A Defense of the Indiscernibility of Identicals more

İnan, İlhan, “A Defense of the Indiscernibility of Identicals”, Revue Roumaine de Philosophie, 61-72, Vol.48, 2004. A Defense of the Indiscerniblity of Identicals 1 By Ilhan Inan In this paper I attempt to defend a law that seems a priori true to some of us, but is denied by others, namely the Indiscernibility of Identicals, generally known as Leibniz’s Law. Though no one in the literature explicitly claims that the law is false, some attempt to show that the law is true only of certain types of properties, while others argue for claims that entail the falsity of it. What I will try to show in this paper is that arguments to the effect that Leibniz’s Law is not universally true of all properties contain certain fallacies, and that any attempt to limit the scope of the law to make it accord with some metaphysical thesis is ad hoc. Overall what I will say will not constitute a proof of the law, but instead it will cast doubt on all such attempts to undermine its universality. I. Introduction Though we may express Leibniz’s Law of the Indiscernibility of Identicals (LL) 2 in its symbolic form as LL. ∀x∀y [x = y → ∀Φ (Φ(x) → Φ(y))] , this doesn’t tell us what exactly the law says since what the variables range over is controversial. Some nominalists who deny the existence of intensional entities such as universals, properties, and concepts and even some anti-nominalists who take identity to be relation between singular terms are at times led to hold that LL is in fact a meta-linguistic principle, where the variables ‘x’ and ‘y’ above range over singular terms, and ‘Φ’ ranges over predicates. This would translate into ordinary language as “if ‘x’ and ‘y’ are coreferential singular terms, and ‘x’ attached to the predicate ‘Φ’ yields a true sentence ‘Φ(x)’, then ‘Φ(y)’ is also true.” This is the Rule of Substitution (RS), and I believe that it is not the correct interpretation of LL. 3 I presented some of the issues discussed in this paper in Utrecht, Holland at the Workshop on Intensional Logic and Natural Language Semantics (August, 1999), in Cracow, Poland at the 11th International Congress on Logic, Methodology, and the Philosophy of Science, (August, 1999) and in UC, Santa Barbara, USA at the Departmental Colloquium (March, 2000). I would like to thank the audiences at these conferences for their valuable comments. However, I should note that there have been substantial changes in my views since then. I owe my thanks to Stephen Voss who gave useful comments on an earlier draft, and to late Arda Denkel with whom one of the last joyful conversations I had before his death was on this issue. 2 It is not clear that Leibniz ever explicitly held this law despite the fact that we attribute it to him. For a discussion of this see F.Feldman, “Leibniz and ‘Leibniz’ Law’” in Phil Rev 79, pp.510-522, Oct 1970. 3 An explicit example of this view appears in D.Kalish, R.Montague, and G.Mar, LOGIC: Techniques of Formal Reasoning, Second Edition, New York, 1980, p.270: “One formulation of the principle [of the 1 İnan, İlhan, “A Defense of the Indiscernibility of Identicals”, Revue Roumaine de Philosophie, 61-72, Vol.48, 2004. In fact there are clear counter-examples to RS, but I will argue that none of them constitutes a counterexample to LL which, I believe, is good enough to show that LL is not RS. Furthermore what justifies the truth of RS (for those predicates that it is true of) is LL. The more common interpretation of LL is that it is a metaphysical doctrine about objects and their properties making no mention of any terms in the language, and thus is not a meta-linguistic principle. In ordinary English we could express LL as “if two objects are the same, then whatever is true of one is true of the other”. The fact that we have some difficulty in expressing LL in natural language (i.e. first talking about two objects and then saying they are the same) should not be taken as any evidence that LL is a meta-linguistic principle. 4 In what follows I will assume that LL is not a meta-linguistic principle, it is expressible only in second-order predicate logic, and it has an ontological commitment to properties (or some such intensional entity). 5 Given this interpretation of the law the question that interests me is whether the law is true for all possible values of ‘Φ’. Saying that ‘Φ’ ranges over properties is of little help, since there is a philosophical dispute on what exactly counts as a genuine property. Some have claimed, or implicitly assumed, or expressed views that entail that some of the so-called relational and modal properties are not genuine properties and thus cannot be values of the variable ‘Φ’. 6 In order to separate the problem of what ‘Φ’ ranges over from the problem of what counts as a genuine property, we may wish to call the values that ‘Φ’ takes “concepts”. So then all properties will be concepts, but perhaps not vice-versa. We can assume that every genuine predicate will denote a concept 7 , hence a concept is the thing that can be true of an Indiscernibility of Identicals] is the assertion that if two things are identical, then anything true of one is also true of the other; we understand this principle to assert that if two names designate the same object, then replacement of one by the other in any sentence cannot change the truth value of that sentence.” 