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

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.

Plato not only permitted live philosophical enquiry to take place in the course of every reader’s every reading of the dialogue, by putting tempting and plausible views on trial, in a situation as near as possible to the open-minded exploratory give and take of dialectical debate with a real interlocutor. He also created a most fitting memorial to the real Socrates – the man himself, who lived and died for the idea that philosophy is best done in open-ended dialogue, and with your whole way of life at stake should you be refuted.

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.