FOM: Cantor and Hilbert knew what they were talking about

[Martin Davis]

At 12:12 PM 12/4/97 -0800, Solomon Feferman wrote:

>As for Hilbert, witness his infamous "proof" of CH by proof theory in "On
>the infinite", his assertion that all mathematical problems are solvable,
>and in particular his call to find a decision procedure for diophantine
>equations.  
>
>Where do we draw the line as to what to accept from each of these truly
>great but flawed thinkers?
>

This is somewhat unfair to Hilbert. What he spoke of was "the conviction ...
that every definite mathematical problem must necessarily be susceptible of
an exact settlement, either in the form of an actual answer to the question
asked, OR BY THE PROOF OF THE IMPOSSIBILITY OF ITS SOLUTION AND THEREWITH
THE NECESSARY FAILURE OF ALL ATTEMPTS". (emphasis mine) With this escape
hatch, his call for a decision problem for diophantine equations was quite
reasonable. Just a few years before Matiyasevich's work, Julia Robinson
(having, as she said, "lost faith") was attempting to find such a decision
procedure.

Martin