Before continuing any further, a very general word about the contents of these handouts (and indeed of this course). As you will have seen, there is relatively little philosophy so far. We said, in very general terms, that the Gödelian incompleteness theorem sinks varieties of what I called “deductivism” as a framework for a philosophical position about basic arithmetic. But otherwise, our discussions up to this point have mostly been mathematical (albeit rather informal maths for the most part). And that’s the way things will continue. As I see it, what will most help get you into a position to understand and assess various philosophical claims about Gödel’s results is to have a really solid grasp of what his theorems actually say and how they are proved. So these handouts will remain primarily an introduction to the mathematics of incompleteness. The philosophical implications are for you to draw out.