Roger Jones's post of April 6, 2011 on Compositionality in my Chapter 4.

April 6, 2011

Dear Roger,

I think we need to agree on some terms so that we can engage with clarity on the issues. I am not at all sure there is an issue between your view and mine. I think we are, as you suggest, talking past each other. But, let's try to sort through all this.

Could you state short, clear definitions of the following terms:

1. compositional truth theory
2. compositional meaning theory
3. compositional semantic theory
4. theory of meaning

When you say "It seemed to me that whatever problems there might be in formal semantics for natural languages, these could not be problems arising from compositionality," perhaps you are right: but, that wouldn't disagree with anything I said. It will depend on how you define the terms above which I am not very clear on.

You wrote the following in your piece in reply to me on March 1, 2011 which is why I took you to be talking about possible worlds:

'A truth conditional semantics is one which gives for each sentence in some language the conditions under which that sentence is true. To do this one must identify the intended subject matter as a range of possibilities in the context of which sentences of the language are to be understood. In the specific case of some ordinary first order language a "possibility" in this sense would be a structure or interpretation of the language. For a language in which contingent propositions are expressed, a "possibility" would be something like a "possible world".'

I apologize for misunderstanding. You say "something like a 'possible world'", and so I take it it now that you have corrected me that I focused too much on the "possible world" part of that last bit, and not enough on the "something like". Please let me know what you do have in mind. That may come out more clearly when you define more precisely what you mean by the terms 1 - 4 above.

I must say, though, that your comments do seem to be addressed towards what I am saying in my chapter 4. You say you want to give reasons why you are "sceptical about all this scepticism." So, I read your remarks in the context of that thought.

I fully agree with you, though, that if there is a "truth conditional semantics" it will be a "compositional semantics" for a natural language. But, as a mathematical point, this need not be the case: it will depend on how you define your terms. If you make compositionality depend on actual syntactic composition, then it is easy to create a mathematically possible language that has a truth conditional semantics that is not "compositional" (in that it doesn't look at the details of syntactic composition and how they bear on--contribute to--the meaning of the sentences of the language. Here it goes: consider the language that has one sentence, "Joe is tall" which is true if and only if Joe is tall. Here is a truth-conditional semantic theory for that language which is not "compositional" in the ordinary sense of dealing with the syntax of the sentence:

"Joe is tall" if and only if Joe is tall.

That's it. So, if you are speaking only about mathematical possibilities, then it will depend on how you define a "compositional semantics" whether or not a truth-conditional semantics of a language need be compositional. If "compositional" means that the truth conditions must be determined by assigning meanings to the sentence parts, then this has not happened in this case. Every finite language (that is, language with finitely many sentences) can be provided with a truth-conditional semantics without there being a "compositional semantics" in the sense just suggested (which is the ordinary sense, I take it).

But, perhaps all this shows is that you meant "mathematical" in a more restricted sense in which it only applies to infinite languages. Fair enough. In that case, it is not easy to come up with a truth-conditional semantics that is not compositional in the above suggested sense.

I don't take there to be any issues here, I am just hoping that by talking through these thoughts you will get a better sense of how I use this sort of language and how I reason about these things.

I don't understand what you mean when you say "Note here that my terminology differs from Russell's, and in particular that "a semantics" is to be understood as an abstract entity, like a function or a set, as distinct from, say a formal system (though that also is an abstract entity)." I have the same thing in mind. I follow David Lewis's formal picture in "General Semantics" pretty tightly in my dissertation, even if I don't accept his suggested possible worlds semantics there. A "composition semantic theory" for me in my dissertation is not thing but an abstract object, a formal mapping in the case of a Compositional Meaning Theory from sentences (with their syntactic structures) and lexical meanings to propositions, and a finitely statable theory (set of sentences) in the case of a Compositional Truth Theory that entails all the required T sentences (in the sense of Tarski) for the language. I am doing nothing whatsoever non-standard in my book. This is just the usual stuff, and it seems it agrees with what you are saying precisely. I am not sure why you are seeing things differently. Perhaps it is because of the typologically crummy version of my dissertation that was all that was available until yesterday. I apologize for that.

