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 In a development of Russell's ideas W V O Quine has argued that Russell's theory allows one to parse proper names as well as descriptions. Since both defi- nite descriptions and proper names purport to denote exactly one entity, Quine suggests that both should be given a similar treatment from the point of view of logical form. Hence, 'Cerberus barks' is analyzed as:
At least and at most one thing is Cerberus and it barks.
Notice that Quine's proposal does not mean eli- minating reference to a unique individual, but rather reconstrues such reference as best expressed through the apparatus of quantification rather than by a pro- per name. A logical regimentation of natural language would, for Quine, thus dispense with any expressions carrying the semantic role of proper names and defi- nite descriptions.
4. StatementsofIdentity
Identity has had an important role in other parts of philosophical and semantic theory. It was a puzzle about the meaning of identity statements which led Gottlob Frege to the hypothesis that names, and other semantically relevant components of sentences, must have both a sense and a reference. In his early work, he took identity to be a relation between signs but later realized that in sentences such as:
The morning star is the evening star
the identity in question is of one and the same celestial body with itself. What makes the statement informa- tive, according to Frege, is that the expressions on either side of the 'is' of identity differ in sense even though they both name the planet Venus. Some phil- osophers, like Strawson and Lockwood, have argued that one role of identity statements is to enable speak- ers to collapse separate files of information held of an object into one larger file. Someone who had separate files of information held under the labels 'morning star' and 'evening star' would, once they accepted the above identity, be able to reorganize their information store.
Not all uses of 'is' in English involve identity. Wri- ters have attempted to distinguish the 'is' of identity, as in the above example, from the 'is' of predication (e.g., 'Jane is a pilot') and the 'is' of constitution (e.g., 'the bust is bronze'). It is easier to have an intuitive grasp of these distinctions than to give satisfactory definitions of them. Recognizing that 'is' can be used to mean 'is constituted from' saves us from being misled by stories like the following. Suppose a sweater made of wool is unraveled and then the same wool is knitted into a scarf. Since the sweater is wool and the scarf is wool, and the wool is the same in each case, there might be a temptation to think the sweater is the scarf. However, the 'is' of constitution does not have the same logic as the 'is' of identity.
David Wiggins has been a prominent defender of
the view that any statement of the form 'a is the same as V is indefinite until an answer is given to the question 'The same what?' The issue of whether genuine identity statements do require such clari- fication, like the issue of whether identity is relative, has been debated in recent analytic philosophy. Such debates lead rapidly into metaphysical problems con- cerning the identity or unity of objects. Theorists gen- erally distinguish two kinds of unity question: unity at a time (synchronic unity) and unity or identity through time (diachronic). One special focus of inter- est in this area is the topic of personal identity and the role of psychological and physical features in deter- mining the unity of the self.
5. Identity and Possible Worlds
With the increasing interest in modal logic since the 1960s, has come also an interest in the issue of identity across possible worlds. Exploring this issue provides a convenient way into the debate between modal realists (such as David Lewis) who believe that objects are tied to particular worlds and have counterparts in other worlds, and others like Saul Kripke who believe that a genuine proper name (a 'rigid designator') denotes one and the same object in any world in which it designates at all. Kripke's account associates well with the causal theory of reference, and has helped establish a new philosophical orthodoxy about state- ments of identity. This is that any identity statement using proper names (or any other designators that are 'rigid' in the Kripke sense) is necessarily true, if it is
true at all.
This can be shown by an argument depending only
on Leibniz's Law as given at the start of this article, together with the fact that, in standard versions of modal logic, any logical truth is a necessary truth. Thus, provided that 'Vx (x=x)' is necessarily true, it follows that it is necessary that Cicero = Cicero. Now suppose 'Tully' is another name for Cicero. It follows by Leibniz's Law that, since 'Cicero=Tully' is true, anything true of Cicero is also true of Tully. But it is necessarily true of Cicero that he is identical with Cicero, so the same thing (that it is necessarily true he is identical with Cicero) is also true of Tully. So if it is true that Cicero is Tully then it is necessarily true that he is Tully.
This particular claim about identity has led to sig- nificant developments in the understanding of natural kind terms. Kripke, Hilary Putnam and others have argued that it is a contingent feature of English that terms like 'water,' 'gold,' and 'hydrogen' refer to the stuff they do. However, it is a necessary feature of something's being water that it is largely H2O, and likewise necessary for a gas's being hydrogen that it has atomic number 2. Since discovering the nature of water and hydrogen involved empirical study, the truth that water is H2O is both necessary, but known a posteriori (through experience). Putnam coined the
Identity
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