1) Someone, such as Sophomore Sam, who asserts that there are no truths does not assert that there are truths.
And yet
2) That there are no truths entails that there is at least one truth. (Why? Because it is impossible for the first proposition to be true and the second false.)
Therefore
3) If someone S asserts that p, and p entails q, it does not follow that S asserts that q. (Assertion is not closed under entailment.)
4) Although Sam does not ASSERT that there is at least one truth when he assertively utters the sentence 'There are no truths,' he is in some relation to the proposition that there is at least one truth. I will say that he PRESUPPOSES it.
Therefore
5) There is a distinction we need to make and it is reasonably labelled the distinction between ASSERTING a proposition and PRESUPPOSING a proposition. An act of asserting can carry a presupposition that is not asserted. Sam's act of asserting that there are no truths presupposes but does not assert that there is at least one truth.
If you don't accept this argument, tell me which premise(s) you reject and why.
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