Abstract

Recall, if you will, the standard objections to the traditional doctrines. While the most subtle of the competing doctrines is, in my opinion, the Aristotelian and scholastic account of abstraction, the objection to this doctrine is that it requires a realism which is too immediate, so that the forms of one's present state of knowledge are allowed to pass as the forms of nature. And although, as I understand it, Aristotelian mathematics is gained by abstraction from an already fairly abstract matter, one naturally expects in this context one true geometry, rather than alternate geometries. At the same time the strength of this view lies in its confidence that our abstractions must refer to the real world. The defect of the standard Lockian doctrine is that it contains an inner inconsistency, the nature of which we shall notice in due course. And upon application the doctrine explodes at once. On the other hand, the strength of the Lockian doctrine, as well as the doctrine of Berkeley and Hume, lies in its reluctance to allow needless entities entrance into reality. The weakness of the doctrine of Berkeley and Hume is that in moving from the impossible image of Locke's doctrine, the emphasis on particularity requires the agency of custom or habit to join the particulars of sense into classes. But the edges of such classes remain always indefinite. Habit, or custom, would seem not to allow the clean separation of abstractions from each other which the results of intellection give us reason to demand in any adequate doctrine. The weakness of the Kantian doctrine lies in its inability to explicate an antecedent reality; that is, in affirming at last the incognizable thing in itself; while the strength of this doctrine derives from its ability to allow the construction of precise abstractions in a somewhat autonomous manner.