[FOM] Frank Quinn article in January Notices
Nick Nielsen
john.n.nielsen at gmail.com
Tue Dec 27 16:38:13 EST 2011
On Tue, Dec 27, 2011 at 7:44 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.
This is a fascinating and subtle reformulation, but by introducing
provability into EM it departs from the historical simplicity of "P or
not-P," which has always been a blunt weapon in the arsenal of
realism. It is the very bluntness of EM, allowing us to prove what we
cannot construct, that has made it the target of constructivists.
Also, is "cannot be true" to be construed as the impossibility of
"not-P" so that it was intended to introduce a modal conception of
"not-P," or is this simply a alternative formulation of "unless we can
prove 'not-P' is false"? If the former, then we have introduced
modality, provability, and knowability into EM, which I think makes it
depart substantially from an intuitive understanding of the principle.
If the latter, then the formulation reduces to the earlier formulation
that you have said is *not* what Quinn meant.
Best wishes,
Nick Nielsen
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