptionsof the other entitiesof the world to fit this possibility(Eve, for example,will now have the propertyof being marriedto a man who lives for 931 years instead of that of being marriedto a man who lives for only 930); and we thus arrive at a descrip-tion of anotherpossible world.3Let us call ourpresentworld "W'"and the possibleworld wehave just indicated "W2". s the Adam of our world W1 the sameperson as the Adam of the possible world W2? In other words,is Adam such that he lives for just 930 years in WI and for 931in W2? And how are we to decide?

One's first thought might be that the propositionthat Adamis in both worlds is incompatible with the principle of the in-discernibilityof identicals.How could our Adambe identicalwiththat one if ours lives for just 930 years and that one for 931?Possibly this question could be answered in the following way:"Comparehe question:How can Adam at the age of 930 bethe same person as the man who ate the forbidden fruit, if theformer is old and the latter is young? Here the proper replywould be: it is not true that the old Adam has propertiesthatrender him discernible from the young Adam;the truth is, rather,that Adam has the property of being young when he eats theforbiddenfruit and the propertyof being old in the year 930, andthat these properties, hough different,are not incompatible. Andso, too, for the differentpossible worlds: It is not true that theAdam of W1 has propertiesthat render him discernible from theAdam of W2; the truth is, rather, that Adam has the propertyofliving for 930 years in W1 and the propertyof living for 931 inW2, and that these properties,though different, are not incom-patible."I think it is clear that we must deal with the old Adam andthe young Adam in the manner indicated; but in this case, onecould argue, we know independentlythat the same Adam is in-volved throughout.But are we justified in dealing in a similarway with the Adam of W1 and the Adam of W2? In this lattercase, one might say, we do not know independently that the

'It should be noted that the possible world in question is not one thatHintikka would call epistemicallypossible, for it could be said to contain certainstates of affairs (Adam living for 931 years) which are incompatible withwhat we know to hold of this world; hence it is not one of the worlds Hintikkais concernedwith in the passage quoted above. But it is logically possible, andthat is all that matters for purposes of the present discussion.

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IDENTITY THROUGH POSSIBLE WORLDS: SOME QUESTIONS 3same Adam is involved throughout. Here, then, is one of thequestions that I do not know how to answer. Let us suppose,however, that we answer it affirmatively.The Adam of this world, we are assuming, is identical withthe Adam of that one. In other words, Adam is such that helives for only 930 years in W1 and for 931 in W2. Let us nowsuppose further that we have arrived at our conception of W2,not only by introducingalterations n our descriptionof the Adamof W1, but also by introducingalterations in our description ofthe Noah of W1. We say; "SupposeAdamhad lived for 931 yearsinstead of 930 and suppose Noah had lived for 949 years insteadof 950."We then arriveat ourdescriptionof W2by accommodatingour descriptions of the other entities of-W1 in such a way thatthese entities will be capable of inhabitingthe same possibleworldas the revised Noah and the revised Adam. Both Noah andAjdam, hen, may be found in W2 as well as in W1.Now let us move from W2 to still another possible worldW3. Once again,we will start by introducingalterations in Adamand Noah and then accommodate he rest of the world to'what wehave done. In W3 Adamlives for 932 yearsand Noah for 948. Thenmoving from one possible world to another, but keeping ourfingers, so to speak, on the same two entities, we arrive at aworld in which Noah lives for 930 years and Adam for 950. Inthat world, therefore, Noah has the age that Adam has in thisone, and Adam has the age that Noah has in this one; the Adamand Noah that we started with might thus be said to have ex-changed their ages. Now let us continue on to still other possibleworlds and allow them to exchangestill other properties.We willimagine a possible world in which they have exchanged the firstletters of their names, then one in which they have exchangedthe second, then one in which they have exchanged the fourth,with the result that Adamin this new possibleworld will be called"Noah"and Noah "Adam."Proceding n this way, we arrivefinallyat a possible world Wnwhich would seem to be exactly like ourpresentworld W1, except for the fact that the Adam of Wnmay betraced back to the Noah of W1 and the Noah of Wnmay be tracedback to the Adam of W'.

