Hume/Problem of Induction

Hey Veeky Forums, I am desperately in need some help making sense of the implications of Hume's proposed problem of induction and Veeky Forums redirected me here.

Hume considers himself to be an empiricist as far as I know, but doesn't his criticism of induction undermine empiricism as a whole? If obtaining knowledge through induction is not logical, then the scientific method, based on empiricism is fundamentally flawed. I get that he says that it's our constant experience of impressions that allows us to form ideas and connect them (which demonstrates his empirical conviction; experience is key to forming ideas and obtaining knowledge) and relate them through the flawed concept of causality.

But again, the flawed concept of causality greatly undermines empiricism, so why is he considered to be an empiricist instead of a skeptic, since he attempts to undermine rationalism but also damages empiricism with his arguments, seemingly rejecting both? Is the fact that he said that we have to accept the limitations of induction and work with that the reason he is considered an empiricist instead of a skeptic?

Finally, which part of his proposed problem of induction undermines rationalism as he claims to be doing? Or does the undermining of rationalism stem EXCLUSIVELY from his ideas & impressions initial framework and not at all from his causality argument?

I feel like I've made a critical misunderstanding in my analysis of Hume and would greatly appreciate it if someone could detect and highlight it to me. Keep in mind I'm not studying philosophy in university, so if you have to introduce new terms to explain stuff please clarify what they mean or use terms that I can refer to online. Thanks in advance.

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*meant hey Veeky Forums

It sounds like you've conflated empiricism with the scientific method.

Empiricism does not allow for induction, the scientific method does - at least as practiced in labs across the world. The alternative would be Popper's brand of falsification, which avoids induction by definitively proving ideas wrong via experiment.

How does 'proving' something wrong by experimentation avoid this problem? You cannot really eliminate it, for the same reasons you cannot accept something supported by experimentation. Experimentation will always merely provide an example of things going a certain way.

en.wikipedia.org/wiki/Falsifiability

This
Btw Hume is the worst empirisist of them all. He goes full rationalism when it comes to thoughts and ideas/math. Its compleatly sound without experience in his book.

>Is the fact that he said that we have to accept the limitations of induction and work with that the reason he is considered an empiricist instead of a skeptic?
Yes
He says that it's better (for living organisms) to be occasionally wrong than absolutely certain

>why is he considered to be an empiricist instead of a skeptic
He's considered both and the most radical of them all in that regard. Locke turning in his grave and shit.

Hume was a toad of sorts you see.

Again, if the scientific method does not lead to 'knowing' due to the problem of induction, I don't see how 'proving and idea wrong via experimentation' would do anything to avoid the issue.

Statements can be deductively proved false, that's the idea that falsification is predicated on.