Suppose that T is taken to be a logical truth—e.g. T has the form φ or not-φ (if you believe that excluded-middle is not a logically valid formula-scheme, take another example). Now consider the following argument:
- Rational subjects at least implicitly know/are rationally committed to logical truths;
- For any φ, if one implicitly knows/is rationally committed to φ then it is not rational for one to suspend judgment about φ;
- Therefore, a rational subject does not suspend judgment about logical truths (1, 2);
- Subject S rationally suspends judgment about T;
- Therefore, T is not a logical truth (3, 4).
If sound, this argument could be used to prove that a number of things we have taken to be logical truths are not after all logical truths. If that is absurd, then one of 1, 2 or 4 must go. Let me say a little bit about each of these
About premise 1: The idea here should be familiar to those who use Kripke-models to formalize epistemic notions: you always know (perhaps implicitly) all propositions that are true in every world that is epistemically accessible to you; since logical truths are true in all of those, all logical truths are known. But in order to accept premise 1 you don’t need to embrace all the idealizations of possible-worlds semantics. There are other ways to motivate 1, however. Here’s one: the way in which subjects cognize commits them to logical truths, because the epistemic goodness of their deductive inferences would seem to depend on those truths, and they are able to recognize this. E.g. when I deduce that ∃x(Fx & Gx) from my belief that (Fa & Ga) I manifest implicit knowledge of/am committed to (Fa & Ga) → ∃x(Fx & Gx) or its necessity thereof. (Implicit knowledge/rational commitment need not be transparent or explicit to the knower herself).
About premise 2: That I implicitly know/am rationally committed to φ in a given cognitive state s means, among other things, that I am prepared to transition from s to a new cognitive state s’ in which I explicitly know/rationally believe that φ. So in s the following norm applies to me: I should not disbelieve that φ or suspend judgment about φ—that would be incoherent of me. Since coherence is a requirement for rationality, that would be irrational of me.
About premise 4: What gives support to it is an argument from appearances. In some cases it seems that it is not irrational for one to suspend judgment about a logical truth, say, because a reliable logician has told one that it is controversial whether that is really a logical truth. Or one might suspend judgment about what is (unbeknownst to one) indeed a logical truth (let it be φ) out of one’s own theoretical reflections: one knows that system S validates φ, and that system S’ does not validate φ, but one is not sure which of these systems is the one that correctly captures logical validity/necessity; each of S and S’ has its own advantages (e.g. one of them is stronger than the other, but the latter one fits the claims of quantum mechanics better).
Initially I feel more inclined to reject 4, but that is because I have this thing with the ‘saving–appearances’ approach to philosophy. But I won’t try to defend this option here—just wanted to put the conflict between 1, 2 and 4 out there.