Event Detail

This paper considers the question: what does it mean for two mathematical structures (or collections thereof) to be inter-definable? This question is particularly pertinent in philosophy of physics where theories are not generally amenable to first order axiomatization. The paper begins by explaining the difficulty of the problem and giving an overview of some naive responses that don’t work well. The middle section then gives an overview of the proposed framework. The underlying idea is to use set theory with atoms (or urelemente) to provide a structural approach to set theory in a ZFC-like setting. This results in a massive generalization of the theory of relative interpretation. The final section considers applications of the approach and closes with some problems for future work.