Philosophy as the Most Exact Science : Philebus 55c-59c

Abstract

Philebus 55c-59c involves some remarkable ideas or features which may provide a crucial source for evaluating the fundamental standpoint and basic character of the philosophy of Plato. That is, (1) the classification of arts and sciences pursued there is by arranging them in a scale of ascending degrees of exactness, (2) the criterion of which is given in terms of the extent to which they are mathematized. Furthermore (3) it is argued that the concept of exactness of arts and sciences should be clearly distinguished from that of utility or profit according to which Gorgias' art of rhetoric claims the first place among the arts and sciences. And finally (4) even though after all Dialectic, the objects of which are permanent and eternal Forms, is placed at the top of this scale of exact knowledge, the reason or meaning of its excellence over mathematics is not explained at all either with respect to their objects or of their method. In view of these ideas or features of Philebus 55c-59c the following interpretation seems to be natural and tempting: that to Plato mathematics is the ultimate and highest paradigm of all exact knowledge because of the exactness of its unit, of its reductive or deductive method, and of the neutrality of mathematical judgements from evaluation, and that even Dialectic owes its exactness to the mathematical method. Opposing this line of interpretation, I first point out that by the distinction between useful or profitable knowledge and exact or precise knowledge Plato does not intend the Aristotelian absolute division of θωρητικη from ποιητικη and πρακτικη, and therefore that it is impossible in the case of Plato to construe the neutrality from value judgement involved in practical knowledge as a necessary condition of exact knowledge. And then I argue, through a closer examination of the descriptions of Dialectic in Phaedrus and the other parts of Philebus, that in Philebus itself Dialectic is taken by Plato to be ultimate, paradeigmatic knowledge through whose analogical exercise alone the other arts and sciences can be what they should be, but in a way quite different from that in which mathematics is ultimate, paradeigmatic knowledge. And finally I conclude that on the basis of the distinction between two kinds of measurement in Politicus 283b-285c, Plato intends to make clear the difference and the relation between the two ways in which these two highest forms of knowledge are paradeigmatic and therefore exact. What Plato emphasizes and tries to convince us of is that there can exist a philosophical meaning of exactness which is not reducible to mathematical, deductive precision and is more excellent than it.