The Sense of Analysis

Abstract

In the previous chapter we saw that Husserl interprets arithmetic, the original science of number, as a branch of formal, ontology. It is an ‘ontology’ in the sense that it aims to establish essential truths about a region of objects, and it is ‘formal’ in the sense that the objects in question are purely formal objects. Ultimately, as we have seen, arithmetic rests on the evidence obtained through eidetic variation over the concrete numbers constituted in acts of collecting and counting. Now Husserl’s clarification of the sense of arithmetic undoubtedly possesses a certain interest in its own right. Systematically, however — that is, in the context of Husserl’s ‘philosophy of arithmetic’ as a whole — this issue is a subordinate one. We saw in Chapter I that Husserl’s ultimate concern was not with elementary arithmetic as such, but rather with the higher mathematical discipline known as analysis.¹ He hoped to contribute to the ‘true philosophy of the calculus’ by clarifying and justifying modern analysis, the mathematical discipline in which he himself had received his doctorate. We must therefore proceed to examine his work in this area. Just how did Husserl attempt to clarify and justify analysis? We shall take up the issue of justification in the final section of this chapter. In the first three sections, we shall be concerned solely with Husserl’s attempt to clarify the sense of analysis.