Friday, January 02, 2009

Divine Liars: The devil's in the details

Hartley Slater falsely supposed that I think there’s no essential difference between the sentential and the propositional formulations of (strengthened) Divine Liars, at the start of his ‘Supposed Liars, Divine Liars and Semantics’ (The Reasoner 3(1), 3–4). My ‘Liars, Divine Liars and Semantics’ (The Reasoner 2(12), 4–5) had merely questioned a presumption of Patrick Grim’s sententially formulated (4) = ‘God doesn’t believe that (4) is true.’ Grim had presumed without comment, let alone justification, that those two instances of ‘(4)’ could be the same proper name. And although such naming practices are fairly standard nowadays, that’s why the idea that their legitimacy is challenged by the paradoxicality of their application to Liar-style sentences could be of some interest.
......Propositional reformulations, such as my tentative (4*) = ‘God doesn’t believe that (4*) ever expresses a true proposition,’ raise different and more difficult considerations, which I’d simply ignored in order to state my question as clearly as I could within a thousand words. An obvious difference is that although a semantic problem with sentences is prima facie a problem with propositions, and vice versa, hardly anyone argues over whether sentences exist. Less obviously, although when considering (4)—which can be so-named even if I’m right about the illegitimacy of that naming practice, if the occurrence of ‘(4)’ within (4) isn’t also as (4)’s name—it had seemed acceptable to implicitly presuppose some ordinary linguistic notion of literal truth, perhaps I should make that notion more explicit when properly reformulating (4) propositionally. So instead of (4*) consider (4**) = ‘God doesn’t believe that the modern English sentence (4**) could ever express any true proposition literally.’
......That’s still pretty tentative, e.g. the modality might be difficult to explicate, and even literal truth is notoriously difficult to define. ‘Snow is white,’ for example, literally means that snow is white, and is true if indeed snow is white, but it’s hard to say what such repetitions mean in other, more general words. Still, there’s presumably some such semantic rule, say (T), that’s both true enough and applicable to such sentences as—for a simpler example (called ‘B’ earlier)—(L) = ‘This sentence is not (now) true.’ The parenthetical ‘now’ is only there to reduce the risk of equivocation, incidentally.
......Suppose, if only for the sake of reductio, that (L) was expressing something literally. What (L) would then be expressing would, via (T), at least include that (L) isn’t true, which is (in view of the self-reference) that it isn’t true that (L) isn’t true, which is (via double-negation elimination) that (L) is true. Now, what I’ve just shown is, I think, that the last two italicised expressions would be expressing the same proposition if (L) was being used to express any proposition literally. And maybe I’ve effectively shown that (L) expresses no proposition literally, i.e. that it’s nonsense. But I’ve certainly not thereby allowed that sentences may express more than one proposition. Recall that Slater said (ibid, 4):
Cooke says, with regard to ‘Liar sentences’, that ‘they do seem to be saying, not only that they are not true, but also, if less obviously, that they are (therefore) true’. So sentences, he allows, may express more than one proposition, even if they may express one proposition more obviously than another. But if so then one cannot immediately derive, with respect to the previous case that the (one and only) proposition that (4*) expresses is (the obvious one) that God doesn’t believe that (4*) ever expresses a true proposition.
A sentence may of course express different propositions, e.g. literally and analogically, or by being equivocal, or when it’s expressed by different people, or at different times or places, or because the language in which it exists changes, etc. But Slater will, I suspect, have difficulty indicating what other proposition could have been expressed by (4*)—or better, (4**)—literally. If he has to use different words to those of (4*), then is it really expressed by (4*)? And if he doesn’t, then why wasn’t it expressed when he used those same words to express the ‘obvious’ proposition?
......Furthermore even if one may, in such a way as Slater’s (above), point unambiguously to one proposition, something like the original problem with (4) would arise. Note that if (4**)—or (4*)—is, as I believe it is, nonsense, then it doesn’t express any proposition literally, and so ideally one wouldn’t be able to derive that it does. But if, counterfactually, (4**) was expressing anything literally, then presumably by (T) that would be the proposition that God doesn’t believe that the modern English sentence (4**) could ever express any true proposition literally. And that does seem like a proposition to me, if only because I’d assert it, in so many words, on the grounds that (4**) is literal nonsense and that God would, were he real, be wise enough to know that. So, whether or not any other propositions are expressible by (4**), literally or otherwise, we’ve something like the problem that (4) presented to theists. That is, if (4**) could be used to express a true thought literally then God doesn’t believe—via the truth of that (last italicised) proposition—that it could be so used, whereas if (4**) couldn’t be so used then that proposition is true, whence any completely omniscient being would believe it.
......Something like it; but as I say, it may be that a reformulation more precise than (4**) is required to yield a paradox sufficiently close to that of (4). In fact, I happen to be agnostic about whether that’s even possible, about whether there’s at least that essential difference between the two sorts of formulation. But the point is that the traditional resolution of Liar-style sentences—that you can’t, by talking nonsense, say that you aren’t telling the truth—applies to any legitimate formulation, and would in particular apply to sentential formulations, were they allowed.

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