more from Volker Halbach

Single Idea 16342

[catalogued under 5. Theory of Logic / K. Features of Logics / 3. Soundness]

Full Idea

One cannot just accept that all the theorems of Peano arithmetic are true when one accepts Peano arithmetic as the notion of truth is not available in the language of arithmetic.

Gist of Idea

You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system


Volker Halbach (Axiomatic Theories of Truth [2011], 22.1)

Book Reference

Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.322

A Reaction

This is given as the reason why Kreisel and Levy (1968) introduced 'reflection principles', which allow you to assert whatever has been proved (with no mention of truth). (I think. The waters are closing over my head).

Related Idea

Idea 16343 The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach]