Mathematics and essence

Abstract

Arithmetic seems to provide philosophers and mathematicians with the typical domain where it makes sense to talk about “essences”, “essential properties” and “necessary propositions”. In this paper I try to examine the subject, following the lines of investigation suggested by Wittgenstein from his middle period on. Beginning with a specific question – Is it part of the essence of the number 3 to be followed by the number 4? –, I intend to examine different aspects of the problem, with three main goals at sight: 1) Understanding more thoroughly the role and limits of formal analysis in philosophical questions, particularly those related to the philosophy of mathematics; 2) Correctly locating the note of “essentiality” and/ or “necessity” commonly associated with arithmetic; and 3) Suggesting a general way of understanding the idea of essence and necessity, in its strict connection with human language and experience.