Re: [HM] Constructivism and root 2

Eric Schechter (schectex@math.Vanderbilt.Edu)
Mon, 09 Aug 1999 10:50:59 -0500

I found a copy of Dummett's book. He said the example is "due to
Benenson". Does anyone on this list have any idea who this Benenson
is, or what paper or book Benenson might have written? I couldn't
find anything helpful on MathSciNet. A search for "Benenson"
turned up 8 articles, none of which seemed (to me) at all related.
Is "Benenson" the name of someone who did a lot of work with
constructivism/intuitionism but didn't publish much? Could it be a
typographical error in Dummett's book -- i.e., should I be searching
on MathSciNet for a slightly different spelling?

Thanks. -- Eric Schechter

> This example appears on pg 10 of Michael Dummett's Elements of
> Intuitionism (OUP, 1977). I had thought that Dummett got the proof
> from Beth's Foundations of Mathematics, but I can't find it there
> at the moment.
>
> Ed Mares

>> There is an example involving the square root of 2, that appears
>> in nearly every introductory text or article about constructivism.
>> ... Does anyone know where it first appeared? ... Eric Schechter