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.

  • How about (4) 'it is raining today' is true, because water is dripping from the sky? Commented May 10, 2016 at 22:13

3 Answers 3


There's no problem in saying that

'7 is a prime number' is true if 7 can only be divided by 1 or itself

since it is of course consistent with

'7 is a prime number' iff 7 is a prime number.

It is important to note that the so-called schema T:

X is true if and only if p

is not Tarski's definition of truth but rather it is a condition that, on his conception, any definition of truth should satisfy (that is, a correct truth definition should entail all instances of schema T). And so it does not mean that p is the only way, so to speak, in which X is true.


The point of Tarski's definition is: A sentence s = 'X' is true iff and only if X holds, i.e.if X is a fact.

This principle applies to both your examples. The sentence '7 is a prime' is true if and only if it is a fact, that 7 is a prime. And the latter holds because the number 7 is divisible only by 1 and itself - which is a fact too.


Yes I think you mix truth with the method of finding the truth. Tarskis definition should stop you from saying that it is raining but you dont believe it is raining , since IF it is raining THEN it is true that it is raining. And you should understand that your belief is false.

We could ask: What then IS truth? And then its questionable if we get much wiser being told that for all statements x, x is true IFF x. https://en.wikipedia.org/wiki/Truth

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