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If syllogistic logic couldn’t handle relations, why did it last two thousand years?

Derek Hollis Fellow
· 6 replies · 194 views
Logic & argumentGreek & RomanIndianIslamicAristotelianismNyayaAristotleGangesaIbn SinaImmanuel Kant#history-of-logic#navya-nyaya#relations#syllogism
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I write verification tools for a living, so I live inside predicate logic. Every so often I'm reminded how much it can do that the syllogism can't. The textbook example (usually credited to De Morgan) is: all horses are animals, therefore every head of a horse is the head of an animal. Obviously valid, and the categorical forms can't even state it, because "head of" is a relation between two things.

That kind of inference is everywhere in mathematics and law. And yet Kant, in the preface to the second edition of the first Critique, could say that logic had not had to take a step backwards since Aristotle, nor been able to take one forward, and looked finished. That was nearly a century before Frege.

So what explains the staying power? A few candidates I can think of:

  1. It covered the arguments people actually needed in theology, law and teaching.
  2. It is decidable and teachable, which made it perfect for a curriculum.
  3. Relational reasoning was being done all along, just informally, so nobody felt the gap.
  4. The longevity is partly an illusion of the European textbook tradition.

I suspect it's some mix, but I'd like to hear from people who know the history better than I do, especially outside Europe.

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6 answers

  1. Layla Haddad

    Fellow

    Your fourth option deserves more weight than you give it. In Arabic logic the system did not sit still. Ibn Sina reworked the modal syllogistic substantially, paid attention to temporal qualifications (whether a predicate holds of the subject for as long as it exists, or only as long as it has some description), and developed hypothetical syllogisms built from conditional and disjunctive premises. Later logicians in the madrasas argued about his innovations far more than about Aristotle's own text. "Two thousand years unchanged" is how it looks from a seventeenth-century Latin schoolroom, not from Isfahan or Cairo.

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  2. Tomasz Wójcik

    Fellow

    I'd defend your second option strongly. A system where every question has a mechanical answer, where the whole of it fits on one page, and where students can be examined on it, is an enormous institutional asset. Predicate logic is undecidable. Nobody could have built a medieval curriculum on it, even if they had had it.

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  3. Fr. Ikechukwu Anyanwu

    Fellow

    From the seminary: the syllogism was never the whole of medieval logic, only the part that got taught first. The scholastics developed theories of supposition (how terms refer in context) and of consequences, which handle a good deal of what the categorical forms cannot. Ockham and Buridan are working well beyond Barbara. The textbooks that survived into the modern period were the simplified ones, and that is partly why Kant could say what he said.

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  4. Govinda Prasad Mishra

    Fellow

    In India the pressure came from another direction. Navya-Nyāya, from Gangeśa's Tattvacintāmaṇi in the fourteenth century, built a very exact technical language for relations: what qualifies what, under which limiting property, by which relation. It is not a syllogistic at all; it is closer to a formal semantics written in Sanskrit. My own pandits in Varanasi still use it to settle disputes about interpretation. So in one part of the world, at least, relations were handled with great precision, just not through categorical forms.

  5. Derek Hollis

    Fellow

    This is humbling and very useful. So the honest version of my question is narrower: why did the European schoolbook version freeze, when Arabic, Indian and even late-medieval Latin logic had moved past it? Fr. Ikechukwu's answer, that the simplified textbooks were what survived, plus Tomasz's point about teachability, seems to cover most of it.

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  6. Henrike Vogel

    Fellow

    A small footnote on Kant, since I have just read that preface with my Kant group. The remark is less a historical claim than a compliment to logic for knowing its limits: it is complete, he says, because it deals only with the form of thought. That makes it more interesting as a symptom. It shows how a well-bounded discipline can mistake its boundary for its completion.

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