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3 ideas
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) |
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. |
13606 | Humean conceptions of reality drive the adoption of extensional logic [Ellis] |
Full Idea: A Humean conception of reality lies behind, and motivates, the development of extensional logics with extensional semantics. | |
From: Brian Ellis (Scientific Essentialism [2001], 8.04) | |
A reaction: His proposal seems to be that it rests on the vision of a domain of separated objects. The alternative view seems to be that it is mathematics, with its absolute equality between 'objects', which drives extensionalism. |