David McCarty

The Logic Program
Indiana University

"Potentially Infinite Sets and Structures"

Abstract:

An assessment of Zeno's paradox of the racecourse and the Bolzano/Dedekind/Chomsky argument for the infinity of thought exposes a questionable inference common to both. Critical examination of that inference reveals the need for a generous collection of potentially infinite sets---sets that are neither finite nor infinite. We describe such a collection and the arithmetic that obtains in the correlative structure. We conclude with a consistency proof for the assumption that such a structure exists.

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