4 The arguments given by Frege in his classic “On Sense and Reference” (P. Geach, and M. Black, eds., Translations from the Philosophical Writings of Gottlob Frege, Oxford: Basil Blackwell, 1970, pp.56-78) and Kripke in Naming and Necessity (Cambridge: Harvard University Press, 1972) against the thesis that identity is a relation between names and not objects can, with some revisions, apply against this claim as well. 5 So nominalists will definitely feel that the discussion to follow is based upon false metaphysical assumptions. Trying to refute their position is certainly not my intention here, however it seems to me that some of the things I will argue for will be of interest even to them. 6 Though I hold that these so-called relational properties are genuine properties, I will try to be neutral on that issue since it will play no role in my argument. In fact if the only reason one holds that these are not genuine properties is that this leads to apparent false instances of LL, by showing that that is not the case we can form a strong argument against them. In any case this is not my main concern. 7 Frege defined a concept as a function from objects to truth values. Stephen Voss pointed out to me that such a definition of a concept makes the truth of LL trivial. In order not to beg the question I will be neutral with respect to the question of what a concept is. İnan, İlhan, “A Defense of the Indiscernibility of Identicals”, Revue Roumaine de Philosophie, 61-72, Vol.48, 2004. object (even if it is not considered as being a genuine property of the object.) Having done this we will be in a position to express the problem without mentioning properties: Is LL true for all concepts? Given that the debate over the truth of LL can be expressed by a disagreement about the correct answer to this question, it really has nothing to do with what counts as a property and what doesn’t. For example one may hold that the so-called relational properties (such as being my favorite toy) are in fact concepts that are not genuine properties of objects, and nevertheless they may still consistently claim that such concepts can be the value of ‘Φ’ in LL. Having said all of this I will nevertheless prefer to use the term “property” rather than “concept” given that the latter notion has some misleading connotations and is ambiguous. 8 Thus throughout the rest of the paper I will use the term “property” in its broadest sense, simply to mean whatever it is that can be true (or false) of an object. II. The Apparent False Instances of LL Certain properties seem to falsify LL. One may for instance compare a man’s height with his height as a boy and claim that though the man is the boy (they are one and the same) the boy is short but the man is not. But when we put the time indexes in the appropriate places we see that such examples do not refute LL at all. However there are more challenging cases. First let us consider one of the arguments Descartes gives for the distinctness of mind and body: I can doubt the existence of my body, but I cannot doubt the existence of my mind; therefore, my body is distinct from my mind. Some authors have criticized this argument by claiming that there is an implicit use of LL that is unwarranted. They claim that for the argument to be sound, being something whose existence can be doubted by me must be a property that can be the value of ‘Φ’ in LL. In order to show that such is not the case they appeal to an argument by analogy. Here is an explicit instance of it by T.C. Moody: Descartes’s argument has subsequently been criticized for the way in which it depends upon the beliefs of the person involved. To make this criticism clear, consider the following example: Is it possible that you could be certain that the Prime Minister of Britain is alive but doubt that John Major is alive? Yes, 8 Though for Frege a concept is what a first-order predicate refers to in a sentential context, some of his followers (such as Alonzo Church) prefer to take it as the sense, rather than the referent of a predicate. This is the ambiguity I have in mind. Moreover many take a concept as a subjective entity (which Frege of course tried to deny), both in daily as well as philosophical language. İnan, İlhan, “A Defense of the Indiscernibility of Identicals”, Revue Roumaine de Philosophie, 61-72, Vol.48, 2004. it is possible if you don’t know that Mr. Major is the Prime Minister. Would it follow, form the fact that you can doubt that Mr. Major is alive, the he is not the Prime Minister? Obviously it wouldn’t…the fact that the body’s existence --but not the mind’s-- can be doubted doesn’t prove anything about whether the mind and the body are identical. Does this invalidate the principle of indiscernibility of identicals? No, but it shows that the principle needs to be clarified a bit. For A and B to be identical, what is required is not that they should have all properties in common; we know that that is too strong. Rather, A and B have to have all properties of a certain sort in common…Let’s call those properties that a thing has that do not depend upon what anybody believes about it its objective properties. Now we can restate the principle of indiscernibility of identicals as follows: A and B are identical if and only if every objective property of A is an objective property of B, and vice versa. If we then claim that being subject to doubt is not an objective property, Descrates’s argument for dualism fails. 