I am reading Hintikka's article on logical consequence in Oxford handbook of Philosophy of math and logic, and he was talking about the meaings of logical constants, when the following excerpt appeared (p.680):
But obviously the truth conditions cannot simultaneously do service both in a definition of truth and in an explanation of the meaning of the sentences in question. In other words,the equivalences of the kind exemplified above (Hintikka is referring to equivalences of truth conditions, such as '~A is true if and only if A is not true') cannot be taken as clauses in a recursive definition of truth, and at the same time can be taken as explaining the meaning of the logical constants exhibited—this would be like solving two unknowns, given only one equation. If we have defined a set S of sentences by saying that it is the least set of sentences containing certain atomic formulas and satisfying certain equivalences, such as
A ∧ B belongs to S if and only if both A and B belong to S,
then obviously we get no information about the meaning of the logical constants by being told again that these equivalences hold. Similarly, a person who does not know what truth is, but is informed that it is a notion satisfying certain equivalences of the kind given above, does not get to know the meaning of the logical constants by then being told again that these equivalences hold. We must conclude that truth conditions can serve as meaning explanations only if we already have a grasp of truth.
It appears that Hintikka is talking about some kind of circularity if we do take truth conditions as the definition of truth and explanation of meaning of sentences.
I get that since the meaning of logical constants is defined recursively, we will have to have a grasp of truth to explain what it means for atomic formulas to be true, e.g. imagine two people discussing these notions:
A: What does a sentence mean?
B: Take conjunction as an example, A ∧ B is true iff A and B are true.
A: Ok, but then what does being true mean?
B: In the case of complex formulas a recursive definition like the one above would work. But recursively, A is true iff ...
In this scenario, at the end it is clear that B would have to resort to some kind of more fundamental definition of truth (ie. define truth in terms of something more fundamental) to explain what it means for atomic formula like A to be true. This is the only possible interpretation I can come up with, but this doesn't feel like what Hintikka is saying; so what is he saying really?
