I hadn’t expected that the reading assignment I was given for the philosophy of logic course would be the only one for which I couldn’t find a Chinese translation…………not even an English electronic version was easy to find.
At last I found the original PDF version, http://www.jstor.org/view/00294624/di982797/98p0002q/0
I ran it through Hanwang Text King OCR myself, and after some preliminary correction it is as follows. Turning it into an electronic text makes it a little easier to read with the help of Kingsoft PowerWord……but it is still awfully painful……
Identity through Possible Worlds: Some Questions
Roderick M. Chisholm
Noûs, Vol. 1, No. 1. (Mar., 1967), pp. 1-8.
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Identity Through Possible Worlds:
Some Questions
RODERICK M. CHISHOLM
BROWN UNIVERSITY
It is now easy to see a simple way of avoiding undesirable existential generalizations in epistemic contexts. Existential generalization with respect to a term–say b–is admissible in such contexts if b refers to one and the same man in all the “possible worlds” we have to consider.
—Hintikka[1]
1 In an article on Hintikka’s Knowledge and Belief, I suggested that certain difficult questions come to mind when we consider the thought that an individual in one possible world might be identical with an individual in another possible world.[2] The present paper is written in response to the editor’s invitation to be more explicit about these questions.
2 Let us suppose, then, that the figure of an infinity of possible worlds makes good sense and let us also suppose, for simplicity of presentation, that we have a complete description of this one. We may consider some one of the entities of this world, alter its description slightly, adjust the descriptions of the other entities in the world to fit this alteration, and then ask ourselves whether the entity in the possible world that we thus arrive at is identical with the entity we started with in this world. We start with Adam, say; we alter his description slightly and allow him to live for 931 years instead of for only 930; we then accommodate our descriptions of the other entities of the world to fit this possibility (Eve, for example, will now have the property of being married to a man who lives for 931 years instead of that of being married to a man who lives for only 930); and we thus arrive at a description of another possible world.[3]
3 Let us call our present world “W1” and the possible world we have just indicated “W2”. Is the Adam of our world W1 the same person as the Adam of the possible world W2? In other words, is Adam such that he lives for just 930 years in W1 and for 931 in W2? And how are we to decide?
4 One’s first thought might be that the proposition that Adam is in both worlds is incompatible with the principle of the indiscernibility of identicals. How could our Adam be identical with that one if ours lives for just 930 years and that one for 931? Possibly this question could be answered in the following way:
5 “Compare the question: How can Adam at the age of 930 be the same person as the man who ate the forbidden fruit, if the former is old and the latter is young? Here the proper reply would be: it is not true that the old Adam has properties that render him discernible from the young Adam; the truth is, rather, that Adam has the property of being young when he eats the forbidden fruit and the property of being old in the year 930, and that these properties, though different, are not incompatible. And so, too, for the different possible worlds: It is not true that the Adam of W1 has properties that render him discernible from the Adam of W2; the truth is, rather, that Adam has the property of living for 930 years in W1 and the property of living for 931 in W2, and that these properties, though different, are not incompatible.”
6 I think it is clear that we must deal with the old Adam and the young Adam in the manner indicated; but in this case, one could argue, we know independently that the same Adam is involved throughout. But are we justified in dealing in a similar way with the Adam of W1 and the Adam of W2? In this latter case, one might say, we do not know independently that the same Adam is involved throughout. Here, then, is one of the questions that I do not know how to answer. Let us suppose, however, that we answer it affirmatively.
7 The Adam of this world, we are assuming, is identical with the Adam of that one. In other words, Adam is such that he lives for only 980 years in W1 and for 981 in W2. Let us now suppose further that we have arrived at our conception of W2,
not only by introducing alterations in our description of the Adam of W1, but also by introducing alterations in our description of the Noah of W1. We say; “Suppose Adam had lived for 981 years instead of 980 and suppose Noah had lived for 949 years instead of 950.” We then arrive at our description of W2 by accommodating our descriptions of the other entities of W1 in such a way that these entities will be capable of inhabiting the same possible world as the revised Noah and the revised Adam. Both Noah and Adam, then, may be found in W2 as well as in W1.