9 This type of argument seems to intuitively appeal to some philosophers. For instance, if we consider the famous Evening Star-Morning Star case, though Babylonians believed that the Evening Star appears in the evening, they did not believe that the Morning Star appears in the evening, given that they had not discovered yet that the Evening Star is the Morning Star. It would seem that from these facts we could derive a contradiction by using the same kind of reasoning that Descartes uses in his argument. We may say: “The Evening Star has the property of being believed by the Babylonians to appear in the evening, but the Morning Star does not have that property. Given that the Evening Star has some property that the Morning Star doesn’t have, using LL we can conclude that they are distinct.” Another context in which the same issue arises is the Barcan-Kripke proof that identity is a necessary relation. Again one may try to show that the proof is unsound using exactly the same tactics and argue that there is an incorrect application of LL within the proof: i. ii. a = b ……(Assumption) a = a …..(Reflexivity of Identity) iii. ∀x∀y [x = y → ∀Φ (Φ(x) → Φ(y))]…..(LL) iv. a = b → [( a = a) → ( a = b)]…..(iii, UI(x/a), UI(y/b), UI(Φ/ x = a)) v. a = b…..(i,iv,MP, ii,MP) Here the crucial stage is to infer line-iv from line-iii where we instantiate ‘Φ’ to the property of being necessarily identical with a. Again an argument by analogy can be employed here which apparently shows 9 Todd C. Moody, Philosophy and Artificial Intelligence, Englewood Cliffs: Prentice Hall, 1993, pp.32-33. İnan, İlhan, “A Defense of the Indiscernibility of Identicals”, Revue Roumaine de Philosophie, 61-72, Vol.48, 2004. that these kind of modal properties cannot be within the range of LL. Consider another famous example due to Quine 10 : “9 is necessarily odd, but the number of planets is not. So one has a property that the other lacks, therefore by LL it follows that the number of planets is not 9”. What seems to give rise to the problem is an instantiation of ‘Φ’ to the property of being necessarily odd. Again we are supposed to conclude that the so-called modal properties cannot be within the range of LL. There have also been debates on several closely related ontological problems that are of relevance. One of them is the question of whether constitution is identity. When we consider a golden statue and the chunk of gold that it is made up of, we can show, by using LL, that these objects are distinct i.e. the statue is not the chunk, which would make it possible for two distinct objects to occupy the same space at the same time. Even if we accept that all the so-called extensional properties of the statue also are true of the chunk, their persistence conditions seem to be different. One can survive a melting process, the other one cannot; one is essentially a statue, the other one is not, etc. If we assume that modal predicates such as “___can survive a melting process” or “___is essentially a statue” denote properties that can be the values of the second-order variable in LL, we get the result that the statue is not the chunk of gold. Ones who feel uncomfortable with this conclusion try to block this kind of argument by claiming that these modal predicates do not denote extensional properties. This is the position of H. Noonan for instance, who calls such predicates “Abelardian” which he defines as “a predicate whose reference…can be affected by the subject term to which it is attached”. 11 Unlike Moody’s position Noonan does not explicitly limit the range of ‘Φ’ in LL to certain kinds of properties, though if his claim that modal predicates are Abelardian is false his argument amounts to the same thing. III. Non-extensional Predicates Let us say that a (one-place) predicate F is “non-extensional” just in case it is possible for there to be two customarily (in the Fregean sense) co-referential terms a and b such that Fa ↔ Fb is not true. There See his From a Logical Point of View, Ch. VIII, Reference and Modality, Harvard University Press, Second Edition, 1980, pp.143. 10 İnan, İlhan, “A Defense of the Indiscernibility of Identicals”, Revue Roumaine de Philosophie, 61-72, Vol.48, 2004. are certain predicates that are genuinely non-extensional. Here is an example due to Quine: Giorgione was so-called because of his size, but it is not true that Barbarelli was so-called because of his size, though Giorgione is Barbarelli. 