Davidson proposed to use Tarski-style truth theory
for the purposes of a compositional meaning theory, and he argued that 'natural languages re compositional because they have an infinity of non-synonymous sentences but are mastered by finite beings' (201).
Roughly speaking, in model theory meanings are entities, whereas in truth theory
they are conditions.
23) By truth theory
or model theory I intend the vague but workable notion of a theory which functions pretty much as the naive theories were intended to function, by those who thought them classically consistent.
Field's answer to that challenge, which could be put as a request for the truth theory
for the set theory ZF used in the model theory, is that 'we have an adequate truth theory
for ZFtme within ZFtme' (356).
The other is the realization that an axiomatic truth theory
of the Tarskian variety meets this constraint.
Part I lays out the history of the program of adopting a Tarski-style truth theory
as a basis for a compositional meaning theory.