ABSTRACT
I argue that the numbers “given to us” by Scottish neo-Fregean logicism are not Fregean objects. To show this, I consider several places in Hale and Wright’s canon where they have defended logicism at the cost of a Fregean ontology, such as their solution to the Caesar problem and their requirement that the objects given by abstraction may not admit of an independent means of specification. I conclude that the implicit ontology of Hale and Wright’s account is a thin conception of objects, distinct from Frege’s own. However, I present the advantages of embracing this diagnosis and re-positioning Hale and Wright’s abstractionist project in order to deliver a neo-Dedekindian logicism.
