- Identity has for long been an important concept in philosophy and logic. Plato in his Sophist puts same among those forms which "run through" all others. The scholastics inherited the idea (and the terminology), classifying same as one of the "transcendentals", i.e. as running through all the categories. The work of Locke and Leibniz made the concept a problematic one. But it is rather recently, i.e. since the importance of Frege has been generally recognized, that there has been a keen interest in the notion, formulated by him, of a criterion of identity. This, at first sight harmless as well as useful, has proved to be like a charge of dynamite.
- The seed had indeed been sown long ago, by Euclid. In Book V of his Elements he first gives a useless definition of a ratio: "A ratio is a sort of relation between two magnitudes in respect of muchness". But then, in definition 5 he answers, not the question "What is a ratio?" but rather "What is it for magnitudes to be in the same ratio?" and this is the definition that does the work.
- This method was used again at long last by Frege, who looked for an answer, not to the question "What is a number?", but rather: "When have we the same number?" and with this there began the fruitful modern philosophical investigation. Philosophical interest in criteria of identity was also stimulated by Wittgenstein, himself inspired by Frege. It is no use, he observed, to try and give a fundamental explanation of a word by pointing to something and saying "This is ..." For the question is, when to use the word again. And you explain nothing by saying: "Whatever is the same as this is...", for you have not made it clear what it is that counts as being the same, just by pointing to something and saying "This". Were you pointing to a colour or a kind of material for example?
- Among the issues debated as a consequence of these developments, is that of relative identity1. Suppose, exemplorum gratia, that, for some substitution we may make for "x" and "y", x is the same cat, man, river, water, letter of the alphabet or god as y, then must everything that is true of x be true also of y? Or might x be the same cat as y (at a given time) but not have the same history as y because the designation of x signifies that its bearer is a cat, and the designation of y that its bearer is a certain parcel of matter? Could x be the same A as Y, though they are two different B's? Controversy has gone on about these matters for the last couple of decades, sometimes in a very confused fashion. Was Leibniz' Law2 at stake? Leibniz was held to have defined identity so that X is identical with y if and only if everything which holds of x holds also of y. The formulation of this is a tricky business, however, because of the logical paradoxes we may run into with unrestricted quantification over properties. Assuming that we can get over these, we had what is called classical identity. Was there any other kind? Could one cite clear instances of this kind, other than ones of the futile form x = x? The opinions that there are criteria of identity in the offing wherever we can speak of actual identities, and that there must always be an answer to the question "The same what?" give substance to these questions. Geach's highly controversial writings forced the issue of relative identity3 on the attention of philosophers.
- Dr. Noonan has introduced some useful terminology into the handling of these questions. Firstly, he speaks of relative and absolute equivalence relations. He defines an absolute equivalence relation to be an equivalence relation such that, if x stands in it to y, there cannot be some other equivalence relation holding between anything and either x or y, but not holding between x and y4. If an equivalence relation is not absolute, then it is relative. Now as an equivalence relation is any relation, like say being the same size as, which is symmetrical, transitive and reflexive, it is obvious that there are a host of relative equivalence relations and no one can cavil at the idea. The question can then be formulated; Which sort of equivalence relation is being the same letter of the alphabet as? The question of identity is obviously closely related to the method of counting. Now for letters, there are different ways of counting, i.e. different counts of the number of letters on a given page; according to what counts as one and the same letter as we assigned a numeral to before, we may get by one way a count of a thousand or so, by another a count of a couple of dozen, by yet another forty or so. We may introduce terms indicating that we are counting different objects, e.g. type-letters, token-letters or type-fount letters. The fact remains that we are applying the operation of counting to the same material in different ways, and that this is what would explain our new terms, not they it. The idea of supposing a new sort of object for every different style of counting that can be devised would seem to let us in for an extraordinary metaphysics — Platonic forms would be merely one among a host of bizarre items, some of which Geach and Noonan have invented. One way out is Quine's: to hold that what we are counting when we count, say, type-letters on a page, is groups.
- This brings out the different character of the other problem, that of identity over time with change of matter. Is being the same man as an absolute equivalence relation? Since a man is a metabolizing material object, a particular parcel of matter is at some moment such-and-such a man. But the histories of the man and the parcel of matter are different. It appears, then, that we have here just another relative equivalence relation. Dr. Noonan introduces a useful notion here: that of a name's being a name of a such-and-such. That is, the criterion of identity connected with the name "Noonan" (in its present application) is precisely that of being the same man as: whatever is the same man as the one I have been calling Noonan in this foreword, I will rightly identify as Noonan in the future. This is opposed to a name's happening to attach to a particular man for the time being, like the name "Black Rod"; this, in Noonan's terminology, is a name of a parliamentary official. Now if we had a name "P" of a particular parcel of matter constituting Noonan at a given time, then at that time P would be a man and would be the same man as Noonan; but this would be merely a relative equivalence relation.
- So much for openers. Noonan clears up many confusions — it is, for example, muddled thinking to believe that the truth of Leibniz' Law5 is at stake — if, that is, it can be formulated. But the question would remain whether "classical identity" is the only absolute equivalence relation. That would entail a certain vacuity or impossibility of real application. Everything would stand in this relation to itself and that would be all.
- Dr. Noonan argues that the only escape from Geach's proposals on relative identity6 is to adopt the views of Quine, making of a continuing object a "four-dimensional worm" with temporal parts. While Noonan rebuts various attacks on Geach, he has his own objections and is inclined himself to adopt the Quinean position.
- Regrettably, to my mind; though I must acknowledge the great pleasure and privilege it was to watch the development of this fast moving and very pure thinker when he was originally working on this subject for his doctorate and I had the enjoyable task of being his supervisor. I always eagerly awaited the next instalment.
- I am myself inclined to reject the thesis (which Noonan finds in Geach) that in an important sense there are no absolute equivalence relations, and to see in these enquiries a pathway to a modern comprehension of Aristotle's per se predication, or to some form of this. Would not the following relation, for example, express an absolute equivalence relation? "x is essentially a man and y is essentially a man and x is the same man as y"?
- However these things may be, it is certain that Dr. Noonan has done a good deal of justice to the difficulty and complexity of the problems. I hope that some of his terminology will become familiar instruments in people's hands, and that the philosophic community will be more clear about what is at stake. I have sketched only a rather elementary opening to the questions. Anyone who thinks them interesting will find a great deal to think about in these pages. There is also a rich discussion of the Lockeian and post-Lockeian problem of personal identity. It is an instance of the clear light that Noonan casts on this question, that he remarks that Locke's explanation of "person" is such that it makes the expression "same person" like "same genius7". For this alone we owe him thanks.
Footnote 7: This thought is worth following up – as it’s not quite the same as my phase sortal stance. “Same genius” picks out a property more essential than (say) “same student”.
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