Author’s Introduction (Full Text)
- 'Object' and 'criterion of identity' are philosophical terms of art whose application is at a considerable theoretical remove from the surface phenomena of everyday linguistic usage. This partly explains their highly controversial status, for their point of application lies precisely where the concerns of linguists and philosophers of language merge with those of metaphysicians.
- The degree of controversy concerning these terms has indeed prompted some scepticism as to their utility (see, for example, "Strawson (Peter) - Entity and Identity", 1976), but a less pessimistic response would be to try to exercise greater care and discrimination in their use (cf. "Lowe (E.J.) - What Is a Criterion Of Identity?", 1989). Both terms are undeniably slippery, especially 'object'.
- Our concern will be with the sense of 'object' in which it is interchangeable with 'thing', but it is important to see that this only coincides with a restricted sense of 'thing'. For we seem to use the word 'thing' in both a narrow and a broad sense, the former associated with the free-standing use of the word and the latter with its use in combination with quantifying adjectives to form unitary quantifier expressions like 'something' and 'everything' (cf. R. Teichmann, Abstract Entities, 1992, pp. 15-16 and 166-7).
- The difference is brought out by reflecting on the two non-equivalent sentences 'Every thing is a thing', which is trivially true, and 'Everything is a thing', which is metaphysically controversial. (The first sentence means 'Everything which is a thing is a thing', and is trivial in just the way as 'Every horse is a horse' is trivial: the second sentence, by contrast, is controversial in rather the way that 'Everything is a horse' would be.)
- As we shall see, some philosophical answers to the question 'What is a thing?'' effectively ignore or deny this distinction. My own view is that the distinction is indeed a genuine one, and that it is the narrower sense of 'thing' that is ontologically significant.
- What is crucial to the status of 'thinghood' in this narrower sense is, I consider, the possession of determinate identity-conditions (see section 3 below). This is where the notion of a 'thing" or 'object' ties in with that of a criterion of identity, for one guarantee that something possesses determinate identity-conditions is that it falls under a general concept which supplies a definite criterion of identity for its instances. (Such a concept may be classed as a 'sortal1'.)
- As I have already implied, the term 'criterion of identity' is, unfortunately, itself the subject of considerable dispute. One problem is that candidates for this title typically take one or other of two quite different logical forms, whose difference turns on the mode of reference they involve to the objects for whose identity they provide a criterion (see section 5).
- Some objects are such that a canonical mode of reference to them by functional expressions of a quite specific kind is available. For instance, to use a famous example of Frege's ("Frege (Gottlob), Austin (J.L.) - The Foundations of Arithmetic", 1953, pp. 74f.) a particular direction may be canonically referred to as the direction of a particular line. (Any expression like this, of the form 'the F of x', may be called a functional expression.) In this particular case the object in question is, of course, not a physical but a geometrical one, and this fact may encourage the thought that it is a peculiarity of those objects for which a functional mode of reference is canonical that they are in some sense abstract objects, with logico-mathematical objects like directions, shapes, numbers and sets providing paradigm examples (cf. "Dummett (Michael) - Frege, Philosophy of Language", 1981, p. 481).
- However, as we shall see, the distinction between ‘abstract’ and 'concrete' objects is itself a highly controversial one, and although it has been argued that this distinction turns ultimately upon differences between the criteria of identity governing objects of these two broad categories (see section 10), it certainly does not appear to be simply related to the distinction between those criteria which do and those which do not involve functional modes of reference to the objects they concern. (For one thing, we have indisputably 'abstract' objects like sets, for which a criterion of identity is available which does not involve a functional mode of reference to them.)
- My own view, I should say, is that the distinction I have alluded to between the two types of identity criteria is not at root, one of fundamental philosophical importance, in the sense of reflecting any basic metaphysical, semantic or epistemological distinction between the categories of objects to which they apply.
- This being so, however, one might expect to be able to supplant one or other type of criterion by the other, and I shall indeed try to show how such an expectation may be satisfied in specific cases (see sections 7 and 8).
- Of course, the very existence of abstract objects is itself a matter of considerable philosophical controversy, though it would be inappropriate to engage in it here (but see further Bob Hale, Abstract Objects, 1987, and Teichmann, 1992, for very contrasting views).
- However, one should at least be clear as to what is meant by ‘abstract object’ before one debates whether or not anything answers to that description. The putative examples I have so far mentioned – all of them logico-mathematical – are at least provided with clear-cut and unimpeachable criteria of identity: but other putative examples like propositions, facts and properties do not appear to be so favoured
- This puts pressure on the idea that propositions and the like possess determinate identity-conditions at all, and correspondingly that they qualify as ‘objects’ or 'things' (in my narrow sense). That may seem no great loss, until we come to reflect that we can, ostensibly at least, quantify over and refer to propositions, facts and properties.
- However, perhaps we can plausibly represent such ‘qualification’ and 'reference' as convenient facons de parler, capable of being paraphrased away innocuously. I think that is correct, despite the fact that the strategy of paraphrastic elimination is one which must be handled with a good deal of caution, as we shall see (section 3).
- But before we can tackle such issues, we need to examine the role which criteria of identity play in our talk about objects of the least controversial varieties.
- Sortals2 and Counting
- What is an Object
- Frege on Concepts and Objects
- Two Forms of Identity Criterion
- The Logical Status and Role of Identity Criteria
- One-level Versus Two-level Identity Criteria
- On the Identity of Cardinal Numbers
- Cardinal Numbers and Counting
- Abstract and Concrete Objects
- The paradoxes of Identity Over Time
Appendix: Informal Proof of (N2)
Text Colour Conventions (see disclaimer)
- Blue: Text by me; © Theo Todman, 2018
- Mauve: Text by correspondent(s) or other author(s); © the author(s)