Re: Epistemology 201: The Science of Science

From: Jason (jasonstevensNOSPAM_at_free.net.nz)
Date: 02/05/05 

Date: Sat, 05 Feb 2005 18:37:54 +1300

Torkel Franzen wrote:
> Jason <jasonstevensNOSPAM@free.net.nz> writes:
>
>
>>So the implication, a formula which is part of the "language of ZFC", is
>>used in the proof.
>
>
> No, there is no formula in the language of ZFC used in the proof.

Okay, so you *must* be suggesting that the implication is not part of
the langauge of ZFC. This is a strange theory of sets indeed.

> Your further comments turn on the existence of derivations in ZFC of
> formalizations of the theorems of mathematics. This is a different
> matter. The simple observation at issue is that ordinary mathematical
> proofs are not formal derivations in ZFC and in fact are nothing like
> formal derivations in ZFC.

If mathematical proofs are informal, then they must be appealing to some
sort of mathematical intuition or know-how. But it is madness to rest
on intuition for proofs, because so many things defy intuition. It is
important to ground maths formally as a resource for when intuition
fails. In this way, proofs can become formal when required, and be
formalisable in principle.

Relevant Pages

  • Re: Epistemology 201: The Science of Science
    ... there is no formula in the language of ZFC used in the proof. ... > formalizations of the theorems of mathematics. ... on intuition for proofs, because so many things defy intuition. ...
    (sci.cognitive)
  • Re: Epistemology 201: The Science of Science
    ... there is no formula in the language of ZFC used in the proof. ... > formalizations of the theorems of mathematics. ... on intuition for proofs, because so many things defy intuition. ...
    (sci.math)
  • Re: what makes it true?
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  • Re: ZFC
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