FOM: Einstein, Godel, Turing, Hardy

[Martin Davis]

At 04:36 PM 1/15/00 -0500, Harvey Friedman wrote:


>His [Einstein's] is an example of the special effectiveness of the 
>foundational approach
>to science. The same is true of other celebrated figures, especially Godel
>and Turing.

It has always been interesting to me to contrast the very different 
philosophical attitudes of Einstein and Gödel. Einstein was heavily 
influenced by the empiricist "positivistic" approach of Ernst Mach that 
provided the background from which he subjected notions like simultaneity 
(that has previously been simply taken for granted) to a penetrating 
foundational analysis. Gödel, on the other hand, was reacting against the 
positivistic mood of the Vienna Circle in being prepared to use 
non-constructive methods in his proof of completeness of first-order logic, 
and especially in his willingness to consider a notion of arithmetic truth 
separate from provability. There is less to go on in understanding Turing's 
philosophical standpoint, but it does seem that his foundational analysis 
of what it means to compute something was aided by a mechanistic view of 
the human mentality.

Martin Davis





                           Martin Davis
                    Visiting Scholar UC Berkeley
                      Professor Emeritus, NYU
                          martin at eipye.com
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                        http://www.eipye.com