more from Volker Halbach

### Single Idea 16322

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

Full Idea

Compositional Truth CT proves the consistency of Peano arithmetic, which is not provable in Peano arithmetic by Gödel's second incompleteness theorem. Hence the theory CT is not conservative over Peano arithmetic.

Gist of Idea

CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA

Source

Volker Halbach (Axiomatic Theories of Truth [2011], 8.6)

Book Reference

Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.106

Related Ideas

Idea 16318
Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents **[Halbach]**

Idea 10122
Second Incompleteness: a decent consistent system can't prove its own consistency **[Gödel, by George/Velleman]**

Idea 16313
A theory is 'conservative' if it adds no new theorems to its base theory **[Halbach, by PG]**