Single Idea 10600

[catalogued under 5. Theory of Logic / K. Features of Logics / 9. Expressibility]

Full Idea

Whether a property is 'expressible' in a given theory depends on the richness of the theory's language. Whether the property can be 'captured' (or 'represented') by the theory depends on the richness of the axioms and proof system.

Gist of Idea

Being 'expressible' depends on language; being 'capture/represented' depends on axioms and proof system

Source

Peter Smith (Intro to Gödel's Theorems [2007], 04.7)

Book Reference

Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.36