Does Tarski's semantic conception of truth X is true if and only if p (where X is the name of a sentence, and p is the sentence itself) apply to all sentences or only to facts (understood as contingent sentences)?
My question is motivated by the following example:
(1) 'it is raining today' is true iff it is raining today
(2) '7 is a prime number' is true iff 7 is a prime number
The first case, which corresponds to a fact, does not pose any problem to me, but, somehow, I am a bit uncomfortable with the second sentence. For I could say that
(3) '7 is a prime number' is true because it can only be divided by 1 or itself.
Or, perhaps, I just mix the concepts of truth and provability? Any input appreciated.