display all the ideas for this combination of philosophers
3 ideas
| 16728 | Logicians acknowledge too few things, while others acknowledge too many [Fitzralph] |
| Full Idea: Those who have been well trained in logic err in recognising too few things, whereas others who are ignorant of logic ascribe to every statement a new entity, postulating more entities than God has ever established as real. | |
| From: Richard Fitzralph (Sentences [1328], II.1.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 22.3 |
| 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. |