1. How (asks Parmenides) can such participation take place? Is the entire Form in each individual object? No: for one and the same Form cannot be at the same time in many distant objects. A part of it therefore must be in one object; another part in another. But this assumes that the Form is divisible--or is not essentially One. Equality is in all equal objects: but how can a part of the Form equality, less than the whole, make objects equal? Again, littleness is in all little objects: that is, a part of the Form littleness is in each. But the Form littleness cannot have parts; because, if it had, the entire Form would be greater than any of its parts,--and the Form littleness cannot be greater than any thing. Moreover, if one part of littleness were added to other parts, the sum of the two would be less, and not greater, than either of the factors. It is plain that none of these Forms can be divisible, or can have parts. Objects therefore cannot participate in the Form by parts or piecemeal. But neither can each object possess the entire Form. Accordingly, since there remains no third possibility, objects cannot participate in the Forms at all.[11] [Footnote 11: Plato, Parmenid. p. 131. A similar argument, showing the impossibility of such [Greek: me/thexis], appears in Sextus Empiric. adv. Arithmeticos, sect. 11-20, p. 334 Fab., p. 724 Bek.] [Side-note: Comparing the Idea with the sensible objects partaking in the Idea, there is a likeness between them which must be represented by a higher Idea--and so on _ad infinitum_.] 2. Parmenides now passes to a second argument. The reason why you assume that each one of these Forms exists, is--That when you contemplate many similar objects, one and the same ideal phantom or Concept is suggested by all.[12] Thus, when you see many _great_ objects, one common impression of _greatness_ arises from all. Hence you conclude that The Great, or the Form of Greatness, exists as One. But if you take this Form of Greatness, and consider it in comparison with each or all the great individual objects, it will have in common with them something that makes it great. You must therefore search for some higher Form, which represents what belongs in common both to the Form of Greatness and to individual great objects. And this higher Form again, when compared with the rest, will have something in common which must be represented by a Form yet higher: so that there will be an infinite series of Forms, ascending higher and higher, of which you will never reach the topmost.[13] [Footnote 12: Plato, Parmenid. p. 132. [Greek: Oi)=mai se e)k tou= toiou=de e(\n e(/kaston ei)=dos oi)/esthai ei)=nai. O(/tan _po/ll' a)/tta mega/la soi do/xê|_ ei)=nai, _mi/a tis i)/sôs dokei= i)de/a_ ê( au)tê\ ei)=nai _e)pi\ pa/nta i)do/nti_, o(/then _e(\n to\ me/ga ê(gei= ei)=nai_.]]