RTragesser at compuserve.com
Tue Aug 18 21:51:20 EDT 1998
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.
This is based on H.'s Being and Time. That work is not at all
representative of Heidegger's thinking at its best (compare with the Basic
Problems of Phenomenology). It was something like a last minute
compilation, H. meeting a publish or perish deadline. It's better future
would be to be cannablized and parts used as footnotes to the range of
infinitely superior and genuinely clear works, mostly lecture courses.
At the same time, Heidegger is very much a philosophers
philosopher, for someonme capable of the greatest depths in reading e.g.
Plato, Aristotle, Kant, . . To not find Heidegger fascinating here is
to be have no sense of those depths.
One central achievement of Heidegger was to discover the sometimes
(to the outsider) extremely subtle adjustments and transformations of basic
ideas and persepctives which achieves a fundamnetal synthesis" of practical
and theoretical understanding, a matter which became dramatically
problematic in Plato and, as a consequence, Aristotle.
John Dewey achieved much the same thing, with greater clarity,
but less depth.
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. (This is
"theoretical" in the old fashioned sense of contemplative, comprehensive,
unified understanding, not hypothetical positing). This tension is most
manifest in the quite obscure interplay between the calculative and
intuitive/insightful aspects of mathematical thought and emphasis. 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). This is understandable since
theoretical understanding tends to not follow the lead of caculative
orders. The most poignant illujstration of this tension I know of occurs
in the introduction to Artin's Geometric Algebra where Artin recommends
braking out of the formal Satz/Beweis pattern ("calculative" ordering) and
substituting for (or supplementing with) some proofs of theorems more
intelligible, "informal", "intuitive" proof (proofs which elaborate
"theoretical understanding" of the mathematics. . .again. .
.warning..."theoretical understanding" meaning more contemplative,
"intuitive", insightful understanding in contrast to the
practical/calculative understanding of what logically depends on what.
Theoretical understanding is very hard won. . .witness Harvey
Friedman's efforts to find a "natural" presentation of ZF.
In any case, the tnesion is that of course there is no theoretical
understanding without calculative understanding. . .and this is true across
all spheres of human knowing. This is what Heidegger and Dewey most
elaborately recognized and realized. Sol Feferman's recent paper on
intuition and monsters is exactly part of the struggle to command and relax
the tension between practical/calculatived understanding in mathematics
and theoretical understanding.
Both Dewey and Heidegger however have remained philsop[hers
philosophers in the sense that they can help us to deeply appreciate the
profounds depths of this tension and the ineliminability of practical or
calculative understanding from genuinely and valuable theoretical
undertstanding, but they don't help us at all with the kinds of case
studies such as Sol has given us.
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