8 Now let us move from W2 to still another possible world W3. Once again, we will start by introducing alterations in Adam and Noah and then accommodate the rest of the world to, what we have done. In W3 Adam lives for 982 years and Noah for 948. Then moving from one possible world to another, but keeping our fingers, so to speak on the same two entities, we arrive at a world in which Noah lives for 980 years and Adam for 950. In that world, therefore, Noah has the age that Adam has in this one, and Adam has the age that Noah has in this one; the Adam and Noah that we started with might thus be said to have exchanged their ages. Now let us continue on to still other possible worlds and allow them to exchange still other properties. We will imagine a possible world in which they have exchanged the first letters of their names, then one in which they have exchanged the second, then one in which they have exchanged the fourth, with the result that Adam in this new possible world will be called “Noah” and Noah “Adam.” Proceeding in this way, we arrive finally at a possible world Wn which would seem to be exactly like our present world W1, except for the fact that the Adam of Wn may be traced back to the Noah of W1 and the Noah of Wn may be traced back to the Adam of W1.
9 Should we say of the Adam of Wn that he is identical with the Noah of W1 and should we say of the Noah of Wn that he is identical the Adam of W1? In other words, is there an x such that x is Adam in W1 and x is Noah in Wn, and is there a y such that y is Noah in W1 and y is Adam in Wn? And how are we to decide?
10 But let us suppose that somehow we have arrived at an affirmative answer. Now we must ask ourselves: How is one to tell the difference between the two worlds W1 and Wn? Shall we say that, though they are diverse, they are yet indiscernible from each other–or, at any rate, that the Adam of W1 is indiscernible from the Adam of Wn (who is in fact the Noah of W1) and that the Noah of W1 is indiscernible from the Noah of Wn (who is in fact the Adam of W1 )? There is a certain ambiguity in “discernible” and in “indiscernible”. The two Adams could be called “discernible” in that the one has the property of being Noah in the other world and the other does not, and similarly for the two Noahs. But in the sense of “indiscernible” that allows us to say that “Indiscernibles are identical” tells us more than merely “Identicals
are identical,” aren’t the two Adams, the two Noahs, and the two worlds indiscernible? Could God possibly have had a sufficient reason for creating W1 instead of Wn?
11 If W1 and Wn are two different possible worlds, then, of course, there are indefinitely many others, equally difficult to distinguish from each other and from W1 and Wn. For what we have done to Adam and Noah, we can do to any other pair of entities. Therefore among the possible worlds which would seem to be indiscernible from this one, there are those in which you play the role that I play in this one and in which I play the role that you play in this one.[4] (If this is true, there may be good ground for the existentialist’s Angst; since, it would seem, God could have had no sufficient reason for choosing the world in which you play your present role instead of one in which you play mine.)
12 Is there really a good reason for saying that this Adam and Noah are identical, respectively, with that Noah and Adam? We opened the door to this conclusion by assuming that Adam could be found in more than one possible world—by assuming that there is an x such that x is Adam in W1 and lives here for 930 years and x is also Adam in W2 and lives there for 931. If it is reasonable to assume that Adam retains his identity through the relatively slight changes involved in the transition from W1 to W2, and so, too, for Noah, then it would also seem reasonable to assume that each retains his identity through the equally slight changes involved in all the other transitions that took us finally to Wn. (These transitions, of course, may be as gradual as one pleases. Instead of it being a year that we take away from Noah in our first step and give to Adam, it could be only a day, or a fraction of a second.)But identity is transitive. And therefore, one might argue, once we allow Adam to exist in more than one possible world, we commit ourselves to affirmative answers to the puzzling questions we have encountered.
13 Is there a way, then, in which we might reasonably countenance identity through possible worlds and yet avoid such extreme conclusions? The only way, so far as I can see, is to appeal to some version of the doctrine that individual things have essential properties. One possibility would be this:
14 For every entity x, there are certain properties N and certain properties E such that: x has N in some possible worlds and x has non-N in others; but x has E in every possible world in which x exists; and, moreover, for every y, if y has E in any possible world, then y is identical with x. (If “being identical with x” refers to a property of x, then we should add that E includes certain properties other than that of being identical with x.) The properties E will thus be essential to x and the properties N non-essential, or accidental.[5]
