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Thesis Logic is the one part of philosophy that settles questions, and the rest should take note

Derek Hollis Fellow
· 5 replies · 195 views
Logic & argumentAnalyticGreek & RomanAristotleGottlob FregeGraham PriestKurt Gödel#incompleteness#logical-pluralism#predicate-logic#progress-in-philosophy
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Where it stands

People like to say that philosophy never makes progress, that we're still arguing about the same questions as Plato. Logic is the counterexample.

For two thousand years, Aristotle's syllogistic could not handle inferences involving relations. "Every horse is an animal, so every horse's head is an animal's head" is obviously valid and has no syllogistic form. Logicians knew it and could not fix it. In 1879 Frege's Begriffsschrift fixed it, with quantifiers and variables that can be nested. Predicate logic captures every valid syllogism (once existential import is made explicit) and the whole range of relational inference that syllogistic missed. Syllogistic is now taught as history.

And logic settled negative questions too. In 1931 Gödel showed that any consistent formal system strong enough for arithmetic contains true statements it cannot prove, and cannot prove its own consistency. The hope of a complete formalization of mathematics wasn't postponed. It was refuted.

So here's my thesis, as someone who proves programs correct for a living. Logic settles questions because it insists that arguments be written in a form where they can be checked. The rest of philosophy could learn from that. Not every question can be formalized, but far more could be made precise than currently are, and precision is what lets a question stay answered.

Tell me why I'm being naive.

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5 replies

For the thesis 1

  1. Tomasz Wójcik

    For Fellow

    I'd defend Derek's core point. Ana Clara is right about which logic is correct, but the theorems hold whichever logic you prefer. Gödel's results aren't opinions about arithmetic, they're mathematics. Nobody serious disputes that Frege's system can express relational inference and Aristotle's cannot. That's settled, and it's more than most philosophical debates can claim.

    Helpful · 2

Against the thesis 3

  1. Ana Clara Ferreira

    Against Fellow

    You're not naive, Derek, but you're running two things together. What logic settled are theorems about systems: this system can prove that, no system of that kind can do this. What it has not settled is which system is the right logic. Intuitionists reject the law of excluded middle for infinite domains. Paraconsistent logicians, Newton da Costa here in Brazil among the pioneers, reject the principle that a contradiction implies everything. Graham Priest argues that some contradictions are true. Classical logic is the default, not the verdict.

    Helpful · 1
  2. Oskar Nyberg

    Against Fellow

    Here's the uncomfortable version. Logic settled these questions precisely at the moment they became mathematical questions, and at that point, many would say, they left philosophy, the way physics left natural philosophy. So the lesson for ethics isn't "be more precise". It's "if you become precise enough, you'll be called something else." The questions that remain in philosophy may be exactly those that resist this treatment.

    Helpful · 3
  3. Govinda Prasad Mishra

    Against Fellow

    In the Indian traditions, inference was always treated as a pramāṇa, a means of knowing. It was never only a matter of form. The five-membered argument of the Naiyāyikas includes an example, and the example has to be something actually observed. So whether logic "settled" anything depends on what you think logic is for. If it's for valid form, yes. If it's for how a person comes to know, the questions are still open.

Other replies

  1. Derek Hollis

    Fellow

    Fair hits all round. I'll narrow it: logic has settled questions about systems, and that's real progress that most of philosophy can't match. Ana Clara and Govinda are right that choosing a logic, and deciding what logic is for, are still philosophical questions, and open ones. Oskar's point I'm still chewing on. If precision means leaving philosophy, then philosophy is the place where the questions wait until someone finds the right notation. I can live with that.

    Helpful · 1