Should we say of the Adam of Wn that he is identical withthe Noah of W' and should we say of the Noah of Wn that heis identical the Adam of W'? In other words, is there an x suchthat x is Adam in WI and x is Noah in Wn,and is there a y such

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4 NOUSthat y is Noah in W' and y is Adam in Wn? And how are we todecide?But let us suppose that somehow we have arrived at anaffirmativeanswer. Now we must ask ourselves: How is one totell the difference between the two worlds W1 and Wn? Shall wesay that, though they are diverse, they are yet indiscerniblefromeach other-or, at any rate, that the Adam of W' is indiscerniblefrom the Adam of Wn (who is in fact the Noah of W') and thatthe Noah of W' is indiscerniblefrom the Noah of Wn (who is infact the Adamof WI')?There is a certain ambiguity n "discernible"and in "indiscernible". he two Adams could be called "discerni-ble" in that the one has the property of being Noah in the otherworld and the other does not, and similarly for the two Noahs.But in the sense of "indiscernible"hat allows us to say that"Indiscernibles re identical" ells us more than merely "Identicalsare identical," aren't the two Adams, the two Noahs, and thetwo worldsindiscernible?Could God possiblyhave had a sufficientreason for creating W' instead of Wn?If W' and Wn are two different possible worlds, then, ofcourse, there are indefinitely many others, equally difficultto dis-tinguish from each other and from W' and Wn. For what we havedone to Adam and Noah, we can do to any other pair of entities.Therefore among the possible worlds which would seem to be in-discerniblefrom this one, there are those in which you play therole that I play in this one and in which I play the role that youplay in this one.4 (If this is true, there may be good groundfor the existentialist'sAngst; since, it would seem, God couldhave had no sufficientreasonfor choosing the world in which youplay your present role instead of one in which you play mine.)Is there really a good reason for saying that this Adam andNoah are identical, respectively,with that Noah and Adam? Weopened the door to this conclusion by assumingthat Adam couldbe found in more than one possible world-by assumingthat thereis an x such that x is Adam in W' and lives here for 930 yearsand x is also Adam in W2 and lives there for 931. If it is reason-

'"She (Ivich) looked at the glass, and Mathieu looked at her. A violentand undefineddesire had taken possessionof him; a desire to be for one instantthat consciousness . .. to feel those long slender arms from within. . . . Tobe Ivich and not to cease to be himself." Sartre, The Age of Reason. CompareN. L. Wilson, "Substance without Substrata," Review of Metaphysics, XII(1959), and A. N. Prior, "Identifiable Individuals," Review of Metaphysics,XIII ( 1960).

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IDENITUY THROUGH POSSIBLE WORLDS: SOME QUESTIONS 5able to assume hat Adamretainshis identity through he relativelyslight changesinvolvedin the transition rom W1 to W2, and so,too, for Noah, then it would also seem reasonableto assumethateach retains his identity through the equally slight changes in-volved in all the other transitionsthat took us finally to Wn.(These transitions,of course,may be as gradual as one pleases.Insteadof it being a year thatwe take away fromNoah in our firststep and give to Adam, it could be only a day, or a fractionof a second.) But identity is transitive.And therefore,one mightargue, once we allow Adam to exist in more than one possibleworld,we commitourselvesto affirmative nswersto the puzzlingquestionswe have encountered.Is there a way, then, in which we might reasonablycounte-nance identity throughpossibleworldsand yet avoid such extremeconclusions?The only way, so far as I can see, is to appeal tosome versionof the doctrinethat individual things have essentialproperties.One possibilitywould be this:For everyentityx, there are certainpropertiesN and certainpropertiesE such that: x has N in some possible worlds andx has non-N in others;but x has E in every possible world inwhich x exists; and, moreover,for every y, if y has E in anypossible world, then y is identical with x. (If "being identicalwith x7 refers to a propertyof x, then we should add that Eincludescertainpropertiesother than that of being identicalwithx.) The propertiesE will thus be essentialto x and the propertiesN twn-essential,or accidental."To avoid misunderstanding,we should contrast this presentuse of "essentialproperty"with two others.

