Algebra-valued models and Logical Pluralism

Santiago Jockwich Martinez

In this talk, we explore the question whether some notion of logical pluralism can be motivated on behalf of the existence of non-classical algebra-valued models of ZF(C). We argue that we can derive two notions of pluralism: a goal-oriented pluralism and a proper pluralism. The salient idea is that there exist several non-classical set theories that employ different underlying logics and which serve equally well for one particular goal: providing a foundation for mathematics.We examine the resulting notion of pluralism and discuss several objections against our proposal such as meaning-variance and the classical meta-theory objection.

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