12 Nobody of course would take this as being a false instance of LL, since “____ is so-called because of his size” is not a predicate that denotes a property independent of a sentential context, and the property it denotes is affected by the subject term, i.e. it is an Abelardian predicate. We cannot point to someone, and meaningfully say, “he was so-called because of his size” and thereby make a true statement unless the term “so-called” takes its anaphoric reference from another source. That is because “____is so-called because of his size” is a non-extensional predicate. However it is quite misleading to say that this predicate denotes a non-extensional property, since it does not denote any property except within the context of a sentence, and given a sentential context the property it denotes is extensional. In the sentence “Giorgione was so-called because of his size” the predicate denotes the property of being called ‘Giorgione’ because of his size which is certainly not an non-extensional property, since it is true of both Giorgione and Barbarelli given that they are one and the same. Such non-extensional predicates that have an indexical character no doubt falsify RS, since depending on the subject term they denote different properties. However we cannot conclude from this example that there is a property for which LL is false. In Quine’s example the predicate is sensitive to what term we use in the subject position to refer to that object making it an Abelardian predicate. There are also genuine non-extensional predicates that are also sensitive to the content (the Fregean sense, or the meaning) of the subject-term we use to denote the object. Contrasting the use of the predicates in the following two sentences should make this clear: (1) The youngest student in the class is younger than everyone else. (2) The youngest student in the class is so because he or she is younger than everyone else. Though the predicate “____is younger than everyone else” is extensional provided that we specify our universe of discourse precisely, the predicate “____is so because she is younger than everyone else” is non- See Harold Noonan, “Indeterminate Identity, Contingent Identity and Abelardian Predicates”, Philosophical Quarterly, (41) 1991, pp.183-93 and “Constitution Is Identity”, Mind, 1993, pp.133-46. The quoted definition is taken from the latter (p.134). 12 Quine (1980), p.139. 11 İnan, İlhan, “A Defense of the Indiscernibility of Identicals”, Revue Roumaine de Philosophie, 61-72, Vol.48, 2004. extensional since what property is denoted by the predicate is sensitive to the content of the subject term that comes in front of the predicate. Sentences of the subject-predicate form with extensional predicates have four important characteristics: (a) substituting another term in the subject position that refers to the same thing as the subject-term of the original sentence preserves truth-value, (b) we may correctly do an existential generalization on the subject-term, (c) when we have the object in question right before us we may correctly say by pointing to the object "this is F”, (d) we can intelligibly talk about the property F independent of any sentential context. (1) meets all four conditions. If the name of the youngest student in the class is ‘Sue’, then “Sue is younger than everyone else” would express a true proposition. It would be correct to say that there is someone who is younger than everyone else. And it would also be correct to say to Sue “You are younger than everyone else”. Furthermore we can intelligibly talk about the property of being younger than everyone else in the class. However none of these conditions hold for (2). In fact saying, “Sue is so because she is younger than everyone else” would be meaningless. Similarly it makes no sense to do an Existential Generalization: “There is someone who is so because she is younger than everyone else.” It would also not make any sense for us to point to Sue and say, “you are so because you are younger than everyone else”, nor to talk about the property of being so because she is younger than everyone else. Extensional predicates denote properties independent of how we refer to the object in question, whereas what property a non-extensional predicate denotes, if any, depends on how we refer. LL of course has the ontological presupposition that there are properties, and an application of LL further presupposes that we have extensional predicates. The latter presupposition reveals itself most clearly when we talk about the property denoted by a predicate, for example when we use definite descriptions such as “the property of being the youngest student in the class”. For non-extensional predicates such talk is ungrounded. We cannot intelligibly talk about the property of being so because she is younger than everyone else (nor about the property of being so-called because of his size.) It seems clear to me that the meta-linguistic Principle of Substitution is only true of extensional predicates. Having said this however, it would be a mistake to claim that LL is not true of certain properties. None of what has been said so far implies that there are non-extensional properties i.e. a İnan, İlhan, “A Defense of the Indiscernibility of Identicals”, Revue Roumaine de Philosophie, 61-72, Vol.48, 2004. property that is true of an object under one description and false under another. For the property denoted by a non-extensional predicate given a certain context is extensional. Going back to Quine’s example, the nonextensional