By Davis Wiggins
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Extra resources for Identity and Spatio-Temporal Continuity
5]. This proof is impossible without the prohibition on branching and is therefore useless to anybody who will not accept Leibniz' Law. Some adherents of R nevertheless believe the strong form of D. How they would demonstrate it I do not know. Both demonstrations of D are still rather formal and leave much unexplained. It will be illuminating to go behind them in a less formal manner by saying a little about sufficient conditions of identity. Leibniz' Law and its contraposition gives a sufficient criterion of difference, but none of identity.
If it cannot do this we shall not have fixed the sense of the iden tity-statements it covers to be the sense of identity-statements. (See also below p. ) If this is right then it opens a route already mentioned to the notion of a IJJaterial sttbstance. For it seems that we are in a position to use freely such a priori knowledge as we have of the notion of identity, viz. its formal properties, to work out the formal requirements which any f will have to satisfy in order to count as competent to elucidate the coincidence or identity conditions for a given kind of individual.
1) The formal properties of identity 3. 1 . include trans1t1v1ty, reflexivity, symmetry, and Leibniz' Law. Regardless of whether the meaning of the notion be completely exhaustible by these formal principles, at least purport of ' = ' and (2) (3) these principles are integml to the '='. f If (1) above is true, then R is false. There are two distinct standpoints from which D and the covering-concept requirement can be maintained. It may be held that a b without being the same g. a is is automatically to provide truth-grounds of 'a=b'.