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Matheology § 211
Posted:
Feb 6, 2013 3:50 AM


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 noncontradictority of the principle for a single assertion is easily recognized; secondly that in studying an extensive group of simple everyday 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 sets.}} [L.E.J. Brouwer: "Lectures on Intuitionism  Historical Introduction and Fundamental Notions" (1951), Cambridge University Press (1981)] http://www.marxists.org/reference/subject/philosophy/works/ne/brouwer.htm
Regards, WM



