Single Idea 11028

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

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 □.

Gist of Idea

λ-abstraction disambiguates the scope of modal operators

Source

Melvin Fitting (Intensional Logic [2007], 3.3)

Book Reference

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.15


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.