Confining ourselves at present to the part of Plato's speculations which we have mentioned, namely, the degrees of knowledge, and the division of our knowing faculties, we may understand, and may in a great degree accept, Plato's scheme. We have already (in the preceding papers) seen that, by the knowledge of real things, he means, in the first place, the knowledge of universal and necessary truths, such as Geometry and the other exact sciences deal with. These we call sciences of Demonstration; and we are in the habit of contrasting the knowledge which constitutes such sciences with the knowledge obtained by the Senses, by Experience or mere Observation. This distinction of Demonstrative and Empirical knowledge is a cardinal point in Plato's scheme also; the former alone being allowed to deserve the name of Knowledge, and the latter being only Opinion. The Objects with which Demonstration deals may be termed Conceptions, and the objects with which Observation or Sense has to do, however much speculation may reduce them to mere Sensations, are commonly described as Things. Of these Things, there may be Shadows or Images, as Plato says; and as we may obtain a certain kind of knowledge, namely Opinion or Belief, by seeing the Things themselves, we may obtain an inferior kind of Opinion or Belief by seeing their Images, which kind of opinion we may for the moment call Conjecture. Whether then we regard the distinctions of knowledge itself or of the objects of it, we have three terms before us.
If we consider the kinds of knowledge, they are
Demonstration: Belief: Conjecture.
If the objects of this knowledge, they are
Conceptions: Things: Images.
But in each of these Series, the first term is evidently wanting: for Demonstration supposes Principles to reason from. Conceptions suppose some basis in the mind which gives them their evidence. What then is the first term in each of these two Series?
The Principles of Demonstration must be seen by Intuition.
Conceptions derive their properties from certain powers or attributes of the mind which we may term Ideas.
Therefore the two series are
Intuition: Demonstration: Belief: Conjecture.
Ideas: Conceptions: Things: Images.
Plato further teaches that the two former terms in each Series belong to the Intelligible, the two latter to the Visible World: and he supposes that the ratio of these two primary segments of the line is the same as the ratio in which each segment is divided[346].
In using the term Ideas to describe the mental sources from which Conceptions derive their validity in demonstration, I am employing a phraseology which I have already introduced in the Philosophy of the Inductive Sciences. But independently altogether of this, I do not see what other term could be employed to denote the mental objects, attributes, or powers, whatever they be, from which Conceptions derive their evidence, as Demonstrative Truths derive their evidence from Intuitive Truths.
That the Scheme just presented is Plato's doctrine on this subject, I do not conceive there can be any doubt. There is a little want of precision in his phraseology, arising from his mixing together the two series. In fact, his final series