predicate “is so-called because of his size” when attached to the name ‘Giorgione’ denotes the extensional property of being called ‘Giorgione’ because of his size. Obviously not only Giorgione but also Barbarelli has this property. Similarly the non-extensional predicate “___is so because she is younger than everyone else” when attached to the definite description “the youngest student in the class” denotes the extensional property of having the property of being the youngest person in the class because she is younger than everyone else. Again it is quite clear that this property belongs “not only” to the youngest person in the class, “but also” to Sue since she happens to be the youngest person. These kinds of predicates are non-extensional because they have indexical terms within them that lead to a shift of reference in different contexts. Consequently the same predicate denotes different properties in different sentential contexts. There are however other kinds of non-extensional predicates that do not seem to involve any indexicality. For instance within the sentence, “The number of female Italian philosophers is increasing”, the predicate “is increasing” is non-extensional since substituting the numeral that denotes that number in place of the subject term would not preserve truth-value. 13 The four conditions for extensionality given above fail again, though this time the failure is not as obvious for conditions (b)(d). By existential generalization we get “there is something that is increasing”, which seems to make sense, but of course if an existential claim is true, there must be something that satisfies the given predicate. But what is this thing that is increasing? Obviously it is not the number that is increasing, and one notices that the search for an object is futile. This indicates that despite the surface grammar of the use of such predicates, they do not seem to denote any property in the context of a sentence. I believe the reason is that though the predicate “is increasing” is a one-place predicate on the surface grammar, it is in fact an abbreviation of a two-place predicate denoting a relation. When we claim that the number is increasing, what we really mean, is not that there is something that is increasing, but rather something like the This is what an Italian philosopher once told me in conversation. It then occurred to me that such a sentence contains a non-extensional predicate. Later it was pointed put to me by Eivind Kolflaath that a similar example was discussed in the literature by Montague and others in the context of the sentence “the temperature is rising”. As I understand it Montague’s own solution to this problem is that the singular term “the temperature” refers to a function (rather than a number) and thus “is rising” is an extensional predicate (within this context) since it is this function that we claim to be rising. For an exposition and a discussion of 13 İnan, İlhan, “A Defense of the Indiscernibility of Identicals”, Revue Roumaine de Philosophie, 61-72, Vol.48, 2004. following: The number of female Italian philosophers now is greater then the number of female Italian philosophers in the past and it will be less then the number of female Italian philosophers in the future. So it seems to me that there is a hidden reference to time, in fact quantification over a vague period of time. Assuming that this is more-or-less the correct interpretation of the sentence we see why such predicates are not true of RS, however they create no problems for LL. 14 IV. Cases Reconsidered In certain cases, the reason why some have been inclined to limit the universality of LL is due to a confusion about the de re/de dicto distinction 15 . Consider the Evening Star/Morning Star case once again. Babylonians believed that The Evening Star appears in the evening sky, but they did not believe that (3) The Morning Star appears in the evening sky. These are of course de dicto beliefs, but when we report these beliefs in de re form though it is true that Babylonians believed of the Evening Star that it appears in the evening sky, it would be a mistake to say that, (4) Babylonians did not believe of the Morning Star that it appears in the evening sky. Montague’s position see D.R. Dowty, R.E. Wall, and S. Peters, Introduction to Montague Semantics, Appendix III, D. Reidel Publishing Company, 1980, pp.279-286. 14 The same goes for a host of other predicates such as “is changing”, “is growing”, etc. that are of the same kind. Unlike the previous group, even when we are given the sentential context such predicates sometimes do not denote properties but rather relations with a quantification over time. For example in the sentence “the color of the leaves are changing” we do not wish to attribute a certain property to the color of the leaves, for if the color of the leaves is green we do not wish to assert that green is changing. 