Re: Epistemology 201: The Science of Science

From: Albert (albertwagner_at_cox.net)
Date: 02/10/05 

Date: Thu, 10 Feb 2005 16:47:30 -0600

Chairman of the David Hilbert Appreciation Society wrote:
> Albert wrote:
>
>> Chairman of the David Hilbert Appreciation Society wrote:
>> <snip>
>>
>>> The successor operation is a primitive operation. It's
>>> equivalent to addition by 1, but according to this axiomatization,
>>> we must define addition in terms of the successor operation because
>>> it's all that we've got.
>>
>>
>>
>> Somehow, that just doesn't sound very professional.
>
>
> That's probably because I'm not a professional.
>
> Since you seem to doubt what I wrote above, you must
> have some reason to think that the existence of the
> addition function can be proven from the first order
> Peano axioms; without reference to the successor operation.
>
> Could you show us a proof or at least give an outline
> of how it works?
>
Nope. I just thought the statement "we must define addition in
terms of the successor operation because it's all that we've
got," was really funny. 

-- 
"Don't you see that the whole aim of Newspeak is to narrow the 
range of thought? In the end we shall make thoughtcrime literally 
impossible, because there will be no words in which to express it."
     -- George Orwell as Syme in "1984"

Relevant Pages

  • Re: Epistemology 201: The Science of Science
    ... >> Somehow, that just doesn't sound very professional. ... > addition function can be proven from the first order ... without reference to the successor operation. ...
    (sci.cognitive)
  • Re: Epistemology 201: The Science of Science
    ... >> Somehow, that just doesn't sound very professional. ... > addition function can be proven from the first order ... without reference to the successor operation. ...
    (sci.math)
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