Full Idea
In the light of incompleteness phenomena, one should not expect a categorical axiomatisation of truth to be feasible, but this should not keep one from studying axiomatic theories of truth (or of arithmetic).
Gist of Idea
We know a complete axiomatisation of truth is not feasible
Source
Volker Halbach (Axiomatic Theories of Truth [2011], 3)
Book Reference
Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.23
A Reaction
This, of course, is because of Gödel's famous results. It is important to be aware in this field that there cannot be a dream of a final theory, so we are just seeing what can be learned about truth.