FOM: Heidegger; practical vs theoretical

Stephen G Simpson simpson at
Wed Aug 19 14:40:24 EDT 1998

Robert Tragesser writes:

 > Steve recently dismissed Heidegger seemingly on the grounds that
 > some variation of the thought that nothing nothings (and, will, if
 > you ain't careful, nothing you) embodies his philosophy.

Well, I would put it this way.  I've never read any works of
Heidegger, but I've heard him quoted as saying "Das Nichts nichtet."
On the basis of that utterly repulsive sample, plus Heidegger's
reputation for deliberate obscurantism, I decided that whatever
nuggets of wisdom might be buried in Heidegger's writings, it wouldn't
be worth my while to dig them out.  I don't know whether "Das Nichts
nichtet" embodies Heidegger's philosophy, and I don't really care.

 > One central achievement of Heidegger was to discover the sometimes
 > (to the outsider) extremely subtle adjustments and transformations
 > of bas= ic ideas and persepctives which achieves a fundamnetal
 > synthesis" of practic= al and theoretical understanding, ...

This doesn't seem like a very novel point.  Are you saying that
Heidegger was the first to discover this? 

 > What does this have to do with fom?  Much depends on -- as the like
 > of Herman Weyl observed -- one appreciating the tension in
 > mathematics between two those two modes of
 > understanding/comprehension: the practical and the theoretical.

I think that many mathematicians and f.o.m. researchers have a very
good appreciation of the tension between the the practical and the
theoretical.  And those who don't have it would not be able to get it
from Heidegger.

 > The reduction of proofs to formal-logical "calculations" rather
 > than their expansion into rounded, resonant, theoretical
 > understanding.  My impression is that FOM research lives mostly
 > within the realm of the calculative (broadly understood).

I don't agree.  A great deal of f.o.m. research involves formal
("calculative"?) explication and analysis of informal ("resonant"?)
notions.  In other words, f.o.m. lives at the borderline between the
two.  This mode of understanding is an essential ingredient of some of
the best f.o.m. research.  Examples: Frege's explication of
"inference", the Church/Turing explication of "calculability", the
Zermelo/Fraenkel explication of "set", ....

As another example, consider the recent FOM discussion of whether
Con(ZFC) is a finite combinatorial statement.  The key to this issue
is an understanding and analysis of the informal or theoretical notion
"finite combinatorial statement".  What do you think of the discussion
so far?  Do you think Heidegger has anything to contribute?


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