By Cynthia Fitterer Klingel, Robert B. Noyed

ISBN-10: 0756502942

ISBN-13: 9780756502942

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But ƒL [ {P} ¼ƒL Hence X0 ƒL Y0 . , ƒL  ‘an , we obtain X0 ‘an Y0 : 8x (Px $ Qx) being analytic we have [ ‘an {8x (Px $ Qx}. We derive from the latter and X0 ‘an Y0 the result that X ‘an Y. 10 I am indebted for the latter point to the anonymous referee mentioned in n. 8. 11 See R. Carnap, The Logical Syntax of Language, (London, 1937), § 50. 38 T E O G R U¨ N B ER G 12 See W. V. Quine, ‘‘Carnap and Logical Truth’’ in The Ways of Paradox and Other Essays (New York, 1966) pp. 116-117. , p. 117. 14 Note that if k1 2 K, and k2 2 K, where k1 and k2 are distinct, then $ k1 ¼ k2 ƒL [ k 9x9y $ x ¼ y holds in classical quantificational logic (with existential presupposition).

There was a lot of, kind of, keeping your hands out of these dirty substantive metaphysical problems and trying to recast them in a way that they can actually be resolved by science and mathematical methods. M: They did that. K: That’s the way they did it. But I think many of their heirs, and I think of people like Kripke, Kit, myself, are dipping more deeply into the substantive metaphysics and arguing about issues that are not going to be resolved by mathematics. Maybe it took a lot of cleaning in order to be able to do that.

But we have shown in sec. 5 that Nd ({$}). Therefore we have Snd ({$}). We must therefore show only Ag ({$} [ k). For this purpose we must show X ƒ{$}[k Y ! X ‘an Y (for every X, Y 2 ps) (6) We have X ƒ{$} [ k Y ! X ƒ{$} Y (7) since the meaning of the members of k does not effect the validity of sequent < X, Y >. For example, since {Fk1 k2 } ƒ{$}[K {$$ Fk1 k2 }, it is the case that {Fk1 k2 } ƒ{$} { $$ Fk1 k2 } (8) On the other hand we have X ƒ{$ {$} Y ! X ‘an Y (9) Indeed in case sequent is { $ }-valid it is valid in all { $ }preserving interpretation so that it depends only on the meaning of the constant ‘‘$’’.

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Ancient Mesopotamia by Cynthia Fitterer Klingel, Robert B. Noyed


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