Page:Mind (New Series) Volume 12.djvu/26

 12 A. E. TAYLOE I were regarded in the same way. Hence the effect of the demonstration that neither view is tenable is to show the necessity of a third doctrine which permits of justice being done at once to the aspect of continuity and to that of discreteness in extension. We may shortly see reason to hold that Plato's view, which is to be at once non-Eleatic and non-Pythagorean, depends upon the recognition of the difference between perceptual and conceptual extension. We must, however, first proceed with our examination of the actual words of the dialogue. To the general argument against the divisi- bility of the Idea Parmenides goes on to append a statement of certain absurd consequences which will follow if we still persist in upholding the Pythagorean view. The nature of these absurdities has not, I think, always been perceived, certainly I myself in my previous articles on the dialogue entirely failed to throw light upon them. From the stand- point we have now reached however they do not seem to present any special difficulty. The first of them, as formu- lated bjr Parmenides, reads thus (131 c-d) : "if you make magnitude itself consist of parts, and say that each of the many magna is magnum in virtue of a portion of magnitude less than magnitude itself, will not the consequence appear absurd?" If we remember that the term //,eye0o9 regularly occurs in Greek philosophical language as the special name for a geometrical magnitude, a quantum of extension, it will not be difficult to seize the speaker's thought. 1 We may expand the reasoning in some such way as this : if the Pythagorean view of the unit of extension is sound, then any finite magnitude, a straight line for example, is a quantum precisely because it contains so many repetitions of the unit of quantity, the point, which latter is on this view avro TO peyeOos ; but the unit itself is also a quantum, and by parity of reasoning must therefore be itself composed of still minuter units " of a higher order," and thus in the last resort every quantum will be composed of quanta less than the supposed ultimate unit itself. Very possibly it may have been the discovery of incommensurables (the significance of which for the history of Greek metaphysics has been so powerfully exhibited by M. Milhaud) which led to the formulation of this particular difficulty, though of course it is really involved in the con- struction of any extended quantum out of indivisible units. 1 See for instances of this use of the word Bonitz's Index Aristotelian, sub. voc., and compare particularly the definition at Metaphysics A 10, 20 a, 9. TrXfjdos p.ev ovv TTOO-OV TI ftiv api6fjiT)Tov fi, fj-fyedos S' eai> p-erpijTov fi KT.