18 A. E. TAYLOR : of distinct qualitative existences. One such formula will define a circle and another an ellipse, but you cannot add the equation of the circle to that of the ellipse as you, can add numbers in arithmetic, in order to obtain a third equation as their sum. The second point is that these numbers, unlike those of the Pythagoreans, are not composed of sensible units. This means that Plato, probably for the first time in the history of thought, distinguished between perceptual and conceptual extension. And it is important to observe that the character of numerical multiplicity belongs to the ex- tended in its conceptual, the character of qualitative unique- ness in its perceptual aspect. As perceived by sight the circle, for instance, is a continuous line with a peculiar qualitative structure of its own, unlike that of any other curve than a circular one, and to a less degree unlike that of another circle with a greater or less degree of curvature. It does not, as a perceived figure consist of or contain points, as the Pythagoreans had thought. It is only when by an act of thought we analyse its construction, and find that it may be mentally represented as the line upon which any position satisfying a certain quantitative relation will be situated, that its aspect of numerical multiplicity becomes apparent. This consideration may perhaps throw light upon the language used in the Timceus (52 b), according to which the space which is the universal unchanging receptacle of generation cannot be perceived by sense, but must be appre- hended by a sort of . " bastard reasoning ". For the space of which Plato is there speaking is not extension as perceived at all; perceptual extension with its content of infinitely various qualities and shapes corresponds to the visible world of changing existence itself, not to its mysterious substrate. By the substrate is meant that indeterminate something which is variously specially determined in its various parts by the different numerical relations or equations upon which the multitude of qualitatively different curves and figures depend, i.e., space, conceived simply as an indefinite plurality of homogeneous quality-less positions. If I am able, in a subsequent article, to examine some of the problems raised by Mr. Benn's treatment of the Timceus, I shall hope to show that failure to realise that Plato's " third form " in that dialogue is conceptual, as distinguished from perceptual, space, has been responsible for some at least of the difficulties which interpreters have found in the doctrine. For Plato then, if we are right in our main contention, the whole of the world of quality belongs as such to the sphere of the sensible; it is only of quantitative relations
