It's a fun paradox, and Peter Eldridge-Smith argues (convincingly, by my lights) that it creates problems for the claim that 'semantic' contradictions can be true, but not 'metaphysically' substantive ones. JC Beall's half of the exchange is available for free here.
(Eldridge Smith's half is available for free too, but if you're reading this on a computer at an institution with an online subscription to Analysis.)
One problem I have with Beall's response is that it's far from clear what sort of "impossibility" he has the resources to assign to base-language contradictions. It's one thing to say that the actual world lacks them--it certainly seems to!--but Beall, of course, can hardly claim that non-trivial worlds containing base-language contradictions are *logically* impossible. As he himself convincingly argues in Spandrels of Truth, dialetheists can hardly go around claiming that some falsehoods are 'more false' than others, such that contradictions involving them really would be explosive, since one could always construct a paradoxical 'spandrel' which attributed precisely this sort of extra-special-super-falseness to itself. If the claim is that they're metaphysically-but-not-logically impossible, I think that requires considerable fleshing out. *Why* would they be metaphysically impossible?
Someone with orthodox views would say that they're metaphysically impossible *because* they're logically impossible. Once we've blocked off that route by accepting (even "purely semantic") true contradictions, an alternative explanation is required.
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Hi Ben,
I've read Beall's half. Although I can't access Smith's half, and I haven't read Spandrels of Truth, I'll present a possible response for Beall: Base-language contradictions are metaphysically impossible because they attribute incompatible properties to something. For example, a tomato can't be both red and not red, and Pinocchio's nose can't both grow and not grow, because the nature of redness is such that its instantiation by a given tomato at a given time precludes it's non-instantiation by that tomato at that time, and similarly for the event or process of Pinocchio's nose growing. (Indeed, similarly for any property or event or process.) But as a deflationist, Beall could say that "true" and "false" don't express (substantive) properties. To assert that some liar sentence is both true true and false isn't to ascribe incompatible properties to it, because it isn't to ascribe properties to it at all. For some liar sentence L, "L is true" has the same content as "L is false", both of which have the same content as L. So base-language contradictions can't be true because a base-language sentence can't be true (false) without something instantiating (failing to instantiate) some substantive property. Not so for spandrels/semantic contradictions. I'm not sure if this makes base-language contradictions *logically* impossible, but if this reply works they don't need to be in order to be metaphysically impossible.
Jason,
Yeah, I agree that some explanation roughly along those lines (despite what from my point of view--and, I'd tend to suspect, maybe Beall's....?--sounds like some uncomfortably heavy-duty, super-realist kind of metaphysics) is probably the best that can be done here to make sense of logically possible but metaphysically impossible base-language contradictions.
Of course, this way of explaining the difference between semantic and metaphysically substantive contradictions does underline why I think deflationism is such a strange fit with the claim that Liar-type sentences (not "Liar-type" in the sense of "paradoxical" but Liar-type in the sense of being, in Kripkean terms, 'ungrounded') are meaningful, truth-evaluable, etc.
Given the assumption that, when one says Sentence S is true, one isn't, in the normal sense, ascribing a property to S, what *is* one doing? I'd say that one is asserting the original sentence--that is to say, one is ascribing whatever original substantive property the original sentence ascribes to its original referent. Hence, like Quine says, when one says "'Snow is white' is true", one is "attributing whiteness to snow"--nothing more, nothing less. If one holds this view about ascriptions of truth to base-language sentences, *and* one thinks that "spandrels" are meaningful, truth-evaluable, etc., then it seems to me that one is in a terribly awkward position when having to explain what on earth we're doing when we say "the Liar is true." Certainly not ascribing a property to anything!
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