[FOM] Frank Quinn article in January Notices
Monroe Eskew
meskew at math.uci.edu
Wed Dec 28 09:42:57 EST 2011
On Dec 27, 2011, at 9:44 AM, "Timothy Y. Chow" <tchow at alum.mit.edu> wrote:
>
> By "excluded-middle reasoning," I think Quinn does *not* mean
>
> the principle that if we know that "not P" is false, then we know
> that "P" is true
>
> but rather
>
> the principle that we cannot know that "P" is true unless we can
> prove that "not P" cannot be true.
>
> With this definition, I think we can recognize the principle as being
> something that is standard among mathematicians but foreign to most
> others.
>
On page 34, at the beginning of the section, "Hilbert's Missed Opportunities," Quinn explicitly defines excluded middle reasoning as proof by contradiction. I think Chow's interpretation cannot be correct.
Best,
Monroe
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