FOM: surreal numbers; Conway's foundational ideas

Martin Davis martin at
Wed May 26 16:46:41 EDT 1999

At 02:47 PM 5/26/99 -0400, simpson at wrote:

>Specifically, what do you think of Conway's idea that formalization is
>irrelevant, ``even for foundational studies'' (page 66)?  Do you take
>this idea seriously?  Some people apparently don't take it seriously,
>e.g. Martin Davis 24 May 1999 20:53:44.  I *do* take it seriously, for
>reasons explained in my posting.

I took it that Conway was saying that the detailed formalization that seemed
so important in the days of Principia Mathematica and several decades after,
is not relevant for foundational studies today - because everyone should
know it can be done, and the details are pretty routine.

I agree up to a point. Working out carefully what can be formalized where is
of the essence of the reverse mathematics program (in which Steve has played
such an important role). Of course, if you look at Steve's book, you won't
see much at the level of predicate calculus (= 1st-order logic). Steve,
quite properly assumes that the details of the formalization have become
routine "and irrelevant even for foundational studies".

                           Martin Davis
                   Visiting Scholar UC Berkeley
                     Professor Emeritus, NYU
                         martin at
                         (Add 1 and get 0)

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