Numbers as Identities in Presence and Absence

Abstract

In the preceding chapter we were concerned with the original presence of number. Following Husserl’s lead, we attempted to describe the ’authentic counting’ in which numbers themselves are given in an originally intuitive manner. As we saw, numbers are not given in sense perception alone, but rather in a complex categorial activity that is founded on sense perception. Numbers are presented authentically when we take stock of the items of a sensuously presented group while comparing the resulting multitude with other multitudes. Now such descriptions of the original presence of number are an essential component of any study of the constitution of number. By themselves, however, they are not sufficient. For numbers have a way of being ‘there’ for us even when we do not have them as authentic presences. We can intend numbers in their absence as well as in their presence. In the current chapter, therefore, we shall study the absence of number. We shall see that the absence of number can take several distinguishable forms. We shall also see that our ability to intend numbers in their absence, however easily it may be overlooked, is of the greatest significance from a phenomenological point of view. Indeed, it seems that we cannot fully explain what we mean by ‘number,’ or clarify what numbers truly are, unless we take account of the fact that numbers are available to us as identities in presence and absence.