Full Idea
Considering the truth axioms in the absence of a base theory is not very sensible because characteristically truth theoretic reasoning arises from the interplay of the truth axioms with the base theory.
Gist of Idea
Truth axioms need a base theory, because that is where truth issues arise
Source
Volker Halbach (Axiomatic Theories of Truth [2011], 21.2)
Book Reference
Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.314
A Reaction
The base theory usually seems to be either Peano arithmetic or set theory. We might say that introverted thought (e.g. in infants) has little use for truth; it is when you think about the world that truth becomes a worry.