Why numbers are sets (Q1868173)

In opposition to the general opinion that there are infinitely many different structures that can play the role of the natural numbers, the author holds that the natural numbers are, in fact, the finite von Neumann ordinals (FVNO). He points out the well-known fact that, in addition to Peano's Postulates, there are other nice properties that will ensure that the structure consists of the natural numbers and he seems to believe that the natural numbers must have those properties, although he gives no justification for that belief. But, beyond this, he claims to give a proof (on pp. 355--356) that the natural numbers are the FVNO. The reviewer was unable to understand this ``proof''. Among other things, the author uses the concepts of NN-universe and NN-conditions and asserts various properties of these concepts, but he does not clearly define or explain the concepts.