It seems to us unwise to have insisted on teaching geometry to the younger Dionysius, tyrant of Syracuse, in order to make him a good king, but from Plato's point of view it was essential. He was sufficiently Pythagorean to think that without mathematics no true wisdom is possible.

Thought is subversive and revolutionary, destructive and terrible, Thought is merciless to privilege, established institutions, and comfortable habit. Thought is great and swift and free.

We know that the exercise of virtue should be its own reward, and it seems to follow that the enduring of it on the part of the patient should be its own punishment.

Adventurous men enjoy shipwrecks, mutinies, earthquakes, conflagrations, and all kinds of unpleasant experiences. They say to themselves, for example, 'So this is what an earthquake is like,' and it gives them pleasure to have their knowledge of the world increased by this new item.

Self-respect will keep a man from being abject when he is in the power of enemies, and will enable him to feel that he may be in the right when the world is against him.

The search for something permanent is one of the deepest of the instincts leading men to philosophy.

The demand for certainty is one which is natural to man, but is nevertheless an intellectual vice. So long as men are not trained to withhold judgment in the absence of evidence, they will be led astray by cocksure prophets, and it is likely that their leaders will be either ignorant fanatics or dishonest charlatans. To endure uncertainty is difficult, but so are most of the other virtues.