### Single Idea 19124

#### [catalogued under 3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth]

Full Idea

If a natural theory of truth is added to Peano Arithmetic, it is not necessary to add explicity global reflection principles to assert soundness, as the truth theory proves them. Truth theories thus prove soundess, and allows its expression.

Gist of Idea

A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness

Source

Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.2)

Book Reference

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.3

A Reaction

This seems like a big attraction of axiomatic theories of truth for students of metamathematics.

Related Idea

Idea 19123
If soundness cannot be proved internally, 'reflection principles' be added which assert soundness **[Gödel, by Halbach/Leigh]**