C and not-C
And then there is this fella Andrew Pessin, who says you can be certain and also uncertain and that way all shall win, all shall have prizes. You do it using the Paradox of the Preface.
Imagine an author writing something like this as a preface to her work:
I am certain, of each and every sentence in this work, that it is true, on the basis of various considerations including the careful arguments and use of evidence which led me to it. And yet I recognize that I am a fallible human being, likely to have made some error(s) in the course of this long work. Thus I am also quite certain that I have made some such error somewhere, even if I cannot say where.
I could buy that if he had made it “I am sure, of each and every sentence” and so on. I could buy it if he had made it I am convinced, or I strongly believe, or I really really think. But by making it “I am certain” he turns the whole thing into gibberish. If you are already quite certain that you have made a mistake somewhere, then you can’t also be certain that you haven’t – you can’t be certain that every sentence is true.
Maybe he meant a kind of colloquial version of ‘certain’ which is like the colloquial version of ‘literal’ in that it doesn’t mean what the word means. I have noticed that a lot of people use the word to refer to claims that they can’t possibly be certain of, and wondered if they actually think it is an exact synonym of ‘sure’ or ‘convinced.’ But if he did…that’s kind of stupid, frankly, since the whole piece depends on that word, and he used it sloppily. You can’t be certain that you have made no mistakes and at the same time certain that you have made a mistake.
Anyway, I avoid this kind of tangle by simply never being certain or even sure that I have made no mistakes.