Il concetto di numero nella fondazione dell'aritmetica in Kant e Dedekind

Abstract

In this article we compare Kant and Dedekind position about foundation of arithmetic and concept of number. This paper is not focused on an exhausting presentation of these concepts and not even on a historical review. We want to show that Dedekind’s approach towards the logical and mathematical foundation of arithmetics seems to be delegitimating if compared with the one of philosphical foundation as it’s been conceived by Kant. Nonetheless, the foundation of arithmetics expressed by Kant, is clearly connected to the entire system of critics and assume a specific meaning that is wider than Dedekind ones. A logical clarification of arithmetics foundations does not deal with the question like the role of mathematics in the knowledge system and his relationship with empirical science. Moreover, it seems rightful to treat the problem within the frame of a philosophical research. In conclusion, we conclude with the proposal of a new evaluation of trascendental logic, in a weaker sense than the one originally intended by Kant, meant to be a philosophical discipline that tries to research refine such questions and possibly find responses for them. We present some considerations about the ontological status of numbers within the theories of Kant and Dedekind.