```Date: Mar 21, 2014 3:51 PM
Author: Virgil
Subject: Re: � 454   Equality and the axioms of natural numbers

In article <fe9e9fb1-c93a-4307-87da-48cb1242957d@googlegroups.com>, mueckenh@rz.fh-augsburg.de wrote:> On Friday, 21 March 2014 09:30:12 UTC+1, Virgil  wrote:The question was: If the five truncated Peano axioms, not more and not > > > less, > > > > > define the natural numbers> > > > > > > > But the "truncated"Peano postulates prove nothing.> > They prove that 1 (or 0) is a natural number.My "truncated PA's readPeano Postulates:There is a set, S, and an object, o, and a function, f, such that1.  o is a member of S2.  if x is in S then f(x) is in S3.  For every x in S, o =/= F(x)4. For every x and y in S, if f(x) = f(y) then x = y5.  If a set T is such that o is a member of T and whenever x is a member of T then also f(x) is a member of T then S is a subset of T. Since that "o" is only specified as being an object and the postulates never mention natural numbers, WM's assumption is, as usual, unfunded.--
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