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Any recommended reading for someone who's never formally studied philosophy?
Karl Popper, "The Logic of Scientific Discovery" is a seminal work in the modern philosophy of science. It proposes to solve the problem of induction, and his proposal of falsifiability is, to my knowledge, the most popular philosophical framework for modern scientific practice. I'd be interested in what the above commenter has to say about Popper, though, as I am not well-read outside of his work, as my focus is on the history of science.
I'm not sure recommending Popper to someone who has never studied philosophy, and who is reading on their own, is a good idea ... I would probably start with a small intro to philosophy book like Blackburn's Think and then try to find lectures or resources that help teach Popper, rather than just diving into source material with no guidance.
Popper is important, but I don't think he is commonly seen to have solved the problem of induction ... he made an attempt, but that's a different story.