I am not a specialist in these areas, but the most important books for me personally on epistemology and logic have been:
On Certainty, by Ludwig Wittgenstein.
The Logic of Scientific Discovery, by Karl Popper.
Aspects of Scientific Explanation, by Carl Hempel.
Meta Math: The Quest for Omega, by Gregory Chaitin.
In addition to these books, Ray Solomonoff’s papers on induction and algorithmic information theory have been very important to my thinking, even though the mathematics are beyond me, because I think I get the basic ideas, and I agree with them.
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