Axiomatizing mathematical conceptualism in third order arithmetic

2009/05/11 by Nik Weaver, Weaver, Nik
Mathematics · #FOS: Mathematics #History and Overview (math.HO) #math.HO

paper · pdf · doi:10.48550/arxiv.0905.1675

31 pages

arxiv created 2009/05/11 · arxiv updated 2009/12/01

Abstract

We review the philosophical framework of mathematical conceptualism as an alternative to set-theoretic foundations and show how mainstream mathematics can be developed on this basis. The paper includes an explicit axiomatization of the basic principles of conceptualism in a formal system CM set in the language of third order arithmetic.

Related

• Mathematical conceptualism
• An ordinal analysis of CM and its extensions
• Subsystems of Second Order Arithmetic
• Conceptual engineering for mathematical concepts
• The concept of a set