15 Some philosophers feel uncomfortable about the de re/de dicto distinction, either because they believe it is a context dependent distinction that can serve no genuine philosophical function, (see, Quine “Intensions Revisited”, in eds. French, Uehling, Wettstein, Contemporary Perspectives in the Philosophy of Language, Minneapolis: University of Minnesota Press, 1979, pp.268-274), or because it wrongly presupposes there are two types of beliefs, knowledge etc. (see J. Searle, Intentionality: An Essay in the Philosophy of Mind, Cambridge: Cambridge University Press, 1983, pp.216-217). Though I personally hold that such claims are based upon fallacious arguments, to be neutral on the matter the argument in the text can be given by using Russell’s Scope Distinction, which I believe none of these philosophers deny. İnan, İlhan, “A Defense of the Indiscernibility of Identicals”, Revue Roumaine de Philosophie, 61-72, Vol.48, 2004. However in order to get a counter-instance to LL we need the truth of (4). So inferring (4) from the fact that Babylonians did not believe (3) is the fallacy responsible for the mistake. If (4) had been true, then pointing to Venus (say on a map) and asking, “Did Babylonians believe of this heavenly body that it appears in the evening sky?” should have been answered negatively. But obviously the Babylonians did believe this, and it seems to me that it makes no sense to claim that no answer can be given to this question unless we specify whether we mean by “this heavenly body” Venus-as-it-appears-in-the-evening-sky or Venus-as-itappears-in-the-morning-sky. Of one and the same heavenly body the Babylonians had conflicting beliefs 16 , however when we report their beliefs we do not have to fall into a contradiction. Similarly in Quine’s modal-example we cannot conclude from the fact that it is not necessary that the number of planets is odd, that the number of planets does not have the property of being necessarily odd. If the number of planets is 9, then the number of planets has the property of being necessarily odd. In the same spirit we can see how ones who have tried to refute Descartes’ argument for mindbody dualism given above have committed the same mistake. As I have argued above this position rests upon conflating de re and de dicto beliefs. Even if a property is not “objective”, it does not follow by the argument Moody gives that such a property is not in the scope of LL. What is required is to show that predicates used in these cases are non-extensional. In fact in a footnote Moody adds, “The particular kind of predicates that correspond to what we are calling ‘objective properties’ are ‘extensional predicates’” (p.33, fn.3). Let us consider the crucial predicate in Descartes’ argument, namely “___is something whose existence cannot be doubted by me”. What evidence is there that this predicate is non-extensional? It seems clear to me that it makes perfect sense to talk about the property denoted by this predicate independent of any sentential context, and there seems to be no problem in doing an existential generalization on it. When Descartes asks in the beginning of the first meditation whether there are any indubitable truths of existence, does he not start a search for a thing whose existence cannot be doubted by him? In other words the project is to find out what objects, if any, falls under the property of being something whose existence cannot be doubted by me. This indicates that if Descartes is right, then no one can doubt his or her own existence. So there is something whose existence cannot be doubted by me, and if I point to myself (my mind, my soul, Obviously they did not have any contradictory de dicto beliefs, i.e. they did not believe and disbelieve the same proposition at the same time. However it does seem to me that they did have contradictory de re 16 İnan, İlhan, “A Defense of the Indiscernibility of Identicals”, Revue Roumaine de Philosophie, 61-72, Vol.48, 2004. or whatever I take myself to be) then I should be able to correctly say “its existence cannot be doubted by me”. The coherence of all this discussion is made possible by the fact that there is a property, namely the property of being something whose existence cannot be doubted by me. It seems clear then that the predicate “___is something whose existence cannot be doubted by me” satisfies conditions (b)-(d) for extensionality given above, and if that is the case, there appears to be no reason for us to claim that it does not satisfy condition (a). If one is a monist, then, I would think that one cannot hold, without contradiction, that the mind and the body do not share all their properties. On the monist view if the existence of the body can be doubted de re, then so can the existence of the mind. After all there is only one thing not two, if monism is correct. It just seems to me to be totally incoherent to claim that my mind is my body, yet I cannot doubt my own existence when I think of myself as my mind, but I can doubt it when I think of myself as my body. Of course, this by itself does not show that Descartes was right in his dualist conclusion, but I believe that it shows that such counter-arguments are fallacious. Let us now reconsider the attempt to refute of the Kripke-Barcan proof for the necessity of identity. If a and b are the same, then either both have the property of being necessarily identical to a or neither have it. When we point to the object in question (given that a and b are the same there must be one and not two objects) and ask whether this object has the property of being necessarily identical to a, the question must have one answer not two. Those who hold that the identity relation at times may be contingently true have to cope with this problem. For instance A. Gallois argues that there may be cases in which objects are “occasionally identical”, i.e. they me be identical at some time and distinct at another. 