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Like the ancient philosopher he sees the world pervaded by

analogies, but he can also tell 'why in some cases a single

instance is sufficient for an induction' (Mill's Logic), while in

other cases a thousand examples would prove nothing. He inquires

into a portion of knowledge only, because the whole has grown too

vast to be embraced by a single mind or life. He has a clearer

conception of the divisions of science and of their relation to

the mind of man than was possible to the ancients. Like Plato, he

has a vision of the unity of knowledge, not as the beginning of

philosophy to be attained by a study of elementary mathematics,

but as the far-off result of the working of many minds in many

ages. 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.