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Thesis For ordinary speech, Aristotle was right: “All S are P” presupposes there are some S

Oskar Nyberg Fellow
· 6 replies
Logic & argumentAnalyticGreek & RomanAristotelianismOrdinary language philosophyAristotlePeter Strawson#existential-import#presupposition#syllogism#vacuous-truth
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Its coordinates: 4.1 Formal Logic · 4.1.1 Propositional Logic · 4.1.2 Predicate Logic +4 more

Where it stands

Modern logic reads "All S are P" as "for anything, if it is S, it is P". If nothing is S, the statement comes out true automatically. So "All the unicorns in my garden are pink" is true, and so is "All the unicorns in my garden are green".

Traditional syllogistic did not work this way. It let you infer "Some S are P" from "All S are P" (subalternation), and it counted moods like Darapti as valid. Under the modern reading those inferences fail whenever S is empty, which is why the count of valid moods drops from 24 to 15.

My thesis: for the way people actually talk, the traditional system was closer to the truth. When someone says "all my students passed", they are not asserting a conditional that would be satisfied if they had no students. They are presupposing that there are students and saying something about them. Strawson argued this in Introduction to Logical Theory (1952): read the existence of S as presupposed rather than asserted, and the old square of opposition holds together nicely.

The vacuous-truth reading is a fine convention for mathematics. As an account of English (or Swedish) it is an artefact of the notation.

What is the best case against this, especially from people who use logic for something other than teaching it?

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6 replies

For the thesis 2

  1. Giulia Ferrante

    For Fellow

    For, from the classroom. In twenty years I have never had a sixteen-year-old accept that "all the unicorns in my garden are pink" is true. They feel cheated, and I think their instinct is tracking something real about what speakers commit themselves to.

    As far as I know the Prior Analytics simply never considers an empty term. Scholars argue about what that silence means, so I won't claim Aristotle had a theory of presupposition. But his terms are always things like "animal" and "man".

  2. Derek Hollis

    For Fellow

    For, from industry. In hardware verification, vacuous truth is a known source of false comfort. You write a property like "every request is eventually acknowledged", the tool says it holds, and then you discover that in your test configuration no request is ever issued. There is a whole literature on vacuity detection because engineers kept being fooled. So the modern reading may be correct, but the ordinary-language instinct Oskar describes is not a mistake people grow out of; it is one that tools have to guard against.

    Helpful · 2

Against the thesis 3

  1. Ana Clara Ferreira

    Against Fellow

    Against. Mathematics is not the exception that proves your rule, it is where the reading earns its keep. "Every counterexample to Fermat's Last Theorem is even" is true, and we want it true; it was useful long before anyone knew the set was empty.

    And ordinary speech has plenty of cases too. "All trespassers will be prosecuted" is written precisely in the hope that the class stays empty. If it presupposed trespassers, the sign would be insulting the passers-by.

    Helpful · 3
  2. Tomasz Szewczak

    Against Fellow

    Partly against. The presupposition reading is attractive, but it is not free. If "All S are P" is neither true nor false when there are no S, you now need truth-value gaps, and with them a three-valued or gappy logic and a story about how gaps propagate through compound sentences. I happen to like many-valued logics, so I'm not frightened of that. But "the traditional system holds together nicely" hides a real bill.

    Helpful · 1

Other replies

  1. Oskar Nyberg

    Fellow

    Good objections, and I'll concede more than I expected. Ana Clara's trespasser sign is decisive against the strong thesis: law-like and prohibitive universals do not presuppose instances, and they are ordinary speech. Tomasz is right that the gap has to be paid for.

    Revised claim: universals that report on a known, already-identified group ("all my students", "all the guests") carry existential presupposition; generic, legal and mathematical universals do not. English uses one form for both jobs, and each logic captures one of them. Derek's example suggests that confusing the two is not just a philosopher's worry.

    Helpful · 3
    1. Ana Clara Ferreira

      Against Fellow

      That revision I can live with. It also matches how I explain it when I tutor: I tell students the modern conditional is a decision about what "all" should mean in a formal language, not a discovery about what it means in Portuguese.