You do realize that Hume held that induction cannot be logically justified? He noticed there is a "problem of induction".

Of course. That is why I mentioned him.

That problem was exploded by Karl Popper. Have you read what he has to say and taken seriously his ideas?

"Exploded". My! What violent imagery. I usually prefer to see problems "dissolved". Less metaphorical debris. And yes, I've read quite a bit of Popper, and admire much of it.

Have you read and taken seriously the ideas of philosophers like David Deutsch, David Miller, and Bill Bartley?

Nope, I haven't.

They all agree with Popper that:

Induction, i.e. inference based on many observations, is a myth. It is neither a psychological fact, nor a fact of ordinary life, nor one of scientific procedure - Karl Popper (Conjectures & Refutations, p 70).

You know, when giving page citations in printed texts, you should specify the edition. My 1965 Harper Torchbook paperback edition does not show Popper saying that on p 70. But, no matter.

One of the few things I dislike about Popper is that he doesn't seem to understand statistical inference. I mean, he is totally clueless on the subject. It is not just that he isn't a Bayesian - it seems he doesn't "get" Pearson and Fisher either. Well, no philosopher gets everything right. But if he really thinks that "inference based on many observations" cannot happen - not just that it is frequently done wrong, but rather that it is impossible - then all I can say is that this is not one of Sir Karl's better moments.

And if what he means is simply that we cannot infer absolute general truths from repeated observations, then I have to call him a liar for suggesting that anyone else ever suggested that we could make such inferences.

But, since you have been recommending philosophers to me, let me recommend some to you. I. J. Good is fun. Richard Jeffrey is not bad either. E.T. Jaynes explains quite clearly how one makes inferences based on observations - one observation or many observations. You really ought to look at Jaynes before coming to this forum to lecture on epistemology.