Thanks to Russell Dale for responding to my question about his views on compositional semantics, and to JLS for his outpouring of material discussing problems with compositionality in natural language semantics, with which I am hopelessly unable to cope!
I'm going to state as concisely as possible why I am sceptical about all this scepticism.
First of all however, let me re-state my alignment with Carnap on the semantics of natural languages.
In the debate over analyticity with Quine, Carnap very early on detached himself from the supposition that his semantics methods could be used to define the notion of analyticity in natural languages.
I concur with his position here, and the implications of this for the present discussion are that I argue for "compositionality" in a limited conditional way, which I will explain shortly.
First of all let me say what I understand by this notion, since it may well be quite different to what Russell has in mind (I have not been able to understand the definition he gives at the beginning of Chapter 4 of his thesis).
I will do this through two other concepts:
"truth conditional semantics"
and
"denotational semantics".
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".
A truth conditional semantics can be completely "abstract" if the semantics is formulated by constructing a model of the space of possibilities in some abstract domain, most likely in the domain of some set theory.
A truth conditional semantics is then the definition of a mapping from the sentences of the language, together with any necessary disambiguating context, to the set of possibilities under which that sentence would be true.
This could alternatively be a boolean valued function over the possibilities, exactly what mathematical representation is chosen is unimportant.
Now it seems to me that natural languages are not used exclusively in such a way as to lead us to expect that a truth conditional semantics would fully describe the meaning (or use) of the language, and so if one does attempt a truth conditional semantics, it will be a partial analysis of the semantics of the language.
More importantly, it is doubtful that natural languages are used in sufficiently regular way for there to be definite and objective truth conditions for sentences in the languages.
Even if these difficulties were not present, the sheer complexity of natural languages may well make a complete model of the truth conditions practically infeasible.
However, it is possible that the construction of a truth conditional partial semantics for a natural language may be helpful in understanding that language even if it is not the whole story.
A denotational semantics (as I here propose to use the term), is a semantics in which not only sentences but also all other grammatical categories are given meaning in a similar manner.
In a truth conditional semantics the sentences are given meanings as functions yielding truth values.
In a denotational semantics the grammatical constituents of sentences are also given meanings, not of the same kind, but of similar kinds, and these are called the denotations of the words or phrases.
In this Frege's distinction between sinn and bedeutung must be born in mind,
(though the crucial distinction here is not exactly that distinction).
The denotation is not the thing which the phrase refers to, firstly because the phrase by itself will often not refer to any particular thing at all, for lack of context, and secondly because the phrase may occur in a "indirect" context.
Finally we come to compositionality.
A denotational semantics is compositional if it defines the denotation of some phrase exclusively in terms of the denotations of its constituents without need to refer to the constituent itself.
We have seen an extended trail of supposed demonstrations or illustrations of reasons why natural languages cannot have compositional semantics.
However, there is little sign that the authors of these have any idea what it takes to demonstrate a negative proposition of this kind.
What they amount to in general, is the identification of some difficulty in a supposed compositional account of some fragment of language, to which the author finds no solution and hence concludes that no solution can be found.
On the basis of the above informal definitions I will now put forward some positive conjectures, which I believe could be followed up by formalisation of the definitions and formal proof of the conjectures:
1. That any language (or part or aspect of a language) which can be given a truth conditional semantics, can also be given a denotational semantics.
2. That any denotational semantics can be rendered compositionally without affecting the truth conditions of the sentences (this might involve changes to the denotations of other syntactic categories).
In my opinion, these conjectures involve no significant mathematical difficulty.
The biggest awkwardness is in choosing a suitable general mathematical representation for grammatically structured languages, which is no big deal.
I shall now say something about Russell's stated principle reasons for scepticism, which seem to be primarily metaphysical/ontological.
He does not understand what kind of thing propositions or other meanings could be.
On this matter there is no need to look beyond set theory.
The most practical way of approaching such a formal semantics is to begin by chosing some way of representing as sets the possible states of affairs (call them what you will) which form the subject matter of the language.
For a natural language, these are sometimes called "possible worlds".
Once we have an abstract model (as sets) of the subject matter, the semantics can be defined using various other related abstract entities.
There are many ways of doing this, principally deployed by theoretical computer scientists or mathematical logicians, and presumably Russell is familiar with some of these.
Semantic methods are very well established in these disciplines, and yet remain controversial in philosophy.
If the source of that controversy were doubts about whether natural languages can be said to have well defined truth conditions, then I would have some sympathy.
But insofar as the doubts are merely about whether a language or fragment of language with well-defined truth conditions can have those truth conditions correctly rendered in a compositional denotational semantics, then I suspect that they are without foundation.
From here we could go in either of two directions.
You might demand that I follow up my conjecture with a proof.
And I might do that, but I don't think I will find time to do that until April.
Alternatively, you might want me to respond to some of the specific refutations.
This I would be happy to do, but not to all of them, so I would be interested to know from Russel, JL, or anyone else, which of the arguments against compositionality they consider most compelling, and then I will give a response to those particular objections.
