Title: NeoRussellian Logicism

Abstract:

The Russellian route for establishing the logicality of mathematics consisted in showing that mathematical entities are nothing but properties of a topic-neutral kind, and that mathematics is a part of higher-order logic. Owing in part to the absence of a result capable of sustaining a Russellian reduction of arithmetic to higher-order logic, the Russellian route for  has been neglected.

In this talk I will sketch how the project of deriving arithmetic from higher-order logic can be carried out once modal resources are available. This result constitutes a first step in the project of defending a neoRussellian logicism according to which all mathematical entities consist of topic-neutral properties and mathematics is a part of higher-order modal logic. Finally, I will consider how to carry out a reduction of set-theory to higher-order modal logic, with sets themselves being identified with properties, and make a case that such a reduction would be especially attractive.