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Das Kalenderblatt 091101

A second negative effect of transfinite theory is that by positioning
transfinite theory as the basis arithmetic and logic, transfinite
theorist have accomplished the unintended goal of basing mathematics
on mystical concepts: namely, the completed infinity. Such a result is
highly attractive to the mystical mind. Again, classical logicians
would abhor the idea of basing reasoning on mystical concepts, but the
mystical mind adores it... gaining further acceptance for transfinite
theory.
This leads to one of the weirdest twists in modern mathematics: The
intuitionalist school, led by LEJ Brouwer actually demanded a higher
degree of logical rigor than the Logicists school that was happy with
a mathematics founded on the slippery slope of transfinite theory,
completed infinities and paradoxes. Of course, we have seen the same
twists in politics. The "people's" party is generally a pseudonym for
a dictatorship. Tax reform almost always leads to higher taxes.
Intuitionism in mathematics does not mean that people rely on their
"intuition." Intuitionist school demands that all axioms be based on
comprehendible ideas. The logistical schools holds that the axioms
don't really matter, so long as symbolic logic used is consistent. The
ideas expressed by the symbols can be insane.
[...]
In my opinion, the fact that schools no longer teach logic is the
worst effect of transfinite theory.
[Kevin Delany: "Curing the Disease"]
http://descmath.com/diag/cure.html

Gruß, WM

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