[FOM] Benenson

[Jay Sulzberger]

On Mon, 5 Nov 2007, Robert Black wrote:

> Introductory treatments of the notion of nonconstructive proof almost
> always give as an example the proof that there is an irrational x
> such that x raised to the power root 2 is rational (because root 2 to
> the root 2 is either rational or not and ...). This proof is
> attributed to 'Benenson'. Does anyone happen to know who Benenson is
> or was? Googling the name gives the proof and various Benensons (e.g.
> the founder of Amnesty International) but doesn't seem to associate
> the proof with any particular Benenson.
>
> Robert

Benenson is Frederick C. Benenson, author of
"Probability, Objectivity and Evidence".  The attribution is
incorrect.  Here is an email to me from Fred Benenson, who is
Frederick C. Benenson's son.  I post this to the FOM mailing list
with the permission of Fred Benenson.

<blockquote
   what="email from Fred Benenson"
   date-of-email="Tue, 6 Nov 2007 11:57:15 -0500">

  Jay,
    That proof is mis-attributed to my father who worked on probability for
  his PhD at Oxford. Here's his story:

  "I would like it if you could put out a refutation of this...it
  is corrected in the 2'nd edition...it's a long story but the
  proof was once mistakenly attributed to me (a long time ago) in a
  book by one Michael Dummett. An interesting important,
  philosopher I knew a bit at Oxford who wrote on intuitionist
  mathemtics...Saul Kripke found the reference to me in the first
  edition of he book and asked me about it...I then told Dummett
  he'd gotten me confused with someone else he knew at the
  University of Birmingham who worked in this area ..he didn't
  think so and seemed annoyed when the proof he attributed to me
  actually turned out to be common knowledge in some circles but I
  insisted that I had never heard of it...I am pretty sure it was
  all sorted out in the second edition....but it was not something
  I ever would have worked on or cared about but there I am
  apparently for posterity known as the alleged author of an
  actually widely known proof with no known author."


  Hope that clarifies it!


  F

</blockquote>

I have allowed ispell to correct two obvious typographic errors,
but otherwise the quote is exact.  Fred further says in a later
email to me:

  Let me know if anyone wants to get in touch...

So, if you wish, write to me and I will send your note to Fred.

oo--JS.