That the demonstrations include assumption both unwarranted and contradictory, mingled with sophistical subtlety (in the modern sense of the words), is admitted by most of the commentators: and I think that the real amount of it is greater than they admit. How far Plato was himself aware of this, I will not undertake to say. Perhaps he was not. The reasonings which have passed for sublime and profound in the estimation of so many readers, may well have appeared the same to their author. I have already remarked that Plato's ratiocinative force is much greater on the negative side than on the positive: more ingenious in suggesting logical difficulties than sagacious in solving them. Impressed, as Sokrates had been before him, with the duty of combating the false persuasion of knowledge, or premature and untested belief,--he undertook to set forth the pleadings of negation in the most forcible manner. Many of his dialogues manifest this tendency, but the Parmenides more than any other. That dialogue is a collection of unexplained [Greek: a)pori/ai] (such as those enumerated in the second book of Aristotle's Metaphysica) brought against a doctrine which yet Plato declares to be the indispensable condition of all reasoning. It concludes with a string of demonstrations by which contradictory conclusions (Both and Neither) are successively proved, and which appear like a _reductio ad absurdum_ of all demonstration. But at the time when Plato composed the dialogue, I think it not improbable that these difficulties and contradictions appeared even to himself unanswerable: in other words, that he did not himself see any answers and explanations of them. He had tied a knot so complicated, that he could not himself untie it. I speak of the state of Plato's mind when he wrote the Parmenides. At the dates of other dialogues (whether earlier or later), he wrote under different points of view; but no key to the Parmenides does he ever furnish. [Side-note: 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.]