15 To avoid misunderstanding, we should contrast this present use of “essential property” with two others.
16 (1) Sometimes the “essential properties” of a thing are said to be just those properties that the thing has necessarily. But it is not implausible to say that there are certain properties which are such that everything has those properties necessarily; the properties, for example, of being either red or non-red, of being colored if red, and of being self-identical.[6] Thus the Eiffel Tower is necessarily red or non-red, necessarily colored if red, and necessarily self-identical; and so is everything else.[7]
17 (2) And sometimes it is said (most unfortunately, it seems to me) that each individual thing is such that it has certain properties which are essential or necessary to it “under certain descriptions of it” and which are not essential or necessary to it “under certain other descriptions of it.” Thus “under one of his descriptions,” the property of being President is said to be essential to Mr. Johnson whereas “under that description” the property of being the husband of Lady Bird is not; and “under another one of his descriptions,” it is the other way around. Presumably every property P of every individual thing x is such that, “under some description of x,” P is essential or necessary to x.
18 But if E is the set of properties that are essential to a given thing x, in the sense of “essential” that we have defined above, then: E will not be a universal property (indeed, nothing but x will have E): some of the properties of x will not be included in E; and E will not be such that there are descriptions of x “under which” E is not, in the sense defined, essential to x.
19 If we accept this doctrine of essential properties, we may say, perhaps, that the property of living for just 930 years is not essential to Adam and therefore that he may inhabit other possible worlds without living for just 930 years in each of them. And so, too, perhaps, for having a name which, in English, ends with the letter “m”. But, we may then go on to say, somewhere in the journey from W1 to Wn, we left the essential properties of Adam (and therefore Adam himself) behind. But where? What are the properties that are essential to Adam? Being the first man? Having a name which, in English, begins with the first letter of the alphabet? But why these properties? If we can contemplate Adam with slightly different properties in another possible world, why can’t we think of him as having ancestors in some possible worlds and as having a different name in others? And similarly for any other property that might be proposed as being thus essential to Adam.
20 It seems to me that even if Adam does have such essential properties, there is no procedure at all for finding out what they are. And it also seems to me that there is no way of finding out whether he does have any essential properties. Is there really a good reason, then, for supposing that he does?
21 The distinction between essential and non-essential properties seems to be involved in one of the traditional ways of dealing with the problem of knowing who.[8] If this way of dealing with that problem were satisfactory, then the doctrine of essential properties might have a kind of independent confirmation. But I am not sure that is satisfactory. The problem of knowing who may be illustrated in this way. I do not know who it was who robbed the bank this morning, but I do know, let us assume, that there is someone who robbed the bank and I also know that that person is the man who drove off from the bank at 9:20 A.M. in a Buick Sedan. For me to know who he is, therefore, it is not enough for me to have information enabling me to characterize him uniquely. What kind of information, then, would entitle me to say that I know who he is? The essentialistic answer would be: “You know who the bank robber is, provided that there is a certain set of properties E which are essential to the x such that x robbed the bank and you know that x has E and x robbed the bank.” But if my doubts about essential properties are well-founded, this solution to the problem of knowing who would imply that the police, though they may finally “learn the thief’s identity” will never know that they do. For to know that one knows who the thief is (according to the proposed solution) one must know what properties are essential to the thief; and if what I have said is correct, we have no way of finding out what they are. How are the police to decide that they know who the thief is if they have no answer to the metaphysical question “What are the essential properties of the man we have arrested?”[9]
22 It is assumed, in many writings on modal logic, that “Necessarily, for every x, x is identical with x” implies “For every x, necessarily x is identical with x,” and therefore also “For every x and y, if x is identical with y, then necessarily x is identical with y.” But is the assumption reasonable? It leads us to perplexing conclusions: for example, to the conclusion that every entity exists in every possible world and therefore, presumably, that everything is an ens necessarium.
23 Why assume that necessarily the evening star is identical with the evening star? We should remind ourselves that “The evening star is identical with the evening star” is not a logical truth, for it implies the contingent proposition “There is an evening star,” and that its negation is not “The evening star is diverse from the evening star.” Wouldn’t it be simpler to deny that “Necessarily, for every x, x is identical with x” implies “For every x, necessarily x is identical with x”? Then we could deny the principle de dicto, “Necessarily the evening star is identical with the evening star,” and also deny the principle, de re, “The evening star is necessarily identical with the evening star.”[10] We could still do justice to the necessity that is here involved, it seems to me, provided we continued to affirm such principles, de dicto, as “Necessarily, for every x, x is identical with x” and “Necessarily, for every x and y, if x is identical with y then y is identical with x,” and such principles, de re, “The evening star, like everything else, is necessarily self-identical.”
