Davidson on Truth and Meaning
Main Claim: A theory of truth for a language, in the style of Tarski, can serve as a
theory of meaning for that language.
Requirements on a theory of meaning for a language L:
(1) It must serve as a theory of understanding for L. That is, it must enable
someone who knows it to use and understand every sentence of L.
(2) It must display how the meaning of a sentence depends on its structure, that is,
how it is formed from the finite stock of words of L according to a finite set of
axioms. This requirement flows from the observations that we have limited
cognitive resources and that languages typically contain a potential infinite
number of meaningful sentences.
(3) It must be empirically testable.
Unpromising theories:
Theories that entail theorems of the form:

‘s means m’, where ‘s’ is replaced by a structural description of a sentence and
‘m’ refers to the meaning of ‘s’.

‘s means that p’, where ‘s’ is replaced by a structural description of a sentence
and ‘p’ is replaced by the sentence itself.
Promising theories entail theorems of the form:

‘s is T if and only if p’, where ‘s’ is replaced by a structural description of a
sentence and ‘p’ is replaced by the sentence itself if the meta-language is the
object language, or a translation of the sentence into the meta-language.

What predicate does ‘T’ stand for? If it stands for the truth predicate then, by
making use of Tarski’s semantic conception of truth, requirements (1) and (2)
can be satisfied. So, the theory of meaning would entail theorems of the form:

For a language L, s means that p in L just in case the following bi-conditional
holds: s is true in L if and only if p, where ‘s’ is replaced by a structural
description of a sentence and ‘p’ is replaced by the sentence itself if the metalanguage is the object language, or a translation of the sentence into the metalanguage. These bi-conditionals are instances of Tarski’s Schema T.
Proving an instance of Schema T:
Say that we want to prove that ‘Caesar is ruthless’ is true in L just in case Caesar is
ruthless.
We begin with a reference axiom:
(A1)
‘Caesar’ refers in L to Caesar.
We now add a satisfaction axiom:
(A2)
For all objects x, x satisfies ‘is ruthless’ in L just in case x is ruthless.
Finally, we add a composition axiom:
(A3) For all sentences s, all predicates p, and all singular terms t, if s = t^p then s is
true in L just in case the referent of t satisfies p.
(1)
‘Caesar is ruthless’ is true in L just in case the referent of ‘Caesar’ satisfies
‘is ruthless’. [A3]
(2)
‘Caesar is ruthless’ is true in L just in case Caesar satisfies ‘is ruthless’.
[A1, 1]
(3)
‘Caesar is ruthless’ is true in L just in case Caesar is ruthless. [A2, 2]