PHYS771 Lecture 3: Gödel, Turing, and Friends Scott Aaronson On Thursday, I probably should've told you explicitly that I was compressing a whole math course into one lecture. On the one hand, that means I don't really expect you to have understood everything. On the other hand, to the extent you did understand -- hey! You got a whole math course in one lecture! You're welcome. But I do realize that in the last lecture, I went too fast in some places. In particular, I wrote an example of logical inference on the board. The example was, if all A's are B's, and there is an A, then there is a B. I'm told that the physicists were having trouble with that? Hey, I'm just ribbin' ya. If you haven't seen this way of thinking before, then you haven't seen it. But maybe, for the benefit of the physicists, we should go over the basic rules of logic? Propositional Tautologies: A or ...