A paradox is different from a result that is merely surprising, but what is the difference? This question touches on matters beyond epistemology, but it is applicable to the major epistemic paradoxes, including preface, lottery, surprise quiz, and knowability. It is the latter that prompts my question.
In the knowability paradox, we purportedly demonstrate that if all truths are knowable, then all truths are known. There is no question that the result is surprising, but what makes it paradoxical? Compare it with Godel’s incompleteness theorems, for example, which are also quite surprising, but not paradoxical. Or compare it to the ontological argument, where it is purportedly shown that if a certain description is possibly exemplified, then it is necessarily exemplified. This, too, is quite surprising, but I doubt it is paradoxical. So, what is the difference?
Perhaps the difference is psychological. Logical results are suprising when they go beyond what we presently believe to be true, and when they concern issues of significance to us. We notice the result which, prior to the proof, we doubted; after seeing the proof, we are convinced and thereby surprised. When the result is paradoxical, however, something additional happens. The proof threatens our intellectual commitments in some way, it threatens our firmly held opinions on matters that are significant to us. Admitting the soundness of a proof to the contrary thus engenders a bit of mental apoplexy: we know something has to give, but it’s hard to see what.
Is there a different account of the distinction? I’m not sure; if you have a different account, please share it. But if we suppose that this account is on track, one has to dig a bit to find a paradox in the knowability result. The result is a conditional: if every truth is knowable, then every truth is known. That’s not a denial of any deeply entrenched viewpoint I hold on issues that are significant to me. So why the fuss? I think there is something paradoxical in the neighborhood here, and I think it has important lessons. But since it depends on the psychological account of the difference between surprising and paradoxical derivations, I’ll hold off to see if there might be a better account of the difference.