display all the ideas for this combination of philosophers
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) |
14943 | Maybe mathematical logic rests on information-processing [Ladyman/Ross] |
Full Idea: It is claimed that mathematical logic can be understood in terms of information-processing. | |
From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.7.5) | |
A reaction: [They cite Chaitin 1987] I don't understand how this would work, but it is still worth quoting. This would presumably make logic rest on processes rather than on entities. I quite like that. |
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. |