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
Source
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.