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Topic: intuitionism
Replies: 16   Last Post: Nov 1, 2009 3:33 AM

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nukeymusic

Posts: 58
Registered: 6/18/08
Re: intuitionism
Posted: Oct 26, 2009 4:41 AM
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On Oct 25, 7:02 am, Keith Ramsay <kram...@aol.com> wrote:
> On Oct 24, 11:01 am, nukeymusic <nukeymu...@gmail.com> wrote:
> |Is the following  a correct interpretation of what Brouwer said
> |concerning the principle of the excluded third?:
> |there exist p : (p or not(p)) is not equal to 1
>
> Brouwer was deeply suspicious of the possibility of
> formalism becoming an end in itself. So we should be
> careful to know what you mean to say by this.
>
> There is a sense in which for a statement to be "equal"
> to 1 or T (verum) just means that it is true. Being not
> equal could well mean being false or absurd. But Brouwer
> did not assert the absurdity of "p or not p" for any p.
>
> In formal terms, ~(p or ~p) is unacceptable in
> intuitionistic logic; one can prove in fact for each p
> that ~~(p or ~p).
> There are formalizations ofintuitionismin which
> "~(for all p)(p or ~p)" is a theorem in fact, even
> though "(for all p)~~(p or ~p)" is also a theorem.
>
> I think it's a much better description of Brouwer's
> point of view to say that it's not justified to assert
> "p or not p" for every p. If you can find his collected
> works try an early paper titled, ""The untrustworthiness
> of the principles of logic" and get it just the way
> that he put it himself.
>
> Keith Ramsay


Maybe there is someone here on the list who owns "The
untrustworthiness
of the principles of logic" and could tell us how Brouwer formulated
it himself, I guess he did it using words only (not symbols)?

regards,
nukey



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