Knowledge

Is there any kind of knowledge that could be called certain?

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I am entirely certain that two and two is four, that the earth is bigger than a peanut, and that Hitler didn't win World War II. Aren't you?

One suggestion that philosophers have come up, for measuring people's degrees of certainty, is to relate it to their willingness to place bets. Of course, there are all kinds of factors that undermine this approach: in the real world, some people avoid gambling altogether for ethical or religious reasons; some might not regard it as worth the effort of betting at all, when the prospective reward is tiny; and, in certain cases, it is hard to conceive who could possibly qualify as the arbiter of whether the bet had been won or lost. But, abstracting away from all of those problems, suppose that we agree that a person's betting inclinations are an accurate guide to their level of confidence. If someone is only willing to place a bet on the truth of a certain proposition when the offered odds are very long, that shows that they are very unconfident. They need the prospect of a very large return to justify risking their stake. On the other hand, if someone is willing to place a bet at very short odds, that shows that they are very confident indeed. They know that they stand to lose a large amount of money if things go wrong for them, and that they won't win much even if things go right: but they're still prepared to go for it anyway, because of just how confident they are that things will go right.

If we take this as a measure of degrees of confidence, then we need to ask how much confidence constitutes 'certainty'. Is a confidence-level of 99% enough to qualify? Or 90%? Or even less? But maybe you're talking about absolute certainty. But we have an answer to that too. If you would be willing to bet absolutely everything you own on the truth of a given proposition, for the prospect of only a tiny reward if you are right, then it seems fair to say that you are absolutely certain of its truth. And personally -- although I can't really envisage how this would ever come up! -- I think that I probably would be willing to bet absolutely everything I own on the truth of a proposition like '2+2=4'. I really am that confident in it.

Now, I've been treating the notion of 'certainty' as a subjective matter, relating to a particular individual's level of confidence. But I'm thinking that perhaps this isn't quite what you had in mind. Is there such a thing as 'objective certainty'? Are there propositions that are certain in themselves, independently of whether anyone feels certain about them? I'm not quite sure what that would even mean. But a better question might be: are beliefs like '2+2=4' demon-proof? This from Descartes: is it possible that there might be an evil demon who could persuade me that 2+2=4, despite the fact that, absolutely speaking, this is false? I have to suspect that, yes, that is indeed just about barely possible. But, as Descartes himself put it: "Why should this alleged 'absolute falsity' bother us, since we neither believe in it nor have even the slightest suspicion of it?" I'm inclined to agree.

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