(1) Sometimes he "essentialproperties" f a thing are saidto be just those propertiesthat the thing has necessarily. Butit is not implausible o say that there are certainpropertieswhichare such that everything has those properties necessarily; theproperties, or example,of being either red or non-red,of beingcoloredif red, and of being self-identical.6Thus the Eiffel Tower6 We could put the doctrinemorecautiously by saying that the distinctionbetween the two types of property holds, not for every entity x, but only forsome entities x. But what reason could there be for thinking that it holds of

some entities and not of others?' Sometimesthese propertiesare called "analyticproperties"or 'tautologi-cal properties";but the property of being colored if red should not be so-called if, as some have argued, "Everything that is red is colored" is notanalytic.

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6 NONSis necessarilyred or non-red, necessarily colored if red, and neces-sarily self-identical;and so is everything else.7(2) And sometimesit is said (most unfortunately, t seemsto me) that each individual thing is such that it has certainpropertieswhich are essential or necessary to it "under certaindescriptionsof it" and which are not essential or necessary to it"under certain other descriptionsof it." Thus "underone of hisdescriptions,"he propertyof being Presidentis said to be essen-tial to Mr. Johnsonwhereas "underthat description"he propertyof being the husbandof Lady Bird is not; and "underanotheroneof his descriptions,"t is the other way around. PresumablyeverypropertyP of every individual thing x is such that, "undersomedescriptionof x," P is essential or necessaryto x.But if E is the set of propertiesthat are essential to a giventhing x, in the sense of "essential' that we have defined above,then: E will not be a universalproperty (indeed, nothing but xwill have E); some of the propertiesof x will not be included inE; and E will not be such that there are descriptionsof x "underwhich" E is not, in the sense defined, essential to x.

If we acceptthis doctrineof essentialproperties,we may say,perhaps,that the propertyof living for just 930 years is essentialto Adam and thereforethat he may inhabit other possible worldswithout living for just 930 years in each of them. And so, too,perhaps,for having a name which, in English, ends with the letter"In".But, we may then go on to say, somewhere in the journeyfrom W' to Wn, we left the essential properties of Adam (andthereforeAdam himself) behind. But where? What are the prop-erties that are essential to Adam?Being the first man? Having aname which, in English, begins with the first letter of the alpha-bet? But why these properties?If we can contemplateAdam withslightly different propertiesin another possible world, why can'twe think of him as having ancestorsin some possible worlds andas having a differentname in others?And similarlyfor any otherpropertythat might be proposedas being thus essentialto Adam.

I From the propositionthat the Eiffel Tower is red and necessarilycoloredif red, it would be fallaciousto infer that the Eiffel Tower is necessarilycolored;this is the fallacy of inferring necessitate consequentis from necessitate conse-quentiae. And from the propositionthat the Eiffel Tower is necessarily red ornon-red, it would be fallacious to infer that the proposition that the EiffelTower is red or non-red is a necessaryproposition;the propositioncould hardlybe necessary, for it implies the contingent proposition that there is an EiffelTower. This latter fallacy might be called the fallacy of inferring necessitatede dicto from necessitate de re.

