Quine on mathematization
Les Schaffer
schaffer at optonline.net
Mon Jul 7 14:25:37 MDT 2003
Jurriaan quotes Quine:
> Mathematize as he will, and seek algorithms as he will, the
> empirical scientist is not going to aspire to an algorithm or proof
> procedure for the whole of his science; he would not want it if he
> could have it. He will want rather to keep a large class of his
> sentences open to the contingencies of future observation. It is
> only thus that his theory can claim empirical import
here is Kline:
"Had the Greeks been less concerned to be logical and precise they
might have casually accepted and opearted on irrational numbers as
had the Babylonians, and as civilizations succeeding the Greeks
did. But the intuitive basis of the idealization was not clear, and
the logical construction was not quite within their power. The Greek
virtue of insisting on exact ceoncepts and proofs was a defect so
far as creative mathematics was concerned."
Some comments on mathematical proofs:
a paper was just recently published in a math journal (packing of
spheres) where the proof was so long that it took a committee of
mathematicians several years to review it, and they STILL were not
able to check the whole thing step by logical step.
Wiles proof of Fermat is another example of the effort it takes to
comprehensively establish a proof based on classical logical grounds.
Nevertheless, and in spite of Godel, mathematicians still use the
statement/proof format. Perhaps to break this dependency will require
some mathematical advance with practical value outside of this
classical realm. yet the notion that scientific and engineering work
ought to advance logically is perfectly legitimate in practical terms,
lest we allow the ruling class to construct buildings that drop
pancake fashion on our heads daily.
So, following Godel, our mathematical axiomatic systems are somehow
incomplete. to quote some character from some generic movie [Bill
Paxton in Aliens II]: whoopy-f&@*!cking-doo.
les schaffer
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