17 An example he considers involves an amoeba which divides into two, where one part ends up in the pond (call it “POND”), and the other is taken to the lab to be analyzed on a slide under a microscope (call it “SLIDE”). Gallois claims that though it is true that POND and SLIDE are identical before the division, they are distinct afterwards. If so it would seem that we could derive a counter-example to LL from this case: before the division POND and SLIDE are identical, but POND has the property of being in the pond after the division, though SLIDE lacks such a property. It would then seem that Gallois would have to give up LL, but fortunately rather then doing that he tries to show that the truth of LL remains unaffected by his beliefs, since they both believed and disbelieved of the same heavenly body that it appears in the evening. Of course no charge of irrationality follows from this. 17 A. Gallois, Occasions of Identity (Oxford: Clarendon Presss, 1998). İnan, İlhan, “A Defense of the Indiscernibility of Identicals”, Revue Roumaine de Philosophie, 61-72, Vol.48, 2004. thesis by claiming that such names are quasi-rigid designators. I am not sure whether he succeeds. Langford and Ramachandran 18 claim he does not, but rather than taking this as a refutation of the occasional identity thesis they propose to limit the scope of LL: “We think it natural to restrict the domain of properties over which the quantifier ‘(…ф)’ ranges over so that time-invoking properties are discounted.” (p.526) They hold that if an object has some property F at time t, then it always has the property of F-at-t, (which is what they call a “time-invoking” property.) They claim that “in 1998, Bill Clinton was the US president; that he has the time-invoking property of being-US-President-in-1998 is true of him now and was true of him in 1997…Indeed, that Clinton possesses this property is surely eternally true.” (p.520) From this they conclude that “(t)ime-invoking properties are therefore not part of the genuine fabric of the world; they do not figure in the world’s basic ontology.” (p. 526) The idea may be that since time-invoking properties are true of objects eternally, they play no role in how things change. But this seems highly suspect. If Clinton had the property of being US President in1998 in 1997, why did he have to work so hard to campaign to become the president? It seems clear to me that this thesis is certainly not an obvious truth as they seem to hold; it may have metaphysical implications on issues about human freedom, future contingencies, and causal determinism. In any case that is another matter. Furthermore, supposing their thesis to be correct, it would seem that we would also have to “discount” mathematical and logical properties, which we would normally take to be eternal. Any view that forbids the application of LL to mathematical objects and their properties must surely be mistaken. Even if this problem is resolved, it appears to me to be clear that narrowing the application of LL to certain types of properties so that it accords with a thesis is totally ad hoc and ungrounded. 19 Going back to the problem of constitution, if we hold that the statue and the chunk of gold are the same, i.e. numerically identical, then either both (there is only one object) have the property of being essentially a statue or they don’t. Again when I point to the object on the table and ask, “Is this essentially a statue?” there must be one unequivocal answer, provided that there is only one object. However ones who hold that the statue is identical with the chunk would have to claim the opposite. But then they are forced to conclude either that predicates such as “___is essentially a statue” and “___can survive a melting process” S. Langford and M. Ramachandran, ‘Rigidity, Occasional Identity and Leibniz’ Law’, The Philosophical Quarterly, 50 (2000), pp.518-26. 18 İnan, İlhan, “A Defense of the Indiscernibility of Identicals”, Revue Roumaine de Philosophie, 61-72, Vol.48, 2004. are non-extensional, or that LL is false. What evidence is there that such modal predicates are nonextensional as Noonan takes them to be? If the only evidence that can be given is to claim that such predicates lead to a failure of substitution (hence condition (a) above is violated) that would be begging the question. If no independent reason can be given, ---and it seems to me that no one has been able to provide any-- then the argument is suspect. The situation is the same for the remaining three conditions (b)-(d). Why can we not do an existential generalization on “The statue is essentially a statue”? Isn’t there something that is essentially a statue? Is it not the case that my bag of objects from which I choose the values of my variables in LL, my universe of