Against Course-Grained Propositions

According to the course-grained view of propositions, propositions are identical iff necessarily equivalent. The usual complaint about this way of thinking about propositions is that it is implausible with regard to various examples involving propositional attitudes (e.g., it leads to logical omniscience). But issues about propositional attitudes are difficult and controversial, and I think it would be better to base one's rejection of course-grained propositions on something else.

So I've been tinkering with a new sort of argument against course-grained propositions. Consider the following claim.

It is logically true that everything is self-identical.

According to the course-grained conception, propositions have no logical form and thus are never logically true. Accordingly, there are two positions that a proponent of the course-grained conception might take on this apparently true claim. The first is to say that this claim is true, in which case he will wish to interpret it as attributing logical truth, not to the proposition that everything is self-identical, but to the sentence ‘Everything is self-identical’. The other approach is to say that the claim is in fact false because it attributes logical truth to a proposition. One would then say that the claim seems true, or is the sort of thing that we would ordinarily say, because it conveys something true—namely, the meta-linguistic proposition that ‘Everything is self-identical’ is a truth of logic—perhaps by means of Gricean or quasi-Gricean pragmatic mechanisms.

It seems to me that both positions fail. To see why, consider this modal claim:

It might not have been logically true that everything is self-identical.

This claim does not seem to be true (in fact, it seems false). But, on the course-grained conception of propositions, the claim should seem true. There are two possibilities. The first possibility is that we are confusing the sentence and the proposition even here, in which case the claim should seem true because it conveys (or expresses) the true proposition that the sentence ‘Everything is self-identical’ might not have been logically true. The second possibility is that we are not confusing the sentence and the proposition, in which case the claim should still seem true, since the proposition is not and could not have been logically true on the course-grained conception. Either way, then, this modal claim should seem true on the course-grained conception. Hence, because the claim seems false, not true, the course-grained conception of propositions is mistaken.

Comments

[Juhani Yli-Vakkuri]

The problem I see here is that there are good reasons for thinking--indeed, something like a proof--that "It is logically true that" is not a content operator at all, but a crypto-quotational operator. For example, "It is logically true that all Fs are Fs" goes from true to false as soon as you replace one of the occurrences of "F" with any other expression, no matter if it's a synonym. That does seem to clash with your claim that this sentence:

(*) It might not have been logically true that everything is self-identical.

is false, but I would rather reject that claim than our usual model-theoretic characterization of logical truth, which is sensitive only to expressions, not their meanings. What's more, I'm not even sure that these ideas are in conflict: (*) could be false for two reasons: 1) because "it is logically true that" is a content operator, or 2) because expressions have their meanings essentially. (Notice: expressions, not strings of sounds and the like.) I'm not unsympathetic to #2. I think Tyler Burge gives a very attractive defense of it in his “Self-Reference and Translation” (in F. Guenthner and M. Guenthner-Reutter, eds., _Meaning and Translation: Philosophical and
Linguistic Approaches_ [London: Duckworth, 1978]). Martin Davies (_Meaning, Quantification, and Necessity_ [London: Routledge and Kegan Paul, 1981]) appears to treat #2 as a matter of convention; I'm not unsympathetic to that either.

[marc moffett]

Hi Juhani,

Although it is not entirely uncontroversial, there are very good reasons for thinking that "It is logically true that" is not a syntactic constituent. Rather, the 'that'-clause, "that everything is self-identical", is an intensional abstract which denotes the proposition expressed by the embedded sentence. Against this background assumption, Chad's sentence

"It is logically true that everything is self-indentical"

should be understood as attributing a property--the property of being logically true--of the proposition denoted by the 'that'-claus. More perspicuously:

"That everything is self-identical is logically true."

Chad,

Could you say a bit more about why I should accept that the denial that propositions have logical form entails that they cannot be logically true? This makes a fair amount of sense if one construes "logically true" as "true in virtue of its form". But you can't mean that, since the sentence "Everything is self-identical" is not true in virtue of its form alone. But even if it were, why should the advocate of coarse-grained propositions accept this analysis of logical truth?

