Tuesday, 6 December 2005
The Great Struggle Between Cantorians and Aristotelians: Much
ado about nothing
Milos Arsenijevic, U. Belgrade, Philosophy
12:05 pm, 817R Cathedral of Learning
Abstract: It will be argued that there are interesting
cases in which two axiomatic systems, or two formal theories, syntactically
and semantically non-trivially different in the standard sense are
rather to be classified as only trivially different. For a strict
comparison of the systems of such a kind the generalized concepts
of syntactically and semantically trivial differences will be formally
defined. It will be shown then that the Cantorian point-based and
an Aristotelian interval-based system of the continuum are just
trivially different in the defined sense, in spite of the fact that,
contrary to Quine’s famous requirement, the variables of the
Cantorian system and the variables of the Aristotelian one can never
range over the elements of one and the same basic set. So, “the
great struggle” (to use Cantor’s phrase) between the
two parties turns out to be “much ado about nothing.”
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