discourse, contains an object that is essentially a statue? It seems to me that ones who hold that constitution is identity have hard time dealing with such questions. If you hold that the statue and the chunk of gold are identical, then your universe of discourse contains one object that is the statue and the chunk of gold, and this object either is essentially a statue or it isn’t. Again when the object is on the table and we ask, “is this essentially a statue?” there must be one and only one answer if we hold that the statue is the chunk. Furthermore I see no reason to claim that it is meaningless to talk about the property of being essentially a statue. It seems clear to me that such modal predicates are not on a par with genuine non-extensional predicates such as “___is increasing” or “___ so-called because of his size”. Arguing that they are by holding that constitution is identity is begging the question. I am not suggesting that all this is sufficient to claim that the statue is identical with the chunk, but rather that if we are going to deny this, we need a different kind of argument. For instance I have said nothing about whether it is legitimate to hold that both “the statue” and “the chunk of gold” are genuine singular terms that refer to objects in the Universe of Discourse. The present essay is not about what the scope of ‘x’ and ‘y’ is in LL, but rather about what the scope of ‘Φ’ is? A discussion of what objecthood is is another matter. 20 Gallois is of the same opinion. See his ‘Langford and Ramachandran on Occasional Identities’, The Philosophical Quarterly, (2001), pp.378-385, especially pp.384-85. 20 E.Olson gives strong arguments that the thesis that consitution is not identity cannot solve what he calls “the indiscernibility problem”. (‘Material Coincidence and the Indiscernibility Problem’, The Philosophical Quarterly, 51 (2001), pp. 337-55.) If he is right about this, and we give up that thesis in effect, then we have two options: either to claim that the chunk is the statue, or deny that statues are objects. If we take the former line we would have to give up LL, but perhaps the latter option is a viable position. 19 İnan, İlhan, “A Defense of the Indiscernibility of Identicals”, Revue Roumaine de Philosophie, 61-72, Vol.48, 2004. V. Conclusion Predicates that falsify RS have an indexical character; the reason they falsify it is not because they denote some unusual properties, but because the property they denote depends upon the sentence in which they appear. This is why such predicates are non-extensional and lead to failures of substitution. An intuitive way to decide whether a predicate is non-extensional is to test whether it allows for existential generalization, to see whether it makes sense to talk about the property denoted by it independent of a sentential context, and to check whether we can intelligibly ask by pointing to an object if it falls under that predicate. If a predicate does pass this test, then the property it denotes should pose no problem for LL, and if it doesn’t, then what property is denoted by that predicate could change from one sentential context to the other. Given a sentential context, the property denoted by a non-extensional predicate in that context, would again pose no problems for LL. As I have argued, the view that a non-extensional predicate denotes a “non-extensional property” that is not true of LL is ungrounded. In fact I see no substantial reason to hold that there are such weird properties, and if so, we should really not apply the extensional/non-extensional distinction to properties at all. Whatever we may wish to call them, just because a property is relational or modal should not constitute any reason for us to exclude it from the range of the second-order variable in LL. All this, in no way, constitutes a proof of the law, for I have said nothing about the issues of vagueness and category-mistake, which may raise problems for the Rule of Substitution, and perhaps for LL as well. Nonetheless, as I have argued, certain philosophical arguments given by some prominent philosophers against Cartesian dualism, against the necessity of identity, for constitutionalism, etc. that try to restrict LL to certain type of properties, are either based on fallacious reasoning or are totally ad hoc. Whatever the context may be, all such positions entail the view that an object may have a property under one description, and not under another; and if there is a non-descriptional form of reference to the object, say by using the indexical “it”, then the question “does it have the property?” would either have no answer, or if it has one, we would be forced to say that the object does and does not have the same property at the same time. Now I do not wish to suggest that this contradictory position is an inevitable result for ones who deny the universality of the law on such grounds, and so it does not follow that LL is a truth of logic. Maybe it is, İnan, İlhan, “A Defense of the Indiscernibility of Identicals”, Revue Roumaine de Philosophie, 61-72, Vol.48, 2004. but that needs to be shown; if not, we should accept LL as a metaphysical doctrine that guides us in testing our metaphysical theses. 15