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Reading group: Prior Analytics I.1–7, slowly, with a Nyāya inference on the table

Giulia Ferrante Fellow
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Logic & argumentGreek & RomanIndianAristotelianismNyayaAristotleGautama (Akṣapāda)#nyaya-inference#prior-analytics#reading-group#syllogism
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Everyone says Aristotle invented formal logic, and I realise I have never read the Prior Analytics closely in company. So here is a proposal: the first seven chapters of Book I, over five weeks, which is where the whole assertoric system is laid out.

Translation. Robin Smith's Hackett translation is the one I'd recommend: clear, with a careful commentary. Jenkinson's older version in the Revised Oxford Aristotle is fine if that is what you have.

Plan.
– Week 1: I.1, the definitions, including the famous definition of a deduction.
– Week 2: I.2–3, conversion of premises (and a first look at modal conversion).
– Week 3: I.4, the first figure.
– Week 4: I.5–6, the second and third figures and how they are proved.
– Week 5: I.7, plus a comparison.

The comparison. Several members here know the Nyāya five-membered inference much better than I do. I'd like us to keep one example of it beside the text throughout ("this hill has fire, because it has smoke…") and ask, week by week, what Aristotle is formalising that the Nyāya form is not, and the reverse. The goal is not to rank them but to see what each one is built to do.

Post your notes under the week. Greek welcome but not required.

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6 replies

  1. Claire Dubois

    Fellow

    Week 1. A translator's note first: Smith renders syllogismos as "deduction", not "syllogism", and after reading I.1 I think he is right. Aristotle's definition is general: an argument in which, certain things being laid down, something other than them follows of necessity because they are so. Nothing in it mentions two premises or three terms. The narrowing to the syllogism in our sense happens in the following chapters. That is worth noticing before we let the word harden.

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  2. Oskar Nyberg

    Fellow

    Week 2. The conversion rules are where I slowed down. "No B is A" converts to "No A is B" without loss. "All B is A" converts only to "Some A is B". Everything later depends on these, because the proofs in chapters 5 and 6 work by converting premises until you reach a first-figure pattern. It is also where the existential import question I raised in another thread is quietly settled: "All B is A" to "Some A is B" only works if there are Bs.

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  3. Vikram Sethi

    Fellow

    Week 3. What struck me as a maths teacher is the letters. Aristotle states the patterns with letters standing for any terms at all, and then uses concrete terms to show that some combinations fail. That is the method of counterexample I spend half my teaching life on. It is often said this is the first use of schematic letters in logic; reading it, I can believe it.

  4. Giulia Ferrante

    Fellow

    Week 4. Chapters 5 and 6 show how the second and third figures are proved: mostly by conversion back to the first figure, and in a couple of cases by reductio. The first-figure deductions are called "perfect" because they need nothing further to be evident. The others are made evident by reducing them. So the system has a foundation and a method, which is more than I had appreciated when I taught it as a list.

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  5. Meera Kulkarni

    Fellow

    Week 5, and the comparison. Reading I.7, where Aristotle shows that everything can be reduced to the universal first-figure deductions, I kept thinking of the Nyāya example member. For Aristotle the perfect deduction is evident with no instance at all. For Nyāya, an inference presented to someone else without an agreed instance is incomplete. One tradition grounds the general claim in its form; the other insists it be anchored in a case both parties have seen. Neither seems to me a failed version of the other.

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  6. Henrike Vogel

    Fellow

    I joined late and only read I.7, but I noticed the same thing as Meera: the confidence that everything reduces to Barbara and Celarent. It is a beautiful economy. I came away understanding why people thought for so long that logic was finished.

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