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Matheology § 188
Posted:
Jan 10, 2013 6:16 AM
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Matheology § 188
In 1960 the physicist Eugene Wigner published an influential article
on "The unreasonable effectiveness of mathematics in the natural
sciences". [E. P. Wigner: "The unreasonable effectiveness of
mathematics in the natural sciences", Communications on pure and
applied mathematics, 13 (1960)] I counter the claim stated in its
title with an interpretation of science in which many of the uses of
mathematics are shown to be quite reasonable, even rational, although
maybe somewhat limited in content and indeed not free from
ineffectiveness. The alternative view emphasizes two factors that
Wigner largely ignores: the effectiveness of the natural sciences in
mathematics, in that much mathematics has been motivated by
interpretations in the sciences, and still is; and the central place
of theories in both mathematics and the sciences, especially theory-
building, in which analogies drawn from other theories play an
important role.
[Ivor Grattan-Guinness: "Solving Wigner's Mystery: The Reasonable
(Though Perhaps Limited) Effectiveness of Mathematics in the Natural
Sciences" Springer Science+Business Media, Inc., Volume 30, Number 3
(2008)]
All correct mathematics has to orient itself by means of reality,
hence natural sciences. Mathematics is applied physics. Cantor
intended to follow that scheme with his transfinite set theory, which
he, by his own protestation, had devised in order to apply it in
natural sciences. Alas his idea of reality was so bad (in contrast to
most of his contemporaries he rejected atomism and Darwinism), that it
could yield only wrong mathematics.
Regards, WM
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