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Matheology § 188
Posted:
Jan 10, 2013 6:16 AM


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 GrattanGuinness: "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



