Tuesday, February 20, 2018
Is Logic Necessary?
I've been looking at Skepticism, following Maddy's 2017, because it connects with the topic of this month's posts: highly evolved apes are unlikely to have a perfect logic, so why should we care if logic gives us paradoxes? We see a tree, we know that it is a tree; that much is ordinary. We cannot rule out its being an alien quasi-stick-insect, of course; but then, we never thought that we had to do that, did we? And now that you come to think about it, don't you think that you could if you examined the tree more closely? Or that some scientists could? Now, we cannot ever rule out the possibility of an error of some kind or other, perhaps an error of a kind that we have never thought about: how could we rule that out? Is that is why the experts on logic think of logic as being formal logics (mathematical models of logic) nowadays? I suppose that experts could be certain about mathematical calculations. However, such logics come with modern definitions of truth, scientific theories of truth, mathematical models of truth, raising the question: What is the truth about truth? The first "truth" in that question is clearly intended to be correspondence truth, but if it does turn out to be the case that the second one cannot be correspondence, then how could the first one be? And if the first "truth" is not correspondence truth, then how satisfying could any answer to any such question be? What if we have, for example, an attractive story about how truth is an attractive story? At the end of the day, we naturally assume that truth is correspondence truth, and that logic is logic, not a mathematical model of logic. Even when it is the experts thinking about the formalities, their metalogic is simply logic; and when they give us theories of their metalogic, they do expect us to think about their presentations of those theories in logical ways. And similarly, we simply assume that trees are not alien quasi-stick-insects of some very convincing kind. We can say that they are very probably not aliens, and then try to justify that "very probably" and maybe wonder why we are doing all of that. But at the end of the day, we are simply such that for us, our logic is necessary. I see a tree, and know that it is a tree. I cannot rule out its being an alien quasi-stick-insect of a very convincing kind, and so my "know" is a sort of gamble: I assume that it isn't an alien. I don't know that it's unlikely to be one (how could I?) but I do know that it's not mad to assume that it isn't one. Since the topic is raised, I admit that it might be an alien, that I don't know that it isn't, that I don't know, in that sense, that it is a tree; but I still claim that I do know that it is a tree, in the ordinary sense. In short, there seem to be at least two senses of "know" in play.
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