However corrupt the history of his life, his philosophy is as much so. Everything engendered by Christian melancholy and love of allegory has been identified with it. The treatment of Plato in Christian times has quite a different character. Numbers have been much used as the expression of ideas, and this on the one hand has a semblance of profundity. For the fact that another significance than that immediately presented is implied in them, is evident at once; but how much there is within them is neither known by him who speaks nor by him, who seeks to understand; it is like the witches’ rhyme (one time one) in Goethe’s “Faust.” The less clear the thoughts, the deeper they appear; what is most essential, but most difficult, the expression of oneself in definite conceptions, is omitted. Thus Pythagoras’ philosophy, since much has been added to it by those who wrote of it, may similarly appear as the mysterious product of minds as shallow and empty as they are dark. Fortunately, however, we have a special knowledge of the theoretic, speculative side of it, and that, indeed, from Aristotle and Sextus Empiricus, who have taken considerable trouble with it. Although later Pythagoreans disparage Aristotle on account of his exposition, he has a place above any such disparagement, and therefore to them no attention must be given. In later times a quantity of writings were disseminated and foisted upon Pythagoras. Diogenes Laertius (VIII. 6, 7) mentions many which were by him, and others which were set down to him in order to obtain authority for them. But in the first place we have no writings by Pythagoras, and secondly it is doubtful whether any ever did exist. We have quotations from these in unsatisfactory fragments, not from Pythagoras, but from Pythagoreans. It cannot be decisively determined which developments and interpretations belonged to the ancients and which to the moderns; yet with Pythagoras and the ancient Pythagoreans the determinations were not worked out in so concrete a way as later.