Full Idea
Tarski preferred an explicit definition of truth to axioms. He says axioms have a rather accidental character, only a definition can guarantee the continued consistency of the system, and it keeps truth in harmony with physical science and physicalism.
Gist of Idea
Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies
Source
report of Alfred Tarski (works [1936]) by Donald Davidson - Truth and Predication 2 n2
Book Reference
Davidson,Donald: 'Truth and Predication' [Belknap Harvard 2005], p.31
A Reaction
Davidson's summary, gleaned from various sources in Tarski. A big challenge for modern axiom systems is to avoid inconsistency, which is extremely hard to do (given that set theory is not sure of having achieved it).