Das Kalenderblatt 090928
- From: WM <mueckenh@xxxxxxxxxxxxxxxxx>
- Date: Sat, 26 Sep 2009 23:54:52 -0700 (PDT)
No matter how much the content of mathematics exploits paradox,
mathematicians express dedication to policing their doctrine against
inconsistency. Mathematicians do not welcome those who attempt
inconsistency proofs of favored theories.
What was profound was that results were contextualized so that they
ceased to be inconsistency threats. The Löwenheim-Skolem paradox;
Skolem's w-inconsistent model of Peano arithmetic (also the
conjunction of Gödel's completeness and incompleteness theorems); w-
inconsistency of Quine's "New Foundations" set theory; independence of
the Axiom of Choice; etc. But mathematics had always proceeded like
this: e.g. Dedekind had taken Galileo's paradox as the definition of
infinity.
The alternative would be that the content of academic mathematics
eventuates from sophistry and majority preference. As to the latter,
Paul Lorenzen says: You will become famous if you please famous people
-- and all famous mathematicians like axiomatic set theory.
I will refer to such considerations as professional discipline (or
even coercion {{Zwang, Nötigung}}). If this is the situation, then the
profession will protect itself from heresies and criticism not by
superior reasoning {{ganz sicher nicht - siehe Das Kalenderblatt
090925 als eines für viele Beispiele}}, but by additional professional
discipline in conjunction with additional casuistry.
Henry Flynt: "IS MATHEMATICS A SCIENTIFIC DISCIPLINE?" (1994)
http://www.henryflynt.org/studies_sci/mathsci.html
Gruß, WM
.
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