"Much of the content of so-called Pythagorean teaching appears to be a mix of mystical gobble-de-gook and adulatory veneration of the genius of the founder."

“Philosophy asks for a reason, not just a scientific fact.”

“In the Protagoras Socrates persuades Protagoras that goodness is identical with pleasure. He advocates a form of hedonism. In the Gorgias, Callicles espouses hedonism and Socrates refutes him. Socrates gets Callicles to admit that, after all, some pleasures are not good. So Socrates holds contradictory views on pleasure in the Protagoras and the Gorgias.”

“Philosophy has come to include, for us, a wide range of theoretical questions that typically look beyond what we can answer by experimental enquiries. While science asks how matter behaves, and tests its theories with observation, philosophy asks what matter is, or how observation can teach us anything. While mathematics asks what the sum of 2 and 7 is, philosophy asks what the number 2 is, and whether 2 plus 7 could ever make anything but 9.”

“Both Democritus and Anaxagoras try to explain the puzzling behaviour of ordinary reality by appeal to a microscopic replica of reality, in which another set of tiny bodies or minute scraps of stuff move around and cause things to happen. As a way to overcome the difficulty of explaining changes in the world, this ultimately emerges as unsatisfying: if there were problems with explaining chemical and physical events as they appear to us, there will be the same problems with explaining the reactions between smaller and yet smaller bodies.”

“Are these good reasons for worrying about the apparent contradiction? Should either make us feel the need of an explanation?”

“Parmenides did for science what Plato would later do for morality and aesthetics as well: he alerts us to the fact that opinions are just opinions, and they may differ widely. There may yet be a single truth, which need not be as anyone thought. To search for knowledge is to search for access to the truth, not to collect other people’s opinions, and philosophy conducts its unrelenting search for truth in the steps of Parmenides, by respecting sound and rigorous logical argument rather than the variegated tapestry of unexamined opinions.”