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Foot-Note

Chaldeans is not very strong and may easily have been inferential as were no doubt many other statements concerning the origin of his philosophy.
Other were probably blunders.

Pythagoras is commonly regarded as a man of mystical tendencies but I am not clear that he was so.
His brotherhood seem to have pursued the most practical ends and all the mysticism of ao much of the number of theory as probably belonged to him is sufficiently explained by the excessive crudeness of his ideas.
He seems to have been something of a charlatan; but the mysticism of the charlatan does not often stand in his light as a worldly way; and I am inclined to think that Pythagoras looked upon numbers as the most practical thing in the world.

That Pythagoras or any of the Pythagoreans made the smallest approach to my categories appear quite impossible I cannot hare fully explain why.
End of Foot Note.