[1] Jaakko Hintikka, Knowledge and Belief: An Introduction to the Logic of the Two Notions (Ithaca: Cornell University Press, 1962), p. 152.
[2] “The Logic of Knowing,” 1ournal of Philosophy, LX (1968), pp. 778-795; see especially pp. 787-795.
[3] It should be noted that the possible world in question is not one that Hintikka would call epistemically possible, for it could be said to contain certain states of affairs (Adam living for 931 years) which are incompatible with what we know to hold of this world; hence it is not one of the worlds Hintikka is concerned with in the passage quoted above. But it is logically possible, and that is all that matters for purposes of the present discussion.
[4] “She (Ivich) looked at the glass, and Mathieu looked at her. A violent and undefined desire had taken possession of him; a desire to be for one instant that consciousness . . . to feel those long slender arms from within . . .To be Ivich and not to ,cease to be himself.” Sartre, The Age of Reason. Compare N. L. Wilson, “Substance without Substrata,” Review of Metaphysics, XII (1959), and A. N. Prior, “Identifiable Individuals,” Review of Metaphysics, XIII (1960).
[5] We could put the doctrine more cautiously by saying that the distinction between the two types of property holds, not for every entity x, but only for some entities x. But what reason could there be for thinking that it holds of some entities and not of others?
[6] Sometimes these properties are called “analytic properties” or “tautological properties”; but the property of being colored ff red should not be socalled if, as some have argued, “Everything that is red is colored” is not analytic.
[7] From the proposition that the Eiffel Tower is red and necessarily colored if red, it would be fallacious to infer that the Eiffel Tower is necessarily colored; this is the fallacy of inferring necessitate consequentiae from necessitate consequentiae. And from the proposition that the Eiffel Tower is necessarily red or non-red, it would be fallacious to infer that the proposition that the Eiffel Tower is red or non-red is a necessary proposition; the proposition could hardly be necessary, for it implies the contingent proposition that there is an Eiffel Tower. This latter fallacy might be called the fallacy of inferring necessitate de dicto from necessitate de re.
[8] Compare Aristotle, De Sophisticis Elenchis, 179 b 3; Petrus Hispanus, Summulae Logicales, ed. I. M. Boehenski (Turin, 1947), 7.41; Franz Brentano, Kategorienlehre (Leipzig, 1933), p. 165.
[9] Hintikka says that we know who the thief is provided that there exists an x such that we know that the thief is identical with x (op. cir., p. 153). But under what conditions may it be said that there exists an x such that we know that the thief is identical with x? Presumably, if ever, when we catch him in the act-when we see him steal the money. But the teller saw him steal the money and she doesn’t know who he is. I have suggested elsewhere a slightly different way of looking at these questions; compare op. cir., pp. 789-791, and “Belietng and Intentionality,” Philosophy and Phenomenological Research, XXV (1964), pp. 266-269, esp. p. 268.
[10] I have discussed this possibility in “Query on Substitutivity,” in Boston Studies in the Philosophy of Science, Vol. II, ed., Robert S. Cohen and Marx W. 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 presumably we should also deny that “It is possible that there exists an x such that x is F” implies “There exists an x such that it is possible that x is F.” But isn’t this what we should do? One could hold quite consistently, it seems to me, that though it is possible that there exists something having the properties that Christians attribute to God, yet nothing that does exist is su.ch that it is possible that that thing has the properties that Christians attribute to God.
Lecture Report for the Logic and Philosophy course on Identity through Possible Worlds: Some Questions
Xingding published on 2006-06-08 11:01:54
1
— The question: how can some individual in one possible world possibly be “identical” to some individual in another possible world?
2
— What does possible worlds theory imply? (Chisholm is an opponent of possible worlds theory.) We fine-tune our description of some thing in this world, then adjust the descriptions of other things to fit this alteration, and then say that that thing in the altered possible world is identical to this thing in this world. Take Adam as an example: we slightly modify his lifespan, changing it from 930 years to 931 years, and then the descriptions of some other things also have to be adjusted accordingly—for instance, Eve was originally married to a man who lived 930 years, but now she is married to a man who lived 931 years. Once these adjustments are made, we arrive at another possible world.
