He is aware that mathematical studies are preliminary to almost every other; at the same time, he will not reduce all varieties of knowledge to the type of mathematics.

He too must have a nobility of character, without which genius loses the better half of greatness.

Regarding the world as a point in immensity, and each individual as a link in a never-ending chain of existence, he will not think much of his own life, or be greatly afraid of death.
Adeimantus objects first of all to the form of the Socratic reasoning, thus showing that Plato is aware of the imperfection of his own method.
He brings the accusation against himself which might be brought against him by a modern logician--that he extracts the answer because he knows how to put the question.

In a long argument words are apt to change their meaning slightly, or premises may be assumed or conclusions inferred with rather too much certainty or universality; the variation at each step may be unobserved, and yet at last the divergence becomes considerable.

Hence the failure of attempts to apply arithmetical or algebraic formulae to logic.