Authentic and Inauthentic Number Representations in Husserlʼs Philosophy of Arithmetic

This paper aims to elucidate the grounds for the distinction between authentic and inauthentic representations in Husserlʼs Philosophy of Arithmetic by considering their central characteristics. The distinction between these two sorts of representation is introduced at the very beginning of the work. Yet the grounds for it are hardly given there. Thus, it may initially seem that the distinction is groundless. However, as we move on to the second part of the book, Husserl accounts for the distinction by mentioning our cognitive incapacity. This incapacity is pertinent to a limit of our number representation: in short, we cannot represent all numbers authentically. Such a limit of authentic number representation is made apparent by reference to the representation itself. Thus, it can be said that Husserlʼs detailed discussion of authentic number representation in the first part of the work is vital to the very ground for the distinction. It goes likewise for his discussion of the inauthentic sort in the second part. To show this point and to consequently give the grounds for the distinction, I make an overview of the central characteristics of both sorts of number representation. At the end of the paper, I conclude with a brief remark on two possible further interpretations of the work: what Husserl means by the logical equivalence between authentic and inauthentic number representations, and what kind of bearing Husserlʼs characterization of inauthentic number representation has on the concept of infinity.