3
— Let us abbreviate the current world as W1 and the possible world referred to above as W2. How are we to judge that Adam is precisely the person who lived 930 years in W1 and 931 years in W2?
4
— To say that Adam exists in both worlds is obviously to violate Leibniz’s “identity of indiscernibles” principle—that is, two things are identical if and only if all their properties are the same.
5
— One possible answer to this question is: first compare this problem—how is the old Adam of 930 years old the same person as the Adam who ate the forbidden fruit? A reasonable answer would be: Adam, when he ate the forbidden fruit, had the property of being “young,” whereas the 930-year-old Adam has the property of being “old”; these two properties are certainly different, but they are not incompatible. Likewise, in different possible worlds, 930 years and 931 years are certainly different, but that does not make the two Adams impossible to recognize as one and the same person.
6
— But granted, one can indeed handle the problem of the old Adam and the young Adam this way; but is it legitimate to apply this line of thought to the problem of transworld identity? In the former problem, we can independently know that what runs through is the same Adam throughout (probably meaning that the change is continuous), but in the transworld problem, if we also admit that slightly different Adams are the same, then……
7~11
— If we suppose that the Adam who lived 930 years in W1 and the Adam who lived 931 years in W2 are the same, then problems arise—for example, by continuously fine-tuning we could make Adam, step by step, into Noah, while at the same time turning Noah into Adam, and then everything would be in chaos, and so on. / — I think these remarks are very uninteresting. We can very easily imagine how he “changes,” but his playing this sort of trick does not explain anything. Rather than showing the absurdity of transworld identity, it is better understood as showing that the transitivity of transworld identity is unreasonable. In general, Chisholm always takes Leibniz’s criterion of identity as the standard of judgment; the absurd conclusions that arise are precisely evidence that Leibniz’s definition of identity is unreasonable.
12
— Chisholm analyzes the matter and says that the premise assumption producing such absurd conclusions is that Adam can be found in different possible worlds; once this is assumed, absurd results inevitably follow: “once we allow Adam to exist in more than one possible world, we commit ourselves to affirmative answers to the puzzling questions we have encountered.” / — But this conclusion is clearly not derived from that single premise alone. If absurd conclusions appear, one should examine the entire line of reasoning and every premise assumption used in it; yet with the other premises used in the derivation, Chisholm either ignores them or dismisses them with a casual “obviously,” as in “But identity is transitive”—transitive? Why is this claim, which is itself a premise, so readily let off the hook? Besides transworld identity, other suspect assumptions include: is identity transitive? Are all properties transformable through fine-tuning? Even if we say that a few grains of millet and a heap of millet can change continuously, can the presence of millet and the absence of millet also transform continuously? Even if 930 years can change into 931 years, can Adam be turned into a woman? As Teacher Chen also mentioned, essentialism is not utterly without merit. Chisholm mentions essentialism later on, but he never once reflects on the transitivity of identity; I will discuss this issue below.
13
— Is there any way that might support transworld identity while avoiding these extremely absurd conclusions? The only way I can currently think of is (essentialism).
14
— The essentialist view says that for a thing x, we should distinguish two different kinds of properties: one essential, primary—E—and one inessential, secondary—N. Things that include or exclude N in different worlds, so long as they all include E, are identical.
15
— To avoid misunderstanding, let me distinguish two kinds:
16
— One kind of essence (necessary property) consists of things such as “red or not red,” “possibly red,” “self-identical,” and so forth. These are indeed invariant, but they are properties possessed by any thing whatsoever.
17
— The other kind is that under one description of a thing, certain properties are essential or necessary, whereas under other descriptions those properties are not essential or necessary. That is to say, under one description, “being the President of the United States” is a necessary property for Johnson, whereas “being Bird’s husband” is not an essential property; under another description of him, the opposite holds. Probably for every thing x, every property P is similar—“under some descriptions of x,” P is essential or necessary for x. / — I think this precisely shows the importance of “under some description” for discussions of identity.)
18
— But such a “essential property” P does not satisfy the earlier definition of identity, namely, “x and only x has P.” / — (But why do we always lack the courage to question the earlier definition?)
19
— If we accept this kind of essentialism, we might say: perhaps living 930 years is not an essential property of Adam, so the same Adam may have different lifespans in different worlds, and so on. But in the process from W1 to Wn, we have lost Adam’s “essence”; but where exactly was it lost? What exactly is Adam’s essence? The first man? The last letter in his name? Why?
