1

Aristotle in the Metaphysics writes:

Others of the same school declare that there are ten principles arranged into two parallel columns:

  • Limit Unlimited
  • Odd Even
  • One Plurality
  • Right Left
  • Male Female
  • Rest Motion
  • Straight Bent
  • Light Darkness
  • Good Evil
  • Square Oblong

This particular arrangement he appears to have taken from Alcmeaon of Croton

Are these pairs of dualities, for want of a better name, related to his own list of categories? This relationship might be in the sense of replacement.

On the face of it, it doesn't appear to be plausible, as they signify all the possible categories under which the subject or a predicate of a proposition might be considered.

But, following the listing of the categories, he states four ways in which they can be considered to be contraries (according to Wikipedia) so there appears to be some suggestion here of a connection.

2

Your list from Aristotle, Met. 986a22ff, numbers ten principles (archai).

The whole passage is part of Aristotle's history of philosophy: Before expanding his own contribution, Aristotle recalls the research to date, i.e. what did his forerunners state about the topic.

After characterizing metaphysics as a knowledge of causes (aitiai) and principles (See sophia, 982a2), Aristotle aims at presenting his own doctrine of four causes (causa naturalis, efficiens, formalis, finalis). Apparently, these four causes are independent from the list of the Pythagorean principles and are talking on completely different levels.

Regarding to principles Aristotle accepts two principles from logic: 1. tertium non datur 2. law of contradiction. Again, quite a different level.

Aristotle authors a separate investigation, named "The categories". From the grammatical structure of propositions Aristotle derives 10 types of predication. They have been taken over as ontological types. Again they are different from the list of the Pythogoreans.

Note. Aristotle does not attribute the list of ten to Alcmaeon of Kroton. He indicates that Alcmaeon used a similar organizing principle, but with quite different pairs.

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