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Re: intuitionism
Posted:
Oct 26, 2009 4:41 AM


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



