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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?

  • It is the meaning of connectives (logical constants) that is at issue, not of atomic formulas. We do explain the meaning of connectives in terms of reducing the truth of expressions with them to the truth of the constituents. But Tarskian recursive "definition" of truth uses (ostensibly) the same process. One equation can not determine two unknowns, hence, despite the appearances, the Tarskian definition has nothing to say about truth. – Conifold Jun 5 '19 at 19:33
  • @Conifold I am sorry but I am afraid I don't quite understand how is the one equation concept relevant...what is that equation analogue to? – Daniel Mak Jun 7 '19 at 14:34
  • The "equations" are the definitional properties of connectives, like "A ∧ B is true iff A and B are true", they are double dipped again in the "definition" of truth for compound sentences. – Conifold Jun 7 '19 at 19:09
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Hintikka seems to be referring to a familar predicament in modern analytic philosophy, and this is the apparent co-dependency of meaning and truth.

That truth depends on meaning, goes without saying. Truth-bearers, the entities to which we attribute truth values (like assertions, propositions, statements) are meaningful entities. In order, in other words, to consider the truth value of a sentence like "the sun is shining" we need to know what the sentence means, what these words mean.

In modern analytic philosophy, at least since Frege, it has been widely believed that (on the other hand) meaning also depends on truth. The meaning of a term is derived from the ways in which the term contributes to the truth values of sentences in which the term appears.

The upshot of the co-dependency between meaning and truth is that in a situation where an interpretation is needed, whether in speaking or in reading, we cannot, in general, determine the meaning of the words first, and then evaluate the truth value of what was stated. We need to determine both, meaning and truth, simultaneously.

These (meaning and truth) are the "two unknowns" that Hintikka seems to be referring to. In his case, the problem is theoretical (defining/explaining the concepts of truth and meaning) rather than practical (determing truth and meaning in a particular case).

In other words, the equivalences of the kind exemplified above 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.

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