Of course, if the objection speaks against the definiteness of the truth conditions for the language, I will probably agree, but I don't actually recall seeing any in of that kind.
Roger Jones
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A denotational approach and/or use of language works in most formal circumstances. But not all. A historian writing about the battle of Verdun will makes use of denotation . And lets say he gets the "facts" correct --as far they may be known. But thats hardly the end of the matter--the Event itself not a matter of denotation or strict truth functionality.
ReplyDeleteRusssell (as in Bertrand) himself moved away from positivism apres-Tractatus did he not. Positivism has its uses--especially for like Silicon valley executives-- but as a Weltanschauung rather limited.
Thank you for you interesting remarks Roger. I will respond more fully later. I just want to say to you about the definition at the beginning of my Chapter 4, that you probably should look at the stuff that follows it in the next page or so, where I define what I mean by the lambda(x) function and the g(x, i) function. It is really quite simple, if very compact. I have used this notation with first term computer science students for many years (that is where I first developed that). It is really quite straightforward once you understand lambda(x), g(x, i), and the sigma notation, which is just from basic algebra. That is, lambda(x) and g(x, i) I created for convenience, but sigma notation is standard algebraic notation here in the U.S. Perhaps in England you use something different, and you are in England, I think, right?). It just means the sum of a number of terms each of which differs from the others by the running variable, i. It is, in a way, just like a "for" loop in a computer language. Like in c, you would write:
ReplyDeletefor (i = 1; i <= lambda(x); i++) {
f(x, i);
}
This is really quite the same as what I am using the sigma for.
I will write more if you are still unclear. Let me know. You will see that what I am doing there is trivial, and it is just to illustrate the concept of a mapping from meaningful parts and structures to meanings (of a sort). It is a pretty clear case of what we want a compositional meaning theory to do, but one that is terribly simple (even if the notation at first seems impenetrable and cumbersome; I apologize for that; but I think in the end, you will see that the notation is really quite simple and elegant).
Yours,
Russell
CORRECTION TO MY COMMENT:
ReplyDeleteActually, the equivalent in c to the sigma notation would be:
sum = 0;
for (i = 1; i <= lambda(x); i++) {
sum = sum + f(x, i);
}
Sorry for the confusion.
Sigma as in big greek E ? Stats, actually. Summation. Done various ways in various codes...int sum something in C (yrs looks close).
ReplyDeleteCan one sum...meanings, or denotations, events?? Only in very limited domains--with integers, functions, data e tc. In terms of real world--history economics, politics, even dare we conversational implicature-- not of much use, except for the olde bell curves.
Will revise ch. 4, with Dale's symbolism, including the big greek Sigma, and trust it is elegant! And will look for an objection for R. B. Jones as it bears on 'truth-conditional' semantics, and ... etc. Thanks for your contributions.
ReplyDeleteI respond to Roger's comment in a separate post.
ReplyDeleteI really did only mean that I did not understand your definition of "compositional-semantic theory",
ReplyDeletei.e. the first paragraph of chapter 4.
I don't have a problem understanding your example, but if you are disputing the possibility of a compositional account of the meaning of natural languages then what you mean by "compositional" is crucial to whether I disagree with you.
Which is why I gave my own definition before claiming that it is possible IF a truth conditional semantics exists, (i.e. if the truth conditions are determinate).
I will follow up on your other message.
Roger
Thanks, Roger. As Dale has pointed out: there's indeed CST (compositional-semantic theory) for which he provides the _algebraic_ illustration (on which or about which we may expand), and there are TWO other variants (other than the algebraic which was just meant as illustration) of special philosophical import here: the less committed CTT (compositional-truth theory) and the one Dale finds objections about: the CMT -- the compositional-meaning theory. On top, as the title of his last chapter, and indeed whole thesis show -- there's 'the theory of meaning'. I.e. there can be a theory of meaning even if there is no compositional-semantic theory. Will see if I can find sources to elaborate, then, on the meaning of 'compositional' simpliciter. It seems that loads of what I outpoured against compositionality and semantics indicate perhaps a different use of 'compositional'. Or not!
ReplyDeleteThis is a bit on the late side, but in response to J's comment.
ReplyDeleteI should put it "a denotation semantics is good for some purposes but not others".
However I don't think an advocacy or use of denotation semantics should be construed as positivistic, even though one might connect denotational semantics with Carnap's semantic methods.
I'm not aware that Russell ever thought himself a positivist (I have to say that he sounds like one to me, in the broad historical sense, but I don't think he ever subscribed to the verification principle which has been taken to be central to the logical positivists).
As to positivism's adequacy as a Weltanschaum, many positivists don't take it as such.
I don't think Carnap did, though he also had doubts later about whether to call himself a positivist.
I am a kind of positivist, but I don't take it to be a Weltanschaum.
However, I see you were talking about a denotational use of language, which is not what I was talking about, so maybe