While it is eye-opening I could hardly recommend the Tractatus unless you get it with a commentary. How about The Routledge Philosophy Guidebook to Wittgenstein and the Tractatus by Michael Morris?
Good call with Karl Popper. On Liberty is archaic somewhat. To recommend just that book by John McCarthy is too narrow, and besides logic and the theory of computation are not a part of philosophy per se. Logic is a tool of philosophers. The theory of computation could possibly be folded into philosophy of mind but I've never seen it done so, there is a strong argument that it should be.
Good call with Karl Popper. On Liberty is archaic somewhat. To recommend just that book by John McCarthy is too narrow, and besides logic and the theory of computation are not a part of philosophy per se. Logic is a tool of philosophers. The theory of computation could possibly be folded into philosophy of mind but I've never seen it done so, there is a strong argument that it should be.