Format: In-person
Chair: Imogen Rivers
Abstract: Modal potentialism is a relatively recent development in the literature on the philosophy of mathematics and philosophy of logic. Potentialism is the view that mathematical objects are generated successively, and that certain generative processes are incompletable. Modal potentialism spells out potentialism using quantified modal logic, taking a modal object language as primitive for mathematics. Many modal potentialists, such as Kit Fine, Øystein Linnebo, and James Studd claim to be platonists about mathematics. Thus, to consistently cash out how to understand the primitive modality, such modal potentialists deny that the primitive modality is metaphysical or temporal.
In this talk I will investigate to what extent modal potentialists can be platonist. I will conclude with a dichotomy for the would-be platonist modal potentialist:
[I]: They are platonist in the unrestricted sense that mathematical objects exist necessarily in the broadest sense. Furthermore, the intended interpretation of their primitive modality predicates over structurally poor representations. Hence, it is not an operation. This is radically different from any proposed account of modal potentialism thus far; and calls for the elucidation of a coherent account of this intended interpretation, and why it gives rise to modal potentialism.
[II] The intended interpretation of their primitive modality is an operation on propositions. Furthermore, they are platonist in the restricted sense that mathematical objects do not exist necessarily in the broadest sense. This calls for the elucidation of what kind of platonist they precisely are. In particular, their account of platonism must deny Counterfactual Independence, which is a core thesis in most accounts of platonism. It states that mathematical objects are counterfactually independent of intelligent agents, or their language, thought, or practices.
