more from Volker Halbach

Single Idea 16315

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

Full Idea

The truth theory TB (Tarski Biconditional) is all the axioms of Peano Arithmetic, including all instances of the induction schema with the truth predicate, plus all the sentences of the form T[φ] ↔ φ.

Gist of Idea

The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals


Volker Halbach (Axiomatic Theories of Truth [2011], 7)

Book Reference

Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.53

A Reaction

The biconditional formula is the famous 'snow is white' iff snow is white. The truth of the named sentence is equivalent to asserting the sentence. This is a typed theory of truth, and it is conservative over PA.

Related Ideas

Idea 16314 Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [Halbach]

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