The concept of a set

Details The concept of a set The concept of a set

2009-05-11

arxiv.org/abs/0905.1677v1

Mathematics

History and Overview

11 pages

Scientific paper

Metaphysical interpretations of set theory are either inconsistent or incoherent. The uses of sets in mathematics actually involve three distinct kinds of collections (surveyable, definite, and heuristic), which are governed by three different kinds of logic (classical, intuitionistic, and minimal). A foundational system incorporating this analysis and based on the principles of mathematical conceptualism accords better with actual mathematical practice than Zermelo-Fraenkel set theory does.

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