A General Framework for a Second Philosophy Analysis of Set-Theoretic Methodology

Penelope Maddy’s Second Philosophy is one of the most well-known approaches in recent philosophy of mathematics. She applies her second-philosophical method to analyze mathematical methodology by reconstructing historical cases in a setting of means-ends relationsMeans-ends relation. However, outside of Maddy’s own work, this kind of methodological analysis has not yet been extensively used and analyzed. In the present work, we will make a first step in this direction. We develop a general framework that allows us to clarify the procedure and aims of the Second Philosopher’sSecond philosopher investigation into set-theoretic methodologySet-theoretic methodology; provides a platform to analyze the Second Philosopher’sSecond philosopher methods themselves; and can be applied to further questions in the philosophy of set theory.