Objects and Identity: An Examination of Relative Identity and its Consequences
Noonan (Harold)
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Back Cover Blurb

  1. The main part of this book is dedicated to a discussion of the Fregean notion of an object and its connection with the notions of identity.
  2. Recently theories of relative dentity have attracted considerable attention among philosophers, largely because of their advocacy by Peter Geach. Two of Geach’s contentions are that the sense of a proper name determines a criterion of identity for the object it names and that such a criterion of identity can be constituted by a relation which does not ensure indistinguishability of its terms.
  3. The author argues that, when the Fregean view that the concept of an object is only explicable via the linguistic concept of a proper name is properly appreciated, these contentions have to be acknowledged to be correct. In arguing for these claims and others the author discusses extensively the views of Michael Dummett, W.V.O. Quine and David Wiggins.
  4. The remainder of the book is devoted to personal identity. It is argued that one thing can become two, and using this premise influential views of Sydney Shoemaker and Bernard Williams are shown to be mistaken.
  5. The final chapter is devoted to a discussion of Locke's views on personal identity: they are defended against the objections of Bishop Butler, Shoemaker, Flew and Williams, but it is argued that a fata! flaw in Locke's discussion is that he assumes that "person", defined in terms of self-consciousness1, conveys a criterion of identity which cannot serve as a criterion of identity for anything except a self-conscious creature.

  1. The Preface tells us that this is an improved version of Noonan’s PhD Thesis, supervised by GEM Anscombe, which explains her authorship of the Preface.
  2. It seems Anscombe was out of sympathy with Noonan’s claims, but supported him anyway.
  3. Noonan differs from Geach, Anscombe’s husband, but Anscombe herself seems to differ from Geach.
  4. Various Chapters make use of previously-published material:-

"Anscombe (G.E.M.) - Objects and Identity: Foreward"

Source: Noonan - Objects and Identity, Foreward

Full Text
  1. 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.
  2. 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.
  3. 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?
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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"?
  11. 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.

In-Page Footnotes ("Anscombe (G.E.M.) - Objects and Identity: Foreward")

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”.

"Noonan (Harold) - Objects and Identity: Introduction"

Source: Noonan - Objects and Identity, Introduction

Full Text
  1. In the first twelve chapters of this book I am concerned with the Fregean notion of an object (the reference of a proper name) and its connection with the notion of identity. I proceed by discussing the views of Peter Geach, David Wiggins, Michael Dummett and W.V. Quine on these topics, and argue finally that the only tenable position is that of Quine.
  2. Geach has argued for the thesis that identity is relative, and that a proper name must be associated with a criterion of identity. In order to interpret Geach's Relative Identity1 Thesis I introduce a distinction between absolute and relative equivalence relations. Geach's thesis turns out to be the claim that (in a sense I explain) there are no absolute equivalence relations. On this interpretation Geach is not claiming that there are counterexamples to Leibniz's Law2, as he has often been taken as doing; I take this to be a good thing since, so far as I can see, any attempt to produce such counterexamples would be quite futile.
  3. The view that a proper name must be associated with a criterion of identity, that is, that the act of endowing a sense on such a name must involve associating it with a criterion of identity, is not peculiar to Geach; of the writers mentioned above it is shared also by Dummett and Wiggins. These writers, like Geach, regard a criterion of identity as a relation which "sustains the application of a name" (to use a neat phrase I owe to Professor Williams), but they believe that only what I call absolute equivalence relations can serve this purpose, whereas Geach, of course, is committed to holding that relative equivalence relations can so serve. I argue that the use of an absolute equivalence relation as a criterion of identity will always be tantamount to the use of a relative equivalence relation as a criterion of identity, so that Wiggins and Dummett must be wrong about this. At this stage I have already argued independently that certain relations which Wiggins and Dummett would regard as paradigm examples of relations capable of serving as criteria of identity and which it seems ought to be so regarded by anyone wishing to maintain the thesis that the introduction of a proper name requires its association with a criterion of identity, are in fact relative equivalence relations, and this, though of course not a conclusive refutation of their view, makes it clear that to maintain it involves swallowing a number of highly unintuitive consequences.
  4. Geach has put forward in association with arguments for his Relative Identity3 Thesis arguments against the customary reduction of restricted quantification to the unrestricted sort. He holds that "Heraclitus bathed in some river yesterday and bathed in the same river today" is not equivalent to "Something is a river and Heraclitus bathed in it yesterday and bathed in it again today". I discuss his argument for this claim and show how neither Wiggins nor Dummett have responded adequately to it.
  5. It can, however, be answered by someone who accepts Quine's thesis that what are ordinarily thought of as continuants are, in fact, "process-things", with temporal parts as well as spatial parts. I explain why this is so.
  6. But to say that someone who accepts Quine's thesis can resist Geach's argument is not to say that he ought to deny Geach's claim. I argue that, in fact, he ought to accept a certain version of Geach's claim. This version is weaker than the one Geach himself accepts, however, and does not have the consequence, as Geach's version does, that general names are a category of expression semantically distinct from the category of predicates.
    • In Chapter Eleven I discuss an argument which would, if successful, establish that Geach was correct in maintaining this distinction, but show that it is not cogent.
    • In Chapter Twelve I then argue that in fact only the weaker version of Geach's claim is tenable. This in fact emerges as a corollary of the refutation of the Relative Identity4 Thesis I there offer; another corollary of this refutation is that, just as Quine maintains, continuants have temporal parts. Chapter Twelve also contains a refutation of the claim that any equivalence relation can serve as a criterion of identity and a characterization of two classes of equivalence relation which can do so (not every equivalence relation which can do so falls in one of these classes, however, as I point out). At the end of Chapter Twelve I explain briefly why the argument Geach has given for the Relative Identity5 Thesis leaves me unconvinced.
  7. The rest of the book is devoted to a discussion of the problem of personal identity.
    • In Chapter Thirteen I argue that "one thing can become two", in a sense in which this is often denied.
    • Using this conclusion as a premiss I argue in Chapter Fourteen that Shoemaker's notion of "quasi-memory6" cannot be used, as he wishes, to defend a mentalistic criterion of personal identity against Bishop Butler's charge of vicious circularity and that in fact only a criterion in terms of bodily continuity can suffice.
    • However (I argue in Chapter Fifteen) though present-day mentalistic accounts of personal identity are vulnerable to Butler's objection, Locke's account, against which the objection was originally made, was not. This is because Locke's aim was to define the identity of persons in terms of the memory beliefs of (immaterial) thinking substances, whereas modem writers attempt to define the identity of persons in terms of the memory-beliefs of persons. Nevertheless, I argue, although Locke's discussion cannot be faulted in the way it is commonly thought, a fatal flaw still remains, namely, that Locke mistakenly assumes that "person", defined in terms of self- consciousness,; conveys a criterion of identity which cannot serve as the criterion of identity for anything except a self-conscious creature.
    I conclude by suggesting that even the view that "person", thus defined, conveys a criterion of identity at all is very doubtful, and that modem discussions of "personal identity" are therefore possibly as lacking in subject matter as John Locke's discussion was.

