CHAPTER III. ADDITIONAL REMARKS ON PLATO. The leading points in Plato's writings which bear upon the philosophy of discovery are these: 1. The Doctrine of Ideas. 2. The Doctrine of the One and the Many. 3. The notion of the nature and aim of Science. 4. The survey of existing Sciences. 1. The Doctrine of Ideas is an attempt to solve a problem which in all ages forces itself upon the notice of thoughtful men; namely, How can certain and permanent knowledge be possible for man, since all his knowledge must be derived from transient and fluctuating sensations? And the answer given by this doctrine is, that certain and permanent knowledge is _not_ derived from _Sensations_, but from _Ideas_. There are in the mind certain elements of knowledge which are not derived from sensation, and are only imperfectly exemplified in sensible objects; and when we reason concerning sensible things so as to obtain real knowledge, we do so by considering such things as partaking of the qualities of the Ideas concerning which there can be truth. The sciences of Geometry and Arithmetic show that there _are_ truths which man can know; and the Doctrine of Ideas explains how this is possible. So far the Doctrine of Ideas answers its primary purpose, and is a reply (by no means the least intelligible and satisfactory reply) to a question still agitated among philosophers: What is the ground of geometrical (and other necessary) truth? But Plato seems, in many of his writings, to extend this doctrine much further; and to assume, not only Ideas of Space and its properties, from which geometrical truths are derived; but of Relations, as the Relations of Like and Unlike, Greater and Less; and of mere material objects, as Tables and Chairs. Now to assume Ideas of such things as these solves no difficulty and is supported by no argument. In this respect the Ideal theory is of no value in Science. It is curious that we have a very acute refutation of the Ideal theory in this sense, not only in Aristotle, the open opponent of Plato on this subject, but in the Platonic writings themselves: namely, in the Dialogue entitled _Parmenides_; which, on this and on other accounts, I consider to be the work not of Plato, but of an opponent of Plato[6]. 2. I have spoken, in the preceding chapter, of Plato's doctrine that truth is to be obtained by discerning the One in the Many. This expression is used, it would seem, in a somewhat large and fluctuating way, to mean several things; as for instance, finding the one _kind_ in many _individuals_ (for instance, the one idea of dog in many dogs); or the one _law_ in many _phenomena_ (for instance, the eccentrics and epicycles in many planets). In any interpretation, it is too loose and indefinite a rule to be of much value in the formation of sciences, though it has been recently again propounded as important in modern times.