Finitist Objects

The aim of the present essay is to enquire the nature of finitist evidence by examining two fundamental problems: (1) what are the objects of finitist evidence, i.e. what are finitist objects? (2) what formal system characterizes finitist evidence? The first problem will be investigated by taking into consideration its historical roots up to Hilbert's work and recent interpretations of Hilbert's finitism by Parsons and Tait. Addresssing the second problem will consist of an examination of IDelta0 and PRA, understood as systems that formalise the idea of finitist evidence, as they have been put forward respectively by Parsons and Tait. While Parsons defends the thesis that finitist objects are quasi-concrete objects and Tait, on the contrary, supports the abstract nature of these objects, in this essay the claim is made that finitist objects are quasi-abstract objects.