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.”