Year: 2009
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Weaver, Nik
Language: English
Subfield: Theoretical Computer Science
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394640466