On a form of intrinsic optimism in Set Theory

2025/11/26 by Manuel Gil Pérez, Pérez, M. Muñoz
Mathematics · Neuroscience · Psychology · #FOS: Mathematics #Free Will and Agency #History and Overview (math.HO) #Logic (math.LO) #Mathematical and Theoretical Analysis #Philosophy and Theoretical Science

paper · pdf · doi:10.48550/arxiv.2512.02045

openalex publication_date 2025/11/26 · openalex created_date 2025/12/04 · openalex updated_date 2026/07/28

Abstract

In this paper we will try to provide a solid form of intrinsic set theoretical optimism. In other words, we will try to vindicate Gödel's views on phenomenology as a method for arriving at new axioms of ZFC in order to decide independent statements such as CH.

Citations

• Intrinsic Justification for Large Cardinals and Structural Reflection
• Wittgenstein on decisions and the mathematical practice
• You Can Enter Cantor's Paradise

Related

• Gödel's Program in Set Theory
• The concept of a set
• Independence Phenomena in Mathematics: a Set Theoretic Perspective on Current Obstacles and Scenarios for Solutions
• Fragments of Frege's Grundgesetze and Gödel's Constructible Universe
• The Essence of Intuitive Set Theory