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Reading group: Aristotle’s Metaphysics Gamma on the firmest principle

Nikos Theodoridis Fellow
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Logic & argumentGreek & RomanIslamicAristotelianismAristotleIbn Sina#elenctic-demonstration#metaphysics-gamma#non-contradiction
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Several recent threads keep coming back to Aristotle's defence of the principle of non-contradiction, usually second-hand. Let's read it. It's short and much stranger than its reputation.

Text: Metaphysics Book Gamma (IV), chapters 3 to 7. Ross's translation is freely available; Christopher Kirwan's Clarendon volume on Books Gamma, Delta and Epsilon has an excellent commentary. Greek for those who want it.

Plan (four weeks):

  • Week 1: Gamma 3. The statement of the principle, with its qualifications: the same thing cannot both belong and not belong to the same subject at the same time and in the same respect. Why does Aristotle call it the firmest of all principles?
  • Week 2: Gamma 4, first half. Why it can't be demonstrated, and the "elenctic" demonstration instead: get the opponent to say something that signifies.
  • Week 3: Gamma 4, second half, and Gamma 5–6. The remaining arguments, then Protagoras and the claim that all appearances are true.
  • Week 4: Gamma 7. Excluded middle, briefly, and how it sits with the sea battle chapter of De Interpretatione.

I teach theology in Thessaloniki, so I'll also bring the Byzantine commentators where they help. Post under the week.

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5 replies

  1. Giulia Ferrante

    Fellow

    Week 1. The Greek for "firmest" is bebaiotatē: the most secure, the one about which it is impossible to be mistaken. Every year my students try to break the principle with cases like "the door is open and not open" (it's ajar). The qualifications are what Aristotle built to block them. "In the same respect" carries most of the weight, and students almost always cheat there.

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  2. Layla Sfeir

    Fellow

    Week 2. For the Arabic tradition this chapter produced one of the most quoted remarks in Ibn Sina's Metaphysics of the Healing: roughly, that someone who denies the principle should be beaten and put to the fire until he admits that being burned and not being burned are not the same. It sounds like a joke, and it partly is. But the point is Aristotle's: the denier's own conduct shows that he doesn't really treat contradictories as equivalent. You refute him by what he does, not by a proof.

  3. Tomasz Szewczak

    Fellow

    Week 2. The elenctic argument establishes, I think, that significant speech requires that a word exclude something. What it doesn't obviously establish is that every assertion excludes its own negation in every case. That's the gap a dialetheist like Priest exploits: he can grant that "man" excludes "not-man" in nearly all cases, and deny it for a few pathological sentences. Whether Aristotle's argument closes that gap is the question I'd like us to argue in Week 3.

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  4. Ikechukwu Anyanwu

    Fellow

    Week 3. I read this with my students, with Aquinas's commentary on the Metaphysics beside it. Aquinas is very good on Gamma 5–6: he treats Protagoras not as a fool but as someone who took appearances seriously and drew the wrong conclusion. That's a useful model for teaching young people to argue with positions they reject.

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  5. Nikos Theodoridis

    Fellow

    Week 4. Gamma 7 states excluded middle quite firmly: there can't be anything between contradictories. Reading it next to De Interpretatione 9, where some readers find Aristotle doubting that statements about tomorrow's sea battle are already true or false, is fascinating. Either he changed his mind, or the two passages are about different things, or the sea battle chapter doesn't deny bivalence at all. Thank you all; this was the best month of reading I've had on the forum.

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