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 read

Peano Postulates:

There is a set, S, and an object, o, and a function, f, such that

1. o is a member of S

2. if x is in S then f(x) is in S

3. For every x in S, o =/= F(x)

4. For every x and y in S, if f(x) = f(y) then x = y

5. 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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