20
— It seems to me that even if Adam has certain essential properties, there is no means whatsoever of discovering them. And that also means there is no way of discovering whether he actually has any essential properties at all.
21
— The distinction between essential and nonessential seems to be related to the discussion of a traditional problem. If one’s treatment of that problem is satisfactory, essentialism may receive a bit of support. But I am not convinced that it is satisfactory. — I don’t know who robbed the bank in the morning, but I know there is a bank robber and that person left the bank at 9:20 a.m. in a Buick Sedan. ………… But how can the police determine that he is the thief if they cannot answer the question of what the essence of the arrested person is?
22~23
— Regarding de re logic and de dicto logic, see pages 327 and following of Logic and Philosophy
My view:
First of all, Chisholm always adheres to Leibniz’s definition of identity without the slightest doubt, which makes the later discussion veer further and further off course.
I think Leibniz’s definition of identity is unreasonable. At most it is mathematical identity—for example, the centroid and the orthocenter of an equilateral triangle can be said to be “identical”—but with that sort of definition, one can at best analyze identity within a static world; it is difficult to analyze any kind of relation in the real world. For example, as Chisholm himself already noted, on what grounds can we say that the young Adam and the old Adam are the same person? His treatment of this in the text is very perfunctory, as if to say that there exists a single Adam running through everything, but what we are asking is precisely how one can say there exists a single Adam running through everything. In any case, according to Leibniz’s definition, I cannot say that I now and I this morning are “identical”; so what exactly is the relation between me now and me this morning? Clearly, the me of this morning and the me of now are the same person, but according to Leibniz one cannot say the two are identical—so who exactly is mistaken? What is the relation between a ship that has had one part replaced and the original ship? If one says it is the same ship, then by accumulating fine-tuned changes we can also turn one ship into another, and then reassemble all the removed parts into a ship exactly the same as the original one. The old puzzle of swapping back and forth between two ships is just like Chisholm’s shifting back and forth between Adam and Noah; one could say that Chisholm has not raised any new problem of transworld identity at all, but has merely raised the old problem of identity again in the context of modal logic.
Second, why must identity be transitive? If W1 is identical to W2, and W2 is identical to W3, does it necessarily follow that W1 is identical to W3? Whether or not this premise is reasonable, Chisholm lets it pass unexamined far too easily; as a logician, that is unquestionably a dereliction of duty.
In modal logic, a “model” in possible-world semantics is 〈W, R, V〉, where W is the set of all possible worlds, V is the valuation, and the key element that cannot be ignored is R—that is, the accessibility relation among possible worlds. In Chisholm’s entire discussion, R is not taken into account, or else is simply set as a universal relation. But in fact, not every modal logical system requires the relation between possible worlds to be necessarily transitive.
There is another question that is easy to overlook—why is it that everyone who admits transworld identity must also admit that the Adam who lived 930 years and the Adam who lived 931 years are identical? Is it possible, while admitting transworld identity, to hold that one cannot say that individuals under fine-tuned alterations are identical? I think one can support transworld identity while not allowing unconditional fine-tuning. This is what I want to say below—the importance of context for cross-world identification. For example: in the possible world involved when we talk about the question “If Adam had lived 931 years, then…,” the Adam who lived 931 years will be identified as “the same” as the Adam in the initial world; but in the possible world involved when we discuss the question “If the last letter of Adam’s English spelling were n, then…,” Adam will not be allowed to be the one who lived 931 years. I will explain this concretely below:
I think that talking about A and B being “identical” is precisely closely related to “under which description”; in other words, it is related to what “difference” we want to talk about between them. The way we speak of their differences is also one of the elements in judging their “identity.” This is not nonsense. For example, how are we even able to talk about “change”? Under what conditions are we qualified to say “A has become B”? In fact, if we do not acknowledge a common point between A and B, if we do not acknowledge that there is something “unchanged” between A and B—in other words, if A and B are two completely different things—then how can we talk about change? Here I want to say: change and constancy are intertwined; if we detach one, we cannot speak of the other.
Is this just playing dialectical tricks? Is it that one can only define identity and difference in a circle? No, that is not the case, because talking about “change” does indeed require presupposing “unchanged,” but we are entitled to speak directly of “difference”: “A has property p, B does not have property p”—this is logically very clear. I am trying to use this to explain what identity means.
