Might someone feel as though they have a rational grasp on a logical certainty, when they are in fact mistaken? If so, should that undermine our own confidence in logic?
(These look like annoying questions, with a whiff of undergrad "anything goes" sophistry about them. But perhaps they're worth taking seriously, at least for the duration of one blog post.)
This is rather different from your run-of-the-mill BIV-based skepticism. There it is suggested that our actual experiences could be misleading. It is not so clear that our actual reasoning could be mistaken. If modus ponens is a valid rule of inference, then presumably it couldn't fail to be so. Still, as recently noted, there's something a bit unsatisfying about such conditionals, if we're not in a position to assure ourselves of the antecedent.
In any case, the initial difference can be overcome with a little abstraction, as in my introductory questions. Rather than asking about the particular things (de re) that we consider self-evidently necessary, we may raise the general (de dicto) question of whether we could find falsehoods to be "self-evident". And if that is a genuine possibility, we should want to find some way to determine that such a scenario is not our actual condition. Lacking such findings, logical skepticism might get off the ground in much the same way that empirical skepticism does.
Worse, logical skepticism might render itself immune to any form of refutation. That is, even if you were to find (what appears to be) a water-tight proof against it, the Most Radical Skeptic could simply iterate her challenge, applying it now to the proof itself. ("Might you not find just as convincing a proof that was actually mistaken? Your certainty is a response to the apparent soundness of the proof. Whether it is actually sound or not is a separate question. We cannot get beyond appearances; your feeble attempts are futile since they merely appeal to further appearances, and so fail to bring us any closer to the impossible goal of directly grasping the raw truth.")
We might try to respond by denying the assumption of phenomenological identity posited in the initial premise. Compare my old post on dream skepticism, and especially the idea that an unnoticed absence is not the same thing as phenomenal presence. Perhaps there is something distinctive about the feeling of genuine rational apprehension, such that you can know when you have it, even though you often won't know when you lack it. (Just like you can know when you're awake, even though you often don't know when you're asleep.) Then -- as briefly discussed in the linked post -- an analogue of my response to dream skepticism might also apply here. We can be confident in the epistemic necessity of Descartes' cogito, even though a drugged logician might be equally confident of some wacky falsehood. The difference is that his confidence would be based on muddle-headedness, whereas ours is based on rational clarity. And even though the muddled one is in no position to tell the two experiences apart, the clear-thinker surely can.
Or maybe not? Are we in a position to be sure that our thoughts are clear and rational? Can we be sure that we're not suffering from logical delusions? I'm not too sure what to say about this. Feel free to drop your opinion into the comments box!
If all else fails, I guess we can always fall back on the old transcendent-practical argument that we've nothing to lose and everything to gain by trusting logical appearances at least to some degree. Most Radical Skepticism leads to total paralysis: the Most Radical Skeptic answers absolutely every question with a hapless shrug. They're hopeless! But the rest of us seem to be doing okay, by comparison.
Of course, I can't say that's a knock-down argument for assuming that logical appearances are reliable. The most annoying skeptic would never grant it (simply because they'd never grant anything). I guess I can merely offer it as friendly advice, and let them make of it what they will...