The 'possibility' of a pattern changing is obvious. There's a possibility of almost anything. But that isn't what Hume's Problem of Induction was about. He said that we have no reason to even think it's more likely than not that any given pattern will continue to its next step.
Imagine that some event has happened 10508325 times in the past, which we have witnessed, and we now must decide the likelihood of it happening yet again. The Problem of Induction states that we have no reason to think it's more likely to happen again than to not.
I'd say that, if it happened in the past that many times, there must have been something causing it in the past. And it's safe to assume that it cause will very likely persist. Or more like, we have no reason to think it should stop. But the same problem arises.
I'm really thinking on the spot here. What if we just consider some completely physical situation, like the sun rising (wow I just realized that was Hume's original example after I decided to use it). With the assumption that all known physical laws are valid - newton's laws, etc - we can say that, since we don't know of any comet coming to interfere with the sun or anything like that, the sun will rise again because it's a physical object following those physical laws.
But the same problem still arises - we have no reason to think that the physical laws themselves are any more likely to remain constant a moment from now than to change.
I understood the argument as soon as I first heard it, and thought I had come up with a way around it. I don't know why I thought I had. I suppose I have to agree, for now. Although it seems like there must be some way around it.
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