FOM: Einstein, Godel, Turing, Hardy
Martin Davis
martin at eipye.com
Sat Jan 15 17:55:14 EST 2000
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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