First, on what grounds can we say that I now and I this morning are the same person? Regarding the problem of identity, I think Quine said it very well in Word and Object; he mentioned the saying “one cannot step into the same river twice,” and Quine pointed out: “‘this river’ means ‘a collection of momentary objects, including the object of this instant, with river-like characteristics’” (p. 62). Quine points out that “in reference, spatial range and temporal range cannot be completely separated.” I think Quine’s insight is profound. From Leibniz to Chisholm, what is in their heads as an understanding of reference is limited merely to a static, ideal, mathematical world, and real problems cannot be properly analyzed with that sort of worldview. However rigorous their logic may be, what use is it if it cannot analyze any real problem at all?
I think that “I” am not a point in the temporal process; rather, “I” includes the whole “process” composed of my experiences (Quine also mentions the word “process.” The reason we say that I now and I in the morning are identical is that, up until the morning, the experiences and process of these two things were the same. The difference between these two selves is that one has experienced half a day more and the other has not; remove the properties relevant to the distinction we are talking about, and the remaining properties of the two are entirely the same, so we say the two are identical.
By extension, in transworld identification: for example, we say that in one possible world I ate breakfast today. In another possible world I did not eat breakfast. How do we distinguish the same me in these two worlds? The method is: first examine the topic we are talking about—whether breakfast was eaten—and then remove from the two people in the two worlds the properties dependent on that event; for example, my condition at noon today depends on whether I ate breakfast, so temporarily remove these properties. What remains is all the properties of those two people that are unrelated to whether breakfast was eaten—for example, here it is the entirety of the experiences, states, and processes before this morning. If these are entirely the same, then we say the two people are “identical.” It should be noted that, in fact, “possible worlds” are precisely something we design according to the needs of the topic at hand, so the actual operation is not to distinguish between two worlds, but rather that when we design possible worlds, the rule we must follow is this: for two things called identical, all their properties must be the same except for the property we are talking about and the properties dependent on it. For example, when we discuss “if Adam lived one year longer, then…,” we set up a possible world in which Adam lived 931 years, but in that world we still think Adam is spelled “Adam.” If we continue to discuss the next question, “if the last letter of Adam’s name were n,” then we are setting up a new “branch” of possible worlds. This second-level branch is a possible world accessible from the first-level accessible world of the original world, but whether an accessible world of an accessible world is still an accessible world depends on the specific circumstances.
My point is this: suppose A and B in two possible worlds differ in property p, and when the topic we are talking about is “if p/non-p, then …” — for example, when talking about “if I had not eaten breakfast, then …” — then before I decided to eat breakfast, all my properties were irrelevant to this topic. Let us examine all the properties that A and B possess that are unrelated to p. If all the p-irrelevant properties that A and B possess are exactly the same, then we may judge A and B to be one and the same object of discourse. In other words, suppose that in two possible worlds there is a person in each world, one of whom has eaten breakfast and the other of whom has not. Then, for instance, the person who did not eat breakfast feels very hungry at noon, but the property of “feeling hungry at noon” is related to whether one has eaten breakfast or not. What that person did yesterday, however, is irrelevant. If we say that the two persons are identical in every respect except for properties related to whether they have eaten breakfast, then we are talking about one and the same object. Conversely, if we wish to speak of the same thing across two worlds, we require that we regard these two individuals as remaining as much alike as possible in every respect except for differences specially specified and properties dependent on those differences.
Of course, the foregoing analysis is too simplified. In the actual use of possible-world semantics, the setup of “difference” is often not so clear-cut. For example, when we say that a proposition is “necessarily” true in all accessible possible worlds, then if we say that “x necessarily has property p,” how are we to identify the location of the individual x in all the accessible possible worlds? I think that if we speak only in abstract terms, it really cannot be made clear. But in any case, I believe that in considering the problem of cross-world identity, one must not ignore the “R” in the possible-world model — how do we design a possible-world model in light of the needs of discussing a certain issue? How do we design the accessibility relation? This is the context in which cross-world identity is discussed: how we distinguish cross-world identity between W1 and W2 depends on how we previously distinguished W1 from W2, and how we connected them.
June 7, 2006
Translated from the Chinese original with AI assistance. The original text is authoritative.
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