he expressly asserted that his predecessor was right, and approved his definite accusation of the sophists that they were occupied not with the universal but with the accidental, that is to say, with not-being. [Sidenote: _Controversies as to the various forms of concept in Plato._] The beginning of the enquiry as to the nature of universals or of ideas is to be seen, on the other hand, in Plato's embarrassments before the questions as to whether there are ideas of everything, of artificial as well as of natural things, of noble things and vile things alike, of things only or also of properties and relations; of good things or also of bad things (καλὸν καὶ αἰσχρόν, ἀγαθὸν καὶ κακόν)[5] He does not escape from the embarrassments, save occasionally, by making strange admissions, by accepting ideas of all the preceding, only to fall immediately afterwards into contradictions, through which however we see the outlines of the problems of to-day. Are the ideas representative concepts (of things) or are they not rather categories (ideas of relation)? Arc opposites particular kinds of ideas (if there exist ideas of base and ugly things, as well as of beautiful and good things)? Is it possible to distinguish, from the point of view of the Ideas, between the natural world and the human world (between natural things and artificial)? Plato himself refers to mathematical knowledge as distinct from philosophic knowledge. [Sidenote: _The philosophic concepts and the empirical and abstract concepts in Aristotle. Philosophy, physics and mathematics._]