### Single Idea 17787

#### [catalogued under 5. Theory of Logic / G. Quantification / 2. Domain of Quantification]

Full Idea

The 'logica magna' [of the Fregean tradition] has quantifiers ranging over a fixed domain, namely everything there is. In the Boolean tradition the domains differ from interpretation to interpretation.

Gist of Idea

Big logic has one fixed domain, but standard logic has a domain for each interpretation

Source

John Mayberry (What Required for Foundation for Maths? [1994], p.410-2)

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.410

A Reaction

Modal logic displays both approaches, with different systems for global and local domains.

Related Idea

Idea 17786
The mainstream of modern logic sees it as a branch of mathematics **[Mayberry]**