ON THE FIRST PART OF PLATO'S PARMENIDES. 5 goes much deeper, and it is this. What I study when, e.g., I investigate the properties of the circle from its Cartesian equation is a universal type of relation between positions; what I should see, even assuming an impossible accuracy of construction, would always be only a special case of this rela- tion. Thus any circle, however accurately drawn, has its own special degree of curvature, according to the length of its radius, or to take a still more striking example, any actual case of a " central conic " must be either ellipse or hyperbola, but the general central conic, of which I may find the equa- tion and investigate the properties, is at once, and as you please to call it, both and neither. And so generally, the object of geometrical study is at once a thing which has no meaning except as a. rule for the determination of visual ex- tension, and is also as such incapable of being given in a visual perception. If we were asked, in the language of the bad old antithesis, " Is the central conic transcendent or immanent ? " there would be no answer, short of the reply, " Both and neither". It may be called immanent, in the sense that it has no actuality except as realised by the construction of a visible outline of which it determines the type ; it must be called transcendent, in the sense that you can never even as a pure " form of intuition " perceive it in its true generality. I said just now that this example takes us into the heart of Plato's thought about the Ideas. Too little attention has sometimes been paid to the various examples of the Ideal existences which are given in the various dialogues. Plato's meaning has been supposed to be adequately indicated by such half-jocular instances as that of the Idea of a bed or table in Republic, 10. If however we set ourselves to pene- trate Plato's meaning by attending to the instances of the Ideas which occur where the conversation is assumed to be between trained members of the philosophic schools, we shall find that he does not allow himself to depend upon popular illustrations of this kind. In the Phcedo, 1 for instance, the 1 Ph&do, p. 74, cttn-6 TO io-oi/ ; p. 75, TO <dv, TO dyadov, TO 8Uaiov ; TO oa-iov as examples of Ideas ; p. 100, TO Kav, TO dyadov, TO fj.eya ; p. 101 ff., fjifyedos, TrXr/Oos, crpiKpoTrfs, povas, 8vas ; p. 104, fj T&V Tpi&v Idea and 17 Idea TOV dpriov (the argument also seems to imply at pp. 104-5 that Oeppov an "" ^vxpov are ideas) ; p. 106, UVTO TO T^S fays ei'Soy. In estimating the value of the references to ideas of bed, table, etc., in the Republic we must bear in mind that none of the interlocutors there -are philosophic companions of Socrates, hence the comparative avoidance of technical terms of the school, and the use of " popular " illustrations. Socrates adopts a different tone when he is talking with philosophers like Simmias and Cebes. The example of the etSos of the shuttle in Cratylus 389 b-d is instructive as showing, on reflexion, why o-/ceuaora are said, in
