- When metaphysical importance is plausibly ascribed to a result in formal logic this is an exciting, not to say stirring, event. In part, this is because visible progress is something not unknown in formal logic, whereas in philosophy — well, some people wonder how much progress there is. My own view is both that there is progress in philosophy, and that formal logic has had at least a little to do with the progress, but it is not always a straightforward matter to read the right philosophical significance into formal results. They serve as nothing else can to destroy nonsense but, beyond that, even theorems may in application provoke controversy. All the same, pace one school of thought, it seems to me that such controversy is almost always metaphysically fruitful and philosophically innovative.
- This paper is to consider one claim of this kind, namely Saul Kripke's contention that the modal2 theorem (a = b) ⊃ □ (a = b) excludes philosophical materialism. It would be ungracious for me to begin a paper which is at least at two points quite critical of Kripke without saying that I believe Kripke is right to hold that the theorem bears upon the mind-body problem (even if it is no help to Kripke's Cartesianism): and that I yield to none in my admiration of the wit, invention and integrity of philosophical purpose which shine through Kripke's writings on these subjects.
- At risk of repeating what may be very familiar I shall start with a summary of Kripke's position in "Kripke (Saul) - Identity and Necessity".
- An earlier and in certain important respects substantially different version of this contribution was published in Philosophia for January 1975 under the title 'Identity, Designation, Essentialism and Physicalism'.
- There is also some overlap at some points with "Wiggins (David) - Essentialism, Continuity, and Identity".
- For the formal development presupposed here of 'necessarily' as a predicate-operator see my 'The De Re "Must": a note on the logical form of essentialist claims' forthcoming, with an Appendix by C. A. B. Peacocke, in Semantics edited by Gareth Evans and John McDowell (Oxford University Press, 1975).
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