[FOM] Frank Quinn article in January Notices
Monroe Eskew
meskew at math.uci.edu
Tue Dec 27 16:55:24 EST 2011
Dear David,
Of course probability and statistics can be developed from a classical foundation. I don't think your example is one of the excluded middle failing, just one where confusion can result from muddying the distinction between statements P and statements about P such as "We reject P," "We believe P," "P is provable," etc. For example, I do not believe that there is a white dog in some house on my street right now. That does not mean that I believe that there is no white dog in some house on my street. But I certainly believe that either there is or there is not a white dog in some house on my street.
Best,
Monroe
On Dec 26, 2011, at 6:30 PM, David Roberts <david.roberts at adelaide.edu.au> wrote:
> Dear Monroe,
>
> I thought I should point out that whenever statistical reasoning is involved in exact sciences (and some inexact ones), one inherently cannot assume excluded middle. Hypothesis testing - in its simplest form asking whether a measurement yields a null result - is full of phrases like 'fail to reject the null hypothesis at x level of uncertainty', which is definitely *not* the same as accepting the null hypothesis. This is one area where beginning students of statistics trip up all the time, mostly because the are expecting, implicitly, EM to hold.
>
> Witness two recent examples, namely faster-than-light neutrinos and the not-quite-discovery of the Higgs particle. Everything is stated in statistical terms, levels of significance and so on. And when they analyze things like the so-called look elsewhere effect in the latter, one can see vestiges of intuitionistic reasoning.
>
> David Roberts
>
>
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