Computability, Finiteness and the Standard Model of Arithmetic

Abstract

This paper investigates the question of how we manage to single out the natural number structure as the intended interpretation of our arithmetical language. Horsten (2012) submits that the reference of our arithmetical vocabulary is determined by our knowledge of some principles of arithmetic on the one hand, and by our computational abilities on the other. We argue against such a view and we submit an alternative answer. We single out the structure of natural numbers through our intuition of the absolute notion of finiteness.