You write "This conjecture I followed up with some remarks about the kind of thing which might in a compositional semantics be the meaning of a sentence (a proposition), to which I said little more than that it would be some kind of set." You said was what I quoted above about "possible worlds" that I now realize I must have misunderstood. But, I hope you can see why I took you to be talking about possible worlds from that. I apologize for the misunderstanding.

Then you write "This is all pretty vague stuff, and the main point was simply the conjecture to the effect that compositionality in itself is in principle not a problem." But, you wrote that you were going to raise scepticism about my scepticism, so I thought you were responding to my arguments about this. If all you are saying is that there can be compositional semantic theories of a simple sort for parts of natural languages, I agree with you one hundred percent. But, if you want to raise doubts about my doubts that compositional semantics will play some sort of meaningful role in a theory of meaning, it seems you have to say a bit more than that. Perhaps I am wrong. Here I am certainly just misunderstanding you.

You wrote "Russell then responded. However, so far as I could see, his response did not actually respond to anything that I wrote." I apologize again. I certainly was trying, as I hope you see. (I try above to show you where I was coming from in your remarks to say the sorts of things I said.)

You wrote "He did not comment on the conjecture which was the main point of my message, nor on the supporting definitions, even though the concepts in terms of which I understand the problem are quite different to the ones he has used."

I comment in this message on the conjecture as you restated it in this recent communication. Your definitions didn't seem so different from mine, so I really didn't see any reason to comment on them. Perhaps you can explain to me what, precisely you see as the difference in your definitions and mine. (That is why I asked you at the top to define some of the basic terms.)

We come to the core of your recent post now. You write: "My point of entry was a negative reaction to Chapter 4, which seems to me to be offering principled reasons why formal semantics has nothing to offer to a theory of meaning. Whether that is Russell's intention is not clear to me, for reasons which will emerge if we progress this question. This is really the material just in 4.1 I am talking about here."

And you continue: "So I would like to know of Russell whether that was what he was intending to do in 4.1. in which case I am interested in looking closer at the arguments which he presents in that section."

Answer: No, that is not what I am doing in section 4.1. In section 4.1 I am NOT arguing that a "formal semantics has nothing to offer to a theory of meaning." I am only arguing that there is nothing a priori in the concept of a formal semantics that makes it NECESSARILY be a part of a theory of meaning for the language the formal semantics is concerned with.

It is one thing to say [F] is a formal semantics for L and another to say [F] is an essential part of [M], a theory of the meaning of L's use by G (some group of people who use L). There is no a priori link from providing [F] to providing [M], and there is no a priori requirement that an [M] use a formal theory [F].

That is all I say in 4.1, really. Nothing more. The real substance of my argument that there will not be an [F] for any [M] of a natural language is given in the remainder of the chapter. But, that is not at all in section 4.1. You have to read on for that.

About your concerns about my definitions of formal semantics, I am quite sure I can satisfy you. I am a math-geek, and I am a computer scientist (my undergraduate work was in Electrical Engineering and I have worked as a software engineer and professor for MANY years). I love formal languages and thinking about them. I don't have any esoteric views about such subjects, and none are required for the arguments I offer in my dissertation. We just need to iron out the way I am talking. I don't think there is ANYTHING at all extraordinary about what I am saying vis-a-vis the formal stuff. The only interesting things I am saying is with regard to the theory of language use: how does our use of language pin down which language we are actually speaking? (See Lewis's "Languages and Language" (1975) or Schiffer's "Actual Language Relations" (1993).) How does use determine meaning? That is the question I am asking. Chapter 4 is my argument that our use of language doesn't need to be understood as employing compositional semantic theories of any sort. I argue this point because while I think compositional semantics is interesting and fun, and terribly useful when you are developing natural language processing programs, I don't believe (for principled and good reasons, I think) that there is any such thing as a fully developed compositional semantic theory for any actual natural language. So, since we use natural languages to mean things, if there are no compositional semantics for natural languages, then it better turn out that there is no a priori requirement that there be compositional semantic theories for natural languages. Thus, chapter 4.

I hope some of that helps. Let me know if not. But, do help me out with what you see as the difference in our definitions, as I request above. You have the advantage over me because you have my dissertation in which I lay out in detail and very precisely what I mean by all the relevant terms. I can't be 100% sure what you are meaning unless you give me definitions yourself.

Thank you for the fun and stimulating conversation Roger!

Yours,
Russell