more from Volker Halbach

Single Idea 16299

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

Full Idea

Often syntactic objects are identified with their numerical codes. …Expressions of a countable formal language can be coded in the natural numbers. This allows a theory of truth to use Peano Arithmetic (with its results) as a base theory.

Gist of Idea

Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory


Volker Halbach (Axiomatic Theories of Truth [2011], 2)

Book Reference

Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.13

A Reaction

The numbering system is the famous device invented by Gödel for his great proof of incompleteness. This idea is a key to understanding modern analytic philosophy. It is the bridge which means philosophical theories can be treated mathematically.