[txrx0000]

The problem of induction doesn't need to be solved because the problem refutes itself when time is brought into the picture.

Let's assume Hume's premise "there can be no demonstrative arguments to prove, that those instances, of which we have had no experience, resemble those, of which we have had experience" is true.

Ok, then how do we know this premise will stay true in the future? Because it is true right now? Because every moment in the future will eventually become the present? But how do we know that? Because it has always happened this way. Time has only ever moved forward, never backward, at least in my experience so far. Oops, this is inductive.

If the premise might not stay true in the future, then that means we've managed to acquire a piece of information about the future: the premise of the problem might not be true by then. We've just gained a bit of knowledge about the future which the premise claims we can't possibly do!

[skybrian]

Knowing that a premise will stay true in the future and knowing that it will become false in the future are both knowing something about the future.

Compare with knowing whether a program will terminate.

[txrx0000]

Thanks to your comment, I realized I've not successfully refuted Hume. The possibility of a truth value change is not a new piece of info about the future. We did arrive at it by deduction, but that info is also an innate part of the propositional logic system, so we already had access to it beforehand. And even though we've never observed Hume's premise change its truth value in the past, the possibility of change has always been there. So Hume's premise does not refute itself, and it still stands. All I can say about it is that the premise does not rule out the possibility that it itself may become false in the future, but this is more of an epistemic boundry technicality rather than an useful insight.

Also, I may have jumped the gun with that comment. I didn't read the whole article the first time around because I thought it was just going to be a hit piece on scientific method when the problem of induction came up. But that isn't the case and they're talking about AI research.