*Modal structuralism simplified*

by Sharon Berry - https://seberry.org/ 

Abstract. *Since Benacerraf’s “What Numbers Could Not Be,” there has been a 
growing interest in mathematical structuralism. An influential form of 
mathematical structuralism, modal structuralism, uses logical possibility 
and second order logic to provide paraphrases of mathematical statements 
which don’t quantify over mathematical objects. These modal structuralist 
paraphrases are a useful tool for nominalists and realists alike. But their 
use of second order logic and quantification into the logical possibility 
operator raises concerns. In this paper, I show that the work of both these 
elements can be done by a single natural generalization of the logical 
possibility operator.*

*- pt*

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