Skip to content
Coordinates of ThoughtHome of Philosophy
Join
Question · Open

Does the dialetheist really believe contradictions, or has she changed the meaning of ‘not’?

Tomasz Wójcik Fellow
· 4 replies · 148 views
Modal & non-classical logicAnalyticGreek & RomanAristotleGraham PriestW. V. O. Quine#change-of-subject#dialetheism#liar-paradox#negation
Follow

A question I keep returning to in my own work. Quine, in Philosophy of Logic (1970), has a famous argument against "deviant" logicians. Suppose someone claims to accept a sentence of the form "P and not-P". Quine says: then whatever they mean by "not", it isn't negation. They haven't denied a law of logic; they've changed the subject. His slogan was "change of logic, change of subject".

Priest's dialetheism says that some contradictions really are true, the liar sentence being the leading example. "This sentence is not true" is both true and not true. Priest insists that his "not" is our ordinary "not", and that the classical theory of negation is the contested theory, not a neutral description of the word.

So who is right? Is there any non-question-begging way to settle whether a dialetheist is disagreeing with the classical logician, or just talking past her?

LikeAnswer
Follow4 answers

Members reply here. Reading is always free.

Sign in to reply

4 answers

  1. Oskar Nyberg

    Fellow

    I think Quine's argument proves too much. If accepting different inferences for "not" means you've changed the meaning of "not", then intuitionists and classical logicians also talk past each other about excluded middle. But they clearly disagree: they argue, they cite reasons, they sometimes change their minds. A theory of meaning that makes every logical dispute verbal is a bad theory of meaning.

    Helpful · 1
    1. Tomasz Wójcik

      Fellow

      Oskar, I'm persuaded on the over-generation point; the intuitionist case is decisive against the strong form of Quine's slogan. Derek's revenge problem is the better way to put what's left: not "you've changed the subject", but "can you say what you disagree with me about, in terms we both accept?"

  2. Giulia Ferrante

    Fellow

    The ancient version of the argument is Aristotle's in Metaphysics Gamma: anyone who denies non-contradiction can't say anything determinate, because if "man" doesn't exclude "not-man" the word signifies nothing. That's close to Quine's point, two thousand years early. Priest discusses Aristotle's arguments at length and thinks they fail. Whether they do is, to my mind, the real battleground: Quine gives a slogan, Aristotle gives an argument.

    Helpful · 2
  3. Derek Hollis

    Fellow

    Practical angle. Dialetheists have trouble with "revenge". If I want to say a sentence is only false, not also true, I need some device the dialetheist can't turn into another true contradiction. Priest's answers to this are subtle and disputed. That's evidence for Tomasz's worry from the other side: it's hard to tell when a dialetheist is disagreeing with you, because the tools you'd use to state the disagreement are the ones in question.

    Helpful · 3