Reply to Roger Jones's post, “Compositionality and Semantcs” from Tuesday, March 1, 2011.

Okay, it is later, and I have finished my teaching and grading for today. And, I have thoroughly read all your comments now Roger. Thank you for them.

There is a difference between

[a] the quasi-practical project of creating partial compositional semantics and then trying to embed these in systems that may, more-or-less well, be capable of processing language

and

[b] answering the philosophical question, what is the nature of meaning.

To do [a] a partial compositional semantics is certainly useful. I know many people who work on such problems every day, and over the years I have myself, as well, as a practical computer engineer.

But, [b] is a very different problem. Numerous philosophers, in attempting to do [b] have tried to do so by appealing to the existence of compositional semantic theories for natural languages.

Let's talk about compositional semantic theories for natural languages. There are two flavors: compositional meaning theories and compositional truth theories.

A compositional truth theory (CTT) is what Tarski in 1933 showed how to give for a formal language. It was Davidson in the 1967 article “Truth and Meaning” who first seriously proposed developing CTTs for natural (rather than merely formal) languages, and embedding these in an overall theory of interpretation (which is tantamount, if such a scheme should work, to a theory of meaning).

Pretty much immediately on delivery of Davidson's theory, people realized that Davidson had not said enough to indicate how a CTT can be at the heart of an adequate theory of meaning. See Hartry Field's classic paper “Tarski's Theory of Truth” (1972) from the Journal of Philosophy and Christopher Peacocke's “Truth Definitions and Actual Lanugages” (1976) from Evans and McDowell, Truth and Meaning (1976). I don't believe anybody has made much of an advance in this style of meaning theory since that time, although Davidson worked on it for the rest of his life, and other continue to work on the possibility. But, it is just a possibility, and there is certainly no proof of concept, if I may. I believe Schiffer's critique of the possibility of such an idea in Remnants of Meaning is probably the last word on the subject as a real possibility. In my dissertation, I go through Schiffer's critique and adopt it myself.

That leaves us, basically, with compositional meaning theories (CMTs). CMTs are different from CTTs. CTTs result in T-sentences, such as

[1] “Onyx is black” is true if and only if onyx is black.

This is not a sentence that reports a relation between two objects, but a sentence that says two sentences are material equivalents:

[2] “Onyx is black” is true

and

[3] Onyx is black.

The sentence [1] reports that [2] is the material equivalent to [3]. The symbolization of [1] in first-order logic is:

[4] P ≡ Q

The theorems of a CMT, however, have a completely different form:

[5] “Onyx is black” means that onyx is black

which has the form:

[6] M(x, p)

where “M” is the meaning relation, x is a sentence, and p is a proposition. The symbolization of [5] is:

[7] M(“Onyx is black”, that onyx is black)

What is that onyx is black? It is a proposition. There are different theories of propositions. The one you seem to favor, Roger, is the one that says that propositions are sets of possible worlds. In that case, that onyx is black stands for the set of all possible worlds in which onyx is black.

The idea of mapping natural language sentences onto propositions construed as sets of possible worlds is one of the most common forms of CMT. No doubt, partial semantic theories are possible in such terms. But, certainly right now, the prospect of an adequate theory of meaning in terms of a CMT that construes propositions as sets of possible worlds seems less than promising, as argued in Schiffer (1987), Remnants of Meaning. I won't review those arguments here, but just lay out the landscape—the framework—I am coming from, so that you have something to go by as you read or reread Schiffer's actual detailed arguments on this question in Remnants. In general, though, the basic problem for CMTs which construe propositions as sets of possible worlds is that there is no adequate answer to the problem that the set of possible worlds in which [8] is true is the same as the set in which [9] is true, and yet [10] can be true without [11] being true:

[8] Mark Twain wrote “The Man That Corrupted Hadleyburg”.

[9] Samuel Clemens wrote “The Man That Corrupted Hadleyburg”.

[10] Sheila believes that Mark Twain wrote “The Man That Corrupted Hadleyburg”.

[11] Sheila believes that Samuel Clemens wrote “The Man That Corrupted Hadleyburg”.

Trying to resolve this problem within an adequate THEORY OF MEANING is the problem. It is one thing to say that it can be done, and it is quite another to show how. Nobody has ever shown how and considering particular attemtps to do so, the matter seems impossible. That is not, again, an argument by itself. But, it is the form of the argument I find persuasive on this question. Perhaps give me some indication if you think that this problem has some reasonable solution so I can think through what you are thinking on this score. I can't think of a way out of this.

Of course, to complete this argument it is necessary to understand what a THEORY OF MEANING does that is different from what a CMT does. This is one of THE MOST MISUNDERSTOOD points among people who discuss such things. A CMT merely maps sentences onto propositions (the referents of that-clauses). How you construe propositions matters, not as much for the CMT, but for the THEORY OF MEANING you embed the CMT in. Just as a Davidsonian CTT must be embedded in a larger theory of interpretation of some sort (see, again, Field (1972) and Peacocke (1976)), likewise, a CMT must be embedded in a larger theory—A THEORY OF MEANING—that explains how the mapping from the x's to the p's of M(x, p) (see [6], above) is actually implemented by a linguistic community. That is, a theory of meaning is the tantamount to David Lewis's request for an Actual-Language Relation. The CMT is one thing, but the theory that says what it is about a community of speakers of the language the CMT describes is another. Sure, you can conflate [8] and [9] in a CMT all you want. But, how will such a CMT be implemented in a community of English speakers who distinguish between [8] and [9] and between [10] and [11]? Without giving a principled answer to this question, whatever your CMT is, you haven't given a THEORY OF MEANING, and that is the quest here.

Perhaps you have answers to these questions, but I didn't really see that in your comments. Let me know if I am missing anything.

--Russell Dale