FOM: Einstein, Godel, Turing, modes of research
Harvey Friedman
friedman at math.ohio-state.edu
Sun Jan 16 00:20:36 EST 2000
Reply to Davis 2:55PM 1/15/00:
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.
Davis wrote:
>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.
This is very interesting and very reasonable analysis of their
philosophical attitudes, and it is reasonable to assume that their
philosophical attitudes influenced their great work.
However, in my opinion, I think that the crucial prerequisite for doing
such foundationally perceptive work is to have a philosophical sensibility
at all. To me, it is of crucial importance only that one knows how to think
philosophically - not that one holds any particularly compelling (or even
particularly coherent) philosophical views.
Let me put it a little differently. It is imperative to understand clearly
the difference between specialized technical work and work that directly
bears on wider intellectual issues. Specialized technical work can of
course be valuable - even essential - in that it may lay needed groundwork
for making groundbreaking advances bearing on wider intellectual issues.
But one must not be under any illusion that a life devoted to specialized
technical work to the virtual exclusion of the direct consideration of
crucial issues of general intellectual interest is going to have anything
more than an infinitesmial chance of achieving anything like a minimal
fraction of the ultimate impact and importance of work like Einstein,
Godel, or Turing.
Even a casual glance at my numerous postings on the FOM e-mail list would
indicate that I make no secret of my interest in deliberately maximizing
the probability that I leave behind contributions with the ultimate impact
and importance of work like Einstein, Godel, and Turing -- but obviously,
attempting to maximize that probability in no way, shape, or form implies
success.
A principal tool that I use in this attempt to maximize is the
consideration of and sensitivity to virtually any remotely coherent
philosophical attitude (in philosophy of mathematics and/or relevant to
f.o.m.), regardless of the obvious inconsistencies that there are between
remotely coherent philosophical attitudes.
I have found that virtually any remotely coherent philosophical attitude
(in philosophy of mathematics and/or relevant to f.o.m.) retains a minimal
amount of life - even after being beaten up so badly that nobody actively
defends it anymore - that is sufficient to suggest new advances in f.o.m.
At least, that's my experience in connection with f.o.m., and I strongly
suspect that this is true throughout the entire intellectual landscape.
Another closely related method that I use to deliberately maximize is to
continually ask at every turn of every consideration of every piece of work
in f.o.m. and mathematical logic, of mine or of anyone else,
would anybody outside the field of f.o.m. and mathematical logic care?
why should anybody outside the field of f .o.m. and mathematical logic care?
and secondarily,
would anybody in f.o.m./mathematical logic who does not presently do this
particular work care?
why should anybody in f.o.m./mathematical logic who does not presently do
this particular work care?
This normally leads to major fruitful expansions and/or modifications of
the projects.
Contemporary workers in mathematical logic - to say nothing of working
mathematicians - do not normally operate in this way.
In fact, I find that workers are generally unaware of these tools, and
particularly unaware of their consistent effectiveness. In fact, they are
generally outright suspicious of and/or hostile to the use of such tools.
They generally seem wedded to the idea that the standard technical problems
of the times have some special significance and don't look for deeper
motivations. This includes many people with extraordinary technical gifts.
If they, too, wish to deliberately maximize, then they operate without the
active and effective use of such tools at their own peril.
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