Combining Philosophers

Ideas for Xenophon, Stephen P. Schwartz and Melvin Fitting

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4 ideas

5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics

11026	Classical logic is deliberately extensional, in order to model mathematics [Fitting]
	Full Idea: Mathematics is typically extensional throughout (we write 3+2=2+3 despite the two terms having different meanings). ..Classical first-order logic is extensional by design since it primarily evolved to model the reasoning of mathematics.
	From: Melvin Fitting (Intensional Logic [2007], §1)

5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive

5829	We refer to Thales successfully by name, even if all descriptions of him are false [Schwartz,SP]
	Full Idea: We can refer to Thales by using the name "Thales" even though perhaps the only description we can supply is false of him.
	From: Stephen P. Schwartz (Intro to Naming,Necessity and Natural Kinds [1977], §III)
	A reaction: It is not clear what we would be referring to if all of our descriptions (even 'Greek philosopher') were false. If an archaeologist finds just a scrap of stone with a name written on it, that is hardly a sufficient basis for successful reference.

5830	The traditional theory of names says some of the descriptions must be correct [Schwartz,SP]
	Full Idea: The traditional theory of proper names entails that at least some combination of the things ordinarily believed of Aristotle are necessarily true of him.
	From: Stephen P. Schwartz (Intro to Naming,Necessity and Natural Kinds [1977], §III)
	A reaction: Searle endorses this traditional theory. Kripke and co. tried to dismiss it, but you can't. If all descriptions of Aristotle turned out to be false (it was actually the name of a Persian statue), our modern references would have been unsuccessful.

5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction

11028	λ-abstraction disambiguates the scope of modal operators [Fitting]
	Full Idea: λ-abstraction can be used to abstract and disambiguate a predicate. De re is [λx◊P(x)](f) - f has the possible-P property - and de dicto is ◊[λxP(x)](f) - possibly f has the P-property. Also applies to □.
	From: Melvin Fitting (Intensional Logic [2007], §3.3)
	A reaction: Compare the Barcan formula. Originated with Church in the 1930s, and Carnap 1947, but revived by Stalnaker and Thomason 1968. Because it refers to the predicate, it has a role in intensional versions of logic, especially modal logic.