[Chad]

Juhani,

Thanks for the comments!

It isn't clear to me how your first reply works. I said that (*) seems false but should seem true given the course-grained conception. Are you saying that (*) doesn't seem false to you? The way you put it sounds as if you think it does seem false but you're willing to accept it anyway (in order to preserve the model-theoretic account). But that isn't at odds with any premise in the argument. Furthermore, I'm not sure I understand why I can't preserve the model-theoretic account.

Also, the sentence 'everything is self-identical' wouldn't have been logically true if it hadn't existed. Since it might not have existed, it might not have been logically true. That holds whether it has its meaning essentially or not.

Marc,

I was assuming that logical truth is something like truth in virtue of logical form. But there is independent reason anyway to think that course-grained propositions can't be logically true. For if course-grained propositions can be logically true, then every necessary proposition is logically true. The proposition that water contains hydrogen is a counterexample to such a view. That much should be clear. And once that is clear, there is no reason for proponents of the course-grained view to reject the intuitively attractive view that logical truth is truth in virtue of logical form.

[marc moffett]

Chad, OK. I take it that coarse-grainers still want a compositional semantics. So, for instance, the predicate "is self-identical" expresses the property of being self-identical, etc. Might they, consequently, try to articulate logical truth in conceptual terms? The thought would be that in the present case, simply understanding the concepts involved (in particular, understanding the concept of self-identity) is sufficient for seeing that the sentence is true/necessary. If so, then the coarse-grainer could take a modified version of the first horn of your dilemma: we are confusing the proposition with something like the interpreted logical form of the sentence (i.e., the "thick" sentence).

[Chad]

I don't see how the "interpreted logical form of the sentence" is supposed to differ from a fine-grained propoistion. Can you explain?

[marc moffett]

It is a sentence (or, rather, the LF of a sentence) with semantic values at the nodes. Some people, of course, think that ILFs are propositions, but I don't off-hand see why one would have to say that. (Indeed, I think that there are such things as ILFs, just set-theoretic constructs, and I definitely don't think they are propositions.)

[Chad]

So "ILFs" are structured entities semantically associated with sentences that have truth-values and bear such properties as logical truth and necessity. That seems to give up the game to me. Maybe it would help if you could tell me what work the course-grained entity would do in that case that wouldn't be more plausibly accomplished by the "ILF".

[marc moffett]

Chad, Well, you might not want ILFs to be propositions for the same reason you don't want sentences to be propositions, namely, they involve syntactic entities and so can't capture attitude ascriptions across monolingual speakers of distinct languages.

Moreover, I didn't say that ILFs were "semantically associated with sentences"--though I am not entirely clear on what that means. Depending on what semantic information you choose to incorporate, there may (or may not) be a propositions located at the top-node of the ILF. There plainly are such things. But it is a contentious, and I think mistaken, philosophical thesis that they are meanings.

Moreover, it might seem more plausible to attribute logical truth to sentences rather than ILFs (as I did above): a sentence is logically true iff it can be seen to be (necessarily?) true simply on the basis of the concepts involved in its associated ILF (i.e., iff one must assign t to the top node of the ILF simply in virtue of one's semantic knowledge).

But look, I invoked ILFs purely for heuristic reasons. The general point is that a person is unlikely to think of a sentence as simply an uniterpreted entity (as linguistic items are so often construed in model theory--see Devon Belcher's dissertation). So in effect, I am accusing you of constructing a false dilemma: either we take the sentences you cite to be about uninterpreted sentences or about propositions. What I am suggesting is that the coarse-grainer might opt for a third entity, interpreted sentences (linguistic items) of some variety and to define logical truth in conceptual or semantic terms.

I think that something like this move is far and away the most natural move for them to make. Well, actually, the other move is to deny your claim that "Everything is self-identical" is not true in virtue of its syntactic logical form. If one accepts that there are underlying levels of syntactic representation, then one might try to argue that the underlying syntax is: (All x)(x = x) rather than (All x)(Sx).