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IDENTITY THROUGH POSSIBLE WORLDS: SOME QUESTIONS 7It seems to me that even if Adam does have such essentialproperties, here is no procedureat all-for finding out what theyare. And it also seems to me that there is no way of finding outwhether he does have any essential properties.Is there really agood reason, then, for supposingthat he does?The distinction between essential and non-essentialproper-ties seems to be involvedin one of the traditionalways of dealingwith the problemof knowingwho.8 If this way of dealing withthat problem were satisfactory,then the doctrine of essentialpropertiesmight have a kind of independentconfirmation.But Iam not surethat is satisfactory.The problem of knowingwhomaybe illustrated n this way. I do not know who it was who robbedthe bank this morning,but I do know,let us assume,that there issomeonewho robbed the bank and I also know that that personis the man who drove off from the bank at 9:20 A.M. in a BuickSedan.For me to know who he is, therefore, t is not enough forme to have information nablingme to characterizehim uniquely.What kind of information, hen, would entitle me to say that Iknow who he is? The essentialisticanswerwould be: "Youknowwho the bank robber is, provided that there is a certain set ofpropertiesE which are essentialto the x such that x robbed thebank and you know that x has E and x robbed the bank."But ifmy doubts about essentialproperties are well-founded,this solu-tion to the problemof knowingwho would imply that the police,though they may finally "learn the thief's identity,"will neverknow that they do. For to know that one knowswho the thief is(accordingto the proposedsolution) one must know what prop-ertiesare essentialto the thief; and if what I have said is correct,we have no way of findingout what they are. How are the policeto decide that they know who the thief is if they have no answerto the metaphysicalquestion "What are the essential propertiesof the man we have arrested?""8 CompareAristotle, De Sophisticis Elenchis, 179 b 3; Petrus Hispanus,SummulaeLogicales,ed. I. M. Bochenski (Turin, 1947), 7.41; Franz Brentano,Kategorienlehre Leipzig, 1933), p. 165.' Hintikka says that we know who the thief is provided that there existsan x such that we know that the thief is identical with x (op. cit., p. 153). Butunder what conditionsmay it be said that there exists an x such that we know

that the thief is identical with x? Presumably, f ever, when we catch him in theact-when we see him steal the money. But the teller saw him steal the moneyand she doesnt know who he is. I have suggested elsewhere a slightly differentway of looking at these questions;compare op. cit., pp. 789-791, and "Believingand Intentionality,"Philosophyand PhenomenologicalResearch,XXV (1964),pp. 266-269, esp. p. 268.

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8 NONSIt is assumed,in many writingson modal logic, that 'Neces-

sarily, for every x, x is identical with x" implies "For every x,necessarilyx is identical with x," and therefore also "For every xand y, if x is identical with y, then necessarilyx is identical withy."But is the assumptionreasonable? t leads us to perplexingcon-clusions: for example,to the conclusionthat every entity exists inevery possibleworld and therefore,presumably, hat everythingisan ens necessarium.Why assume that necessarily the evening star is identicalwith the evening star?We should remindourselvesthat "The eve-ning star is identical with the evening star" s not a logical truth,for it implies the contingent proposition "There is an eveningstar,"and that its negation is not "The evening star is diversefrom the evening star." Wouldn't it be simpler to deny that"Necessarily, or every x, x is identical with x" implies "Foreveryx, necessarily x is identical with x"? Then we could deny theprinciple de dicto, "Necessarily he evening star is identical withthe evening star,"and also deny the principle,de re, "Theeveningstar is necessarily identical with the evening star."0LWe couldstill do justice to the necessity that is here involved, it seems tome, providedwe continued to affirmsuch principles,de dicto, as"Necessarily, or every x, x is identical with x" and "Necessarily,for every x and y, if x is identical with y then y is identical withx," and such principles,de re, "The evening star, like everythingelse, is necessarilyself-identical."

10 I have discussed this possibility in "Queryon Substitutivity," n BostonStudies in the Philosophy of Science, Vol. II, ed., Robert S. Cohen and MarxW. Wartofsky (New York: The Humanities Press, 1965), pp. 275-278.If we deny that "Necessarily,for every x, x is F" implies "For every x,necessarily x is F," then presumablywe should also deny that "It is possiblethat there exists an x such that x is F" implies "There exists an x such that itis possible that x is F." But isn't this what we should do? One could holdquite consistently, it seems to me, that though it is possible that there existssomething having the properties that Christiansattribute to God, yet nothingthat does exist is such that it is possible that that thing has the properties thatChristiansattribute to God.