Difficulties about the Cognizability of Ideas. If Ideas are absolute, they cannot be cognizable: if they are cognizable, they must be relative. Doctrine of Homo Mensura 72 Answer of Sokrates--That Ideas are mere conceptions of the mind. Objection of Parmenides correct, though undeveloped 73 Meaning of Abstract and General Terms, debated from ancient times to the present day--Different views of Plato and Aristotle upon it 76 Plato never expected to make his Ideas fit on to the facts of sense: Aristotle tried to do it and partly succeeded 78 Continuation of the Dialogue--Parmenides admonishes Sokrates that he has been premature in delivering a doctrine, without sufficient preliminary exercise 79 What sort of exercise? Parmenides describes: To assume provisionally both the affirmative and the negative of many hypotheses about the most general terms, and to trace the consequences of each _ib._ Impossible to do this before a numerous audience--Parmenides is entreated to give a specimen--After much solicitation he agrees 80 Parmenides elects his own theory of the _Unum_, as the topic for exhibition--Aristoteles becomes respondent _ib._ Exhibition of Parmenides--Nine distinct deductions or Demonstrations, first from _Unum Est_--next from _Unum non Est_ 81 The Demonstrations in antagonising pairs, or Antinomies. Perplexing entanglement of conclusions given without any explanation _ib._ Different judgments of Platonic critics respecting the Antinomies and the dialogue generally 82 No dogmatical solution or purpose is wrapped up in the dialogue. The purpose is negative, to make a theorist keenly feel all the difficulties of theorising 85 This negative purpose is expressly announced by Plato himself. All dogmatical purpose, extending farther, is purely hypothetical, and even inconsistent with what is declared 87 The Demonstrations or Antinomies considered. They include much unwarranted assumption and subtlety. Collection of unexplained perplexities or [Greek: a)pori/ai] 88 Even if Plato himself saw through these subtleties, he might still choose to impose and to heap up difficulties in the way of a forward affirmative aspirant 89 The exercises exhibited by Parmenides are exhibited only as illustrative specimens of a method enjoined to be applied to many other Antinomies 91 These Platonic Antinomies are more formidable than any of the sophisms or subtleties broached by the Megaric philosophers _ib._ In order to understand fully the Platonic Antinomies, we ought to have before us the problems of the Megarics and others. Uselessness of searching for a positive result 93 Assumptions of Parmenides in his Demonstrations convey the minimum of determinate meaning. Views of Aristotle upon these indeterminate predicates, Ens, Unum, &c. 94 In the Platonic Demonstrations the same proposition in words is made to bear very different meanings 95