more from John Mayberry

### Single Idea 17788

#### [catalogued under 5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic]

Full Idea

First-order logic is very weak, but therein lies its strength. Its principle tools (Compactness, Completeness, Löwenheim-Skolem Theorems) can be established only because it is too weak to axiomatize either arithmetic or analysis.

Gist of Idea

First-order logic only has its main theorems because it is so weak

Source

John Mayberry (What Required for Foundation for Maths? [1994], p.411-2)

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.411

A Reaction

He adds the proviso that this is 'unless we are dealing with structures on whose size we have placed an explicit, finite bound' (p.412-1).