Abstract:

The topic of this talk is informal provability, i.e., provability as it is understood in mathematical practice rather than in proof theory. In particular, we will argue that (i) "provable informally" differs conceptually from "formally provable (in a recursively axiomatized system S)", (ii) the notion of informal provability has semantic and intuitive components that the notion of formal provability lacks (and it is possible to make sense of Gödel's view on these kinds of components), and (iii) the logic of informal provability differs from the logic of formal provability. In our final part (iv) we will deal with the question whether there are true but informally unprovable statements, and if so whether this could be proven informally.