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This chapter analyzes the most comprehensive account of the Pythagorean theory of principles in Aristotle's extant work: the first part of Metaphysics A5. It looks at the passage where Aristotle indicates what he considers to have been the intermediate steps, the additional premises, as it were, between the initial act of taking up the mathēmata and the fully fledged Pythagorean theory according to which the principles of the mathēmata are the principles of all things. The chapter deals with a piece of historiographical reasoning, which claims that some of the opinions attributable to the so-called Pythagoreans actually caused the coming-to-be of other opinions equally well attributable to them. The testimony provided by Alexander of Aphrodisias enables one to assess the function of the resemblances in Aristotle's historiographical reconstruction as outlined in Metaph. A5.
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