more from John Mayberry

Single Idea 17778

[catalogued under 5. Theory of Logic / K. Features of Logics / 1. Axiomatisation]

Full Idea

The central dogma of the axiomatic method is this: isomorphic structures are mathematically indistinguishable in their essential properties.

Gist of Idea

Axiomatiation relies on isomorphic structures being essentially the same


John Mayberry (What Required for Foundation for Maths? [1994], p.406-2)

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.406

A Reaction

Hence it is not that we have to settle for the success of a system 'up to isomorphism', since that was the original aim. The structures must differ in their non-essential properties, or they would be the same system.