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December 1st, 2009

Correspondence Theory and Paradoxes

I’ve been rereading John Bigelow and Robert Pargetter’s “Science and Necessity”, which is full of good stuff. (Sadly, it isn’t in the Rutgers library, so it was a bit harder to read than it should have been.) They open with a defence of the correspondence theory of truth against various rivals. Much like I think the JTB theory of knowledge, and the “UnGettierized” JTB theory (as discussed here) fail because of the paradoxes, I think the correspondence theory of truth fails for the same reason. I assume this isn’t a new point. (It is at least implicit in several arguments Roy Sorensen has made, for instance.) The problem is that (Co) is obviously true.

(Co) (Co) does not correspond to reality.

Assume (Co) corresponds to reality. Then it is true, assuming at least the correspondence theory. So it does not correspond to reality, assuming only the weaker version of the T-schema (that if p is true, then p). That contradicts our original assumption. So (Co) does not correspond to reality. And that’s what it says, so presumably it is true. (Though this step does require a p, therefore p is true inference, which some might find problematic.) So something that does not correspond to reality is true, contradicting the correspondence theory.

Bigelow and Pargetter, like many defenders of correspondence, focus primarily on various kinds of ‘anti-realist’ alternatives to the correspondence theory, such as coherentist and pragmatist theories. But I don’t think those are the major problems for the correspondence theory, or truthmaker like alternatives to correspondence. Rather, the paradoxes are the real problem.

Posted by Brian Weatherson in Uncategorized

6 Comments »

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6 Responses to “Correspondence Theory and Paradoxes”

  1. djc says:

    Ah, the universal refutation of all theories of truth. To refute “For all S, S is true iff S has phi”, consider D: “D does not have phi”. One can even refute the theory that holds that S is true iff S is true this way!

    December 1st, 2009 at 10:12 am
  2. Andrew Bacon says:

    “[…] That contradicts our original assumption. So© does not correspond to reality. And that’s what it says, so presumably it is true. (Though this step does require a p, therefore p is true inference, which some might find problematic.)”

    That last step seems to be more like an application of necessitation (if |- p then |- T(“p”)). Necessitation is much weaker than the axiom (p->T(“p”)) or the rule p |- T(“p”) both of which I’m much less inclined to believe than the principle that you can’t prove untrue things.

    @djc: you can’t get a contradiction from “S is true iff S is true” without some extra assumptions which are already contradictory (as it’s already a theorem of propositional logic.)

    December 1st, 2009 at 10:33 am
  3. Brian Weatherson says:

    Good point Andrew, this is a weaker rule than I was suggesting. So it’s unlikely the proof fails there.

    Dave, doesn’t this suggest there is no such thing as a theory of truth?

    December 1st, 2009 at 11:31 am
  4. djc says:

    Andrew: Indeed. Brian: The observation that analogous reasoning refutes tautologies as well as substantive theories might be taken to suggest that the problem lies with the reasoning, not with the theories. (Cue: solution to the Liar paradox, which alas I don’t have.)

    December 1st, 2009 at 12:53 pm
  5. Brian Weatherson says:

    The problem is that the reasoning looks a bit like reasoning that leads to paradox, and a bit like unproblematic reasoning we use all the time. So I’m not sure that we should reject the reasoning just because of the first analogy.

    Here’s a slightly more substantive way of putting the point. Correspondence theories of truth are committed to the solution to the Liar paradox generalising to explain what’s going on with (Co). That might be right, but I don’t know why I should believe it is right, or what grounds correspondence theorists have given me to believe it is right.

    December 1st, 2009 at 12:59 pm
  6. jon says:

    Brian,
    If we have Tp -> p and necessitation (for T), then our theory of truth is inconsistent. So the correspondence theorist probably shouldn’t be too worried that there are truths which don’t correspond to reality.

    However, do you really need a truth-predicate to run your argument? If the correspondence theorist agrees to “If p corresponds to reality, then p” (for all p), you can run the first part of your argument and conclude that (Co) does not correspond to reality, and hence that (Co). This seems pretty embarrassing: the correspondence theorist is committed to asserting (Co) (on the basis of proof) but also committed to saying that (Co) doesn’t correspond to reality.

    December 1st, 2009 at 1:05 pm

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