All Questions

1) (By Goedel's) One can not prove, in PA, a formula that can be interpreted to express the consistency of PA. (Hopefully I said it right. Specialists correct me, please). 2) There are proofs (...

In his paper, "Completed versus Incomplete Infinity in Arithmetic" (which can be found here), the late Edward Nelson defines the notion of 'counting number' as follows: 0 is a counting ...