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How can I tell an argument is valid when I don’t know what its words mean?

Kavya Menon Fellow
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Logic & argumentAnalyticGreek & RomanAristotelianismAlfred TarskiAristotle#logical-form#syllogism#validity
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Its coordinates: 4.1 Formal Logic · 4.1.1 Propositional Logic · 4.1.2 Predicate Logic +4 more

Forgive me if this is basic; I'm very new to formal philosophy.

I met this pair of arguments in a logic primer:

All whales are mammals. All mammals are warm-blooded. So all whales are warm-blooded.

All zorps are blickets. All blickets are frumious. So all zorps are frumious.

(I was delighted to see "frumious" there. It's from Lewis Carroll's "Jabberwocky".)

The book says both are valid, and I can see the second one is, even though I have no idea what a zorp is. That is what puzzles me. If I don't know what any of the words mean, what exactly am I recognising? Is validity just a matter of grammar? And if so, why does it matter so much to philosophers?

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4 answers

Accepted answer

  1. Vikram Sethi

    ✓ Accepted answer Fellow

    You are recognising the form, Kavya. Replace the content words with letters and both arguments become: All A are B. All B are C. So all A are C. An argument is valid when there is no possible case in which its premises are true and its conclusion false. This form has that property whatever A, B and C stand for, so every argument with this form is valid, about whales, zorps or anything else.

    This was Aristotle's discovery. In the Prior Analytics he used letters in exactly this way, as placeholders, which is why he is usually counted as the founder of formal logic.

    The same idea gives you a test for invalid arguments. Take a suspicious argument, keep its form, and fill it with content that makes the premises plainly true and the conclusion plainly false. "All cats are mammals. All dogs are mammals. So all cats are dogs." Same form as a common bad argument, and obviously broken. I use this with my students all the time.

Other answers

  1. Sam Ellery

    Fellow

    This is why "that doesn't follow" is a different objection from "that's not true". In debate rounds students mix them up constantly. Validity is about the connection between premises and conclusion. Truth is about whether the premises match the world. You can have one without the other in either direction, and seeing which one you're attacking is half the battle.

    Helpful · 1
  2. Oskar Nyberg

    Fellow

    One refinement. It isn't quite grammar alone. You understood the zorp argument because you know what "all" means, and "so". Words like all, some, not, if and and carry the logical weight, and the content words can be swapped out freely. Which words count as genuinely logical is itself an old and real question. Tarski worked on it, and nobody has a fully agreed answer. But for your purposes Vikram's account is right.

    Helpful · 2
  3. Kavya Menon

    Fellow

    This is lovely. So the form is like metre in a poem: you can tell a line is a sonnet line before you know what it's about. And the logical words are the stressed syllables. I'll try the counterexample test on my family's arguments at dinner, though I suspect that won't make me popular.

    Helpful · 3