[marc moffett]

One follow up point. Maybe we are confusing the propositions with ENGLISH sentences. And one might think that to individuate a syntactic string as a sentence of English one must invoke semantic information. So, for instance, the linguistic string "Everything is self-identical" is an English sentence only if it involves English words (that isn't quite right, but close enough to make the point). And you might think that "self-identical" is an English word only as an interpreted item. So is an English word, but isn't. It is this point that I am trying to get mileage out of.

[Added: Actually, having just glanced back at Juhani's post, I realize that he is at least in part making the same point.]

Jhani, I also wanted to clarify the point I was making in response to your post. There are very good reasons for thinking that the complentizer "that" is a syntactic constituent of the CP. The general point I was getting at was that one needs to give a general semantic treatment of 'that'-clauses which is not tied to the specifics of 'logical truth'. If you think that all 'that'-clauses are quasi-syntactic, then nothing I said is relevant to your point--but I think that would be a mistake.]

[Chad]

Marc,

Sorry for the slow reply--I've been busy with two committees etc. etc. So let me make sure I understand the general sort of response you are suggesting: you think that there may be a reasonable way of looking at expressions (as "thick" or "interpreted" expressions) according to which there are some sentences that had to be logically true--sentences S such that, necessarily, S is logically true. Is that right? Would these things be necessary existents?

[marc moffett]

I think that pretty much gets it.

Are they necessary existents? Doubtful, but it depends on your ontology. If you take languages to be abstract objects (Katz) and you take abstract objects to exist necessarily, then yes.

[marc moffett]

Chad, A follow up question. Rather than read "logically true" as "true in virtue of its logical form" why not read it instead as "a truth of logic"? So understood, whether or not a given proposition is logically true depends a bit on how narrowly or widely you construe logic.

Something like what I was trying to push is covered in (I think) section 2 of the SEP entry on logical truth.

[Chad]

I think that something is a truth of logic iff it is true in virtue of its logical form (or something like that). Of course whether one counts a proposition as logically true will still depend upon how narrowly or widely one construes logic, since one's view of logical form will co-vary with one's view of the scope of logic.

I was supposing (plausibly I think) that, necessarily, a thing is logically true only if it exists. Thus, if it is necessary that a thing is a truth of logic, then it is necessary that it exists. So if you appeal to some special notion of sentence in the present context, you'll have to build in necessary existence. But no sentence-like entity exists necessarily. Or at least I didn't think it is plausible that any sentence-like entity exists necessarily. One reason is that I think that sentences have their meanings because of certain activities on the part of language users. But if a sentence exists necessarily (and has its meaning necessarily), then it has to at least possibly exist and have its meaning quite independently of any language users. That seems implausible to me.

[marc moffett]

Regarding the modal claim. There is, of course, the familiar disinction between being true at a world and being true in a world. A conceptualist might claim, for instance, that a sentence/proposition may be logically true simply in virtue of being true at a world (i.e., when evaluated relative to that world). Such a person might, however, deny that the sentence/proposition is true in that world (e.g., if it is a world with no sentient beings).

Second, you say that "sentences have their meanings because of certain activities on the part of language users." But this is pretty contentious. If you take the Schiffer/Lewis view of meaning in a population, you end up with an antecedent specification of languages as functions functions from forms to meanings.

[Chad]

There are several ways to draw the true-in/true-at distinction. In drawing it, I think you face a dilemma. On the one hand, you can go for an account like, say, Adams's original account, in which case you don't get to say that 'S is logically true' is true-at worlds in which S doesn't exist. (That's because, for Adams, if a claim is true-at a world but not true-in that world, then it has to be the *negation* of some claim about an object that doesn't exist in that world.) Alternatively, you can give a different account--one on which you allow predications about objects that do not exist in a given world to be true-at that world. But, following Adams, I don't see the difference between saying that and denying serious actualism--roughly, the thesis that, necessarily, a thing has properties only if it exists. I was presupposing serious actualism. If you are willing to deny serious acutalism, then perhaps we can just agree on the conclusion that course-grainers can't be serious actualists.