Consider this theory. To utter a sentence is to offer a description of a proposition. Sometimes, whether contingently or necessarily, no proposition meets the description. That is a case of nonsense. Sometimes more than one proposition meets the description. That is a case of vagueness (ambiguity is a case where the sentence's words fail to determine the proposition, but the sentence as a whole does—in agreement with how one might read Frege on tense, I take the context to be a part of the sentence or, in his terminology, the "expression"). Subintensional vagueness is when the propositions that meet the description necessarily have the same truth value. Intensional vagueness is when they possibly have different truth values. Extensional vagueness is when they actually have different truth values. I suspect that subintensional vagueness occurs all over the place.

How do these descriptions work? I think in a recursive way. For instance, the sentence "*F*(*a*)" describes a proposition that applies *F*ness to *a*. What does it mean to say that a proposition "applies" *F*ness to *a*? Well, we can say this: necessarily, a proposition that applies *F*ness to *a* is true if and only if *a* exists and has *F*ness. But this is not sufficient to determine the concept of application—after all, there are many propositions that satisfy this description, such as the proposition that God knows that *a* has *F*ness and the proposition that *a* has *F*ness or 2+2=5. We can lay down a few more conditions on application. A proposition that applies *F*ness to *a* is not going to be truthfunctionally complex if *F* is not truthfunctionally complex. (But truthfunctional complexity needs to be defined, and it is hard to do that.) The functor *application* from property-object pairs to propositions is *natural*. Maybe something can be said about explanatory priority.

But, on the present theory, there is little reason to think that filling out the above story will narrow down the notion of application, or of *F*ness for that matter, so far as to ensure that there is only one proposition that meets the description given by the sentence "*F*(*a*)". Similar points apply to truthfunctionally complex sentences. Thus, "*s* and *u*" describes a proposition which the output of the conjunction functor as applied to the propositions described by "*s*" and by "*u*". But we cannot give an unambiguous definition of the conjunction functor. So subintensional vagueness is everywhere.

Now we have a story to tell about the classic liar sentence: "This is a falsehood." Such a sentences attempts to describe a proposition that denies truth to itself. But there is no reason to suppose that there is such a proposition, and indeed there is a very good reason to suppose that there isn't—namely, that the supposition that there is such a proposition immediately leads to a logical contradiction (what better argument could one ask for?). (One might try Goedel numbering and diagonalization. But Goedel numbering works for sentences, not propositions, and because of subintensional vagueness, the correspondence between sentences and propositions is not one-to-one.)

The contingent liar is tougher, but perhaps some generalization of the solution will work. (It might help if some propositions are contingent beings.)

## 2 comments:

Your theory assumes that we can begin with propositions. Is a proposition what an assertive expression means, more or less? E.g. "the cat is on the mat" means that the cat is on the mat. The meaning is the cat being on the mat. Surely we begin with the way things are, which is being described. To utter a sentence is often to offer a description of something, which is different to your theory; or do you say that the cat being on the mat is a proposition?

I think we know what it is for a cat to be on a mat, and so we know the meaning of "the cat is on the mat," but I doubt that many of us are clear about such terms as 'proposition'. And so Liars can be taken to be some evidence that propositions are not basic elements. E.g. if Liars are fairly true because they're rather nonsensical, in a loopy sort of way (as described in that link), then the only proposition is the one that's true (and false). Now, we could have a paraconsistent propositional logic, but such formal logics are just mathematical models of actual reasoning, and the meaning of such sentences involves more than that they're true and false (as in a simple equivocation), but also that their meaning is very weak.

In addition to my queasiness about propositions generally, I have the following objection. Descriptions are singular terms, so on this view, every sentence is a singular term. (Very Fregean.) But (a) this is weird, and (b) in fact sentences don't behave this way in English, unless we put them in quotes, in which case I think we're then dealing with names (or descriptions) of sentences.

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