By Evert W. Beth (Eds.)
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Modern logic has no difficulty in showing that Plato's Principle of the Idea, if handled adequately, does not, intrinsically, give rise to any logical difficulties. As a matter of fact, the (weak) s-axiom which was introduced by Hilbert 43) can be interpreted as a new version of this principle. It is true that in modern logic it is not usual to take explicitly into account the occurrence of corruptible entities. But it has been shown by Bolzano 44) that we may give a consistent interpretation of sentences involving a time determination without referring to corruptible entities.
Then there is an entity a which has the following property: for any entity x distinct from a, we have (i) the fact that x has the property A presupposes the fact that a has the property A, and (ij) the fact that a has the property A does not presuppose the fact that x has the property A. ) The absolute entity a may be construed to correspond to what is called by Plato, e16or; or Mea. Therefore, the principle which has just been derived as a special case of the Principle of the Absolute, will be called the Principle of the Idea.
The first book of the Metaphysics consists for a considerable part of a discussion of Plato's lecture On the Supreme Good. The differences of opinion are often overstressed and we can scarcely expect to obtain from Aristotle's comments a fair picture of Plato's views with which, moreover, the reader is apparently supposed to be already completely 18 THE PREHISTORY OF RESEARCH INTO FOUNDATIONS familiar. The general programme set forth in Plato's lecture, the search for the principles and for the manner in which the things generate from them, is taken over by Aristotle.
A Study in the Philosophy of Science by Evert W. Beth (Eds.)