I did have a few questions in regards to the nature of scientific explanation and furthering (or ‘advancing’, if you prefer) scientific knowledge. Hume had recognized that the problem of induction can not be justified by an inductive rule (that would be circular) or a deductive rule (or else the principle wouldn’t be inductive – we cannot deduce the truth of induction from the axioms of logic). This of course being Hume’s fork.
However, does Karl Popper’s interpretation of scientific methods being deductive (or falsifiable) solve this problem more so than science on the inductive interpretation? In short, Im just curious if we are reasonable in rejecting Hume’s skepticism, but sound in still adhering to science hinging off of induction.
I did a lot of work on this question in my MA thesis. My full answer is a bit long but I hope it’s easy to follow. For the Reader’s Digest version, I’d say that I’m not a fan of deductive arguments and I prefer inductive arguments. (Actually, I love abductive arguments much more but that’s another issue!) I’m very sympathetic to Popper’s criterion of falsifiability but it’s not a necessary condition for science–it’s just preferable. I’ll try to contextualize and elaborate on some of the hidden talking points in your question so some of the readers can follow along.