Review of Metaphysics 37 (1):136-138 (1983)

Abstract
Husserl describes arithmetic as a branch of formal ontology. It is an ontology because its goal is to lay out the essential truths about a region of objects, and it is formal because the determinate region of number deals with a characteristic of every possible object. The mathematical experience proper requires something more than the constitution of "concrete numbers" in acts of collecting and counting, for its objects are "ideal numbers" that emerge from eidetic variation over corresponding concrete numbers. With remarkable clarity, Miller coordinates Husserl's various writings on the nature of number by stressing the key theme of identity in presence and absence. Concrete numbers are "determinate multitudes" which are not presented in sensuous intuition, but rather in sensuously founded categorial operations, i.e., explication, in which the parts of an indiscriminately given whole are explicitly articulated as parts, and comparison, in which the multitude generated through such explication is explicitly related to other multitudes. These operations account for the original presence of number. But we can intend numbers in their absence as well as in their presence. For example we may intend a determinate multitude in the absence of the sensuous group in question, or we may experience a different mode of absence when an intended number is frustrated by subsequent intuitive registration, or we may deploy the distinctive absence generated by signs in the process of calculating without authentic articulation of the relevant determinate multitudes. The presence of ideal numbers requires the free play of fantasy, for we must imagine collections of items and also imagine ourselves counting the items in order to disengage their purely formal character. We must discern an identical presence of "four" in a cluster of persons, a collection of apples, and even in some arbitrarily contrived group such as a "feeling, an angel, the moon, Italy." The absence of generic community in the latter example helps us to appreciate what Husserl means by the purely formal nature of arithmetic. Formal ontology is not restricted in scope to some particular region, but is concerned with properties that belong to every possible object precisely as such. Thus, whereas Euclidean geometry is a regional ontology, set-theory and number-theory must be considered as branches of formal ontology, for the basic concepts of these disciplines are strictly formal. Anything that can be thought of can be counted.
Keywords Catholic Tradition  Contemporary Philosophy  General Interest
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ISBN(s) 0034-6632
DOI revmetaph1983371149
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