"Noonan (Harold) - Absolute and Relative Identity"

Source: Noonan - Objects and Identity, Chapter 1

"Noonan (Harold) - Diachronic Identity as Relative Identity"

Source: Noonan - Objects and Identity, Chapter 2

"Noonan (Harold) - Synchronic Identity as Relative Identity"

Source: Noonan - Objects and Identity, Chapter 3

"Noonan (Harold) - Quine on Synchronic Identity"

Source: Noonan - Objects and Identity, Chapter 4

"Noonan (Harold) - Sortal Concepts and Identity"

Source: Noonan - Objects and Identity, Chapter 5

"Noonan (Harold) - On the Notion of a Criterion of Identity"

Source: Noonan - Objects and Identity, Chapter 6

"Noonan (Harold) - Absolute Identity and Criteria of Identity"

Source: Noonan - Objects and Identity, Chapter 7

"Baldwin (Thomas) - Reviews: Sameness and Substance by David Wiggins; Objects and Identity by Harold Noonan"

Source: Philosophy, Vol. 57, No. 220 (Apr., 1982), pp. 269-272

Author’s Introduction
  1. Although Wiggins and Noonan have each written a book about identity, and have thus written books on the same topic, their views are so different that no one could accuse them of having written the same book.
  2. Wiggins' book starts off from the views of his earlier book Identity and Spatio-Temporal Continuity: that is, he again maintains that all identities are dependent upon sortal1 concepts (the dependency thesis D) whilst rejecting the thesis that it could be the case that a is the same f as b but not the same g as b (the relativity thesis R, where f and g are sortal2 concepts).
  3. The arguments against R cover familiar ground, but D is worked out afresh, and the discussion of D leads into two new chapters in which the role of sortal3 concepts is developed in detail.
  4. The real essences of natural kinds4 are presented as paradigm cases of sortal5 concepts, and these concepts are then contrasted with those which inform our individuation6 of artifacts and other non-natural things. The essentialism implicit in this account of sortal7 concepts is next taken up and developed at length, along lines Wiggins has already made familiar. The resulting position is characterized as one of sober 'conceptual realism': to be contrasted with an anti-conceptualist realism, which involves the denial of D, and an anti-realist conceptualism, which involves the rejection of the essentialist characterization of sortal8 concepts.
  5. Finally, Wiggins turns to personal identity, where he argues against neo-Lockean accounts which rely on memory and neo-Humean accounts which treat personal identity as a matter of convention: in their place he argues that persons are members of a natural kind9 Homo sapiens – whose typical members have the psychological attributes we ascribe to ourselves.

COMMENT: Reviews of
→ "Wiggins (David) - Sameness and Substance" and
→ "Noonan (Harold) - Objects and Identity: An Examination of Relative Identity and its Consequences".

"Noonan (Harold) - Restricted and Unrestricted Quantification"

Source: Noonan - Objects and Identity, Chapter 8

"Noonan (Harold) - Absolute Identity and Criteria of Identity Concluded"

Source: Noonan - Objects and Identity, Chapter 9

"Noonan (Harold) - Events, Continuants and Diachronic Identity"

Source: Noonan - Objects and Identity, Chapter 10

"Noonan (Harold) - Counterpart Theory and the Necessity of Identity"

Source: Noonan - Objects and Identity, Chapter 11

"Noonan (Harold) - Absolute and Relative Identity Concluded"

Source: Noonan - Objects and Identity, Chapter 12

"Noonan (Harold) - Can One Thing Become Two?"

Source: Noonan - Objects and Identity, Chapter 13

"Noonan (Harold) - Memory and Quasi-Memory"

Source: Noonan - Objects and Identity, Chapter 14

"Noonan (Harold) - Locke on Personal Identity"

Source: Noonan - Objects and Identity, Chapter 15

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