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Topic: Matheology § 211
Replies: 1   Last Post: Feb 6, 2013 4:11 AM

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Posts: 18,076
Registered: 1/29/05
Matheology § 211
Posted: Feb 6, 2013 3:50 AM
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Matheology § 211

The belief in the universal validity of the principle of the excluded
third in mathematics is considered by the intuitionists as a
phenomenon of the history of civilization of the same kind as the
former belief in the rationality of pi, or in the rotation of the
firmament about the earth {{or the assumption that every particle has
definite position and velocity at every time.}} The intuitionist tries
to explain the long duration of the reign of this dogma by two facts:
firstly that within an arbitrarily given domain of mathematical
entities the non-contradictority of the principle for a single
assertion is easily recognized; secondly that in studying an extensive
group of simple every-day phenomena of the exterior world, careful
application of the whole of classical logic was never found to lead to
error. [This means de facto that common objects and mechanisms
subjected to familiar manipulations behave as if the system of states
they can assume formed part of a finite discrete set, whose elements
are connected by a finite number of relations.] {{Unfortunately this
principle, without any justification, has been applied to infinite
[L.E.J. Brouwer: "Lectures on Intuitionism - Historical Introduction
and Fundamental Notions" (1951), Cambridge University Press (1981)]

Regards, WM

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