Divine Liars: the devil's in the details

Hartley Slater, on page 4 of his ‘Supposed Liars, Divine Liars and Semantics’ (The Reasoner 3(1), 3–4), said, about my (4*) = ‘God doesn’t believe that (4*) ever expresses a true proposition’ (in my ‘Liars, Divine Liars and Semantics,’ The Reasoner 2(12), 4–5), that:

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.

The Liar sentence ‘this sentence is not true,’ where the phrase ‘this sentence’ is referring to that very sentence, seems to be saying that what it is saying is not true, in which case it would also be saying that it is not true that what it is saying is not true, so it would also be saying that what it is saying is true. Does that mean that that sentence expresses two propositions?

Well, the proposition expressed by the self-referential ‘this sentence is not true’ seems to be that that sentence is not expressing a true proposition, and that certainly seems to be a different proposition to the proposition that that sentence is expressing a true proposition, because were it the case that that sentence expressed a true proposition, the first of those two propositions would seem to be false, and the second true.

That self-referential sentence seems to be saying, of itself, that it is not true. But if that sentence is saying of itself that it is not true, then it is not standing outside itself when it says that it is not true. It is not like when I say that it is not true. And when it says that what it is saying is not true, so that it is also saying that it is not true that what it is saying is not true, the latter is just part of what that sentence says when it says that it is not true. Because the former includes the latter, there is a sense in which there is only one proposition here, albeit one with a very strange part. There is also a sense in which we are talking about two propositions here, because the latter is only part of the former, and it is a part that seems to contradict the former. But the latter is part of the former, and this self-referential sentence is a very simple sentence, so we can see that it is not equivocating, and so I think that the former proposition with that very strange part is all that that self-referential sentence would be expressing, were it expressing a proposition. Perhaps that strangeness is so extreme that no proposition is being expressed. But the main thing here is that:

When we think of the proposition that that sentence is not expressing a true proposition, we might be thinking of the proposition that would be true were that sentence not expressing a true proposition, or we might be thinking of the very strange proposition that that sentence would be expressing were it expressing something propositional.

Because those are two propositions, not one, talk of propositions seems to have brought with it an increased risk of equivocation, not increased clarity. With other kinds of sentences, talk of propositions may well introduce clarity, but for these self-referential sentences, we might be better off sticking with talk of sentences and their meanings, logical and other. After all, formal languages are usually designed to avoid self-referential sentences.