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Topic: Infinity: The Story So Far
Replies: 16   Last Post: Mar 7, 2014 8:31 AM

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Peter Percival

Posts: 2,623
Registered: 10/25/10
Re: Infinity: The Story So Far
Posted: Mar 5, 2014 4:07 PM
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Virgil wrote:
> In article <4cfd9bb3-5708-4ed7-9285-e2735a4fcd85@googlegroups.com>,
> mueckenh@rz.fh-augsburg.de wrote:
>

>> But he claimes that the Peano-axioms supply the natural numbers of formal
>> mathematics. So the natural numbers of formal mathematics are:
>> 1, -10, 100, -1000, ...

>
> Only in wierd places like WM's wild weird world of WMytheology.
> Elsewhere, the successor operation is denoted by adding one.


I don't think that is correct. The successor of x may be denoted S(x)
or x' or in other ways. If S(x) is read as "multiply x by -10" and that
reading is consistent with S's axioms, then that possible meaning for S
is not excluded and "natural number" meaning one of "1, -10, 100, ..."
is not excluded either. Russell makes a similar point in his
/Introduction to mathematical philosophy/.

--
Madam Life's a piece in bloom,
Death goes dogging everywhere:
She's the tenant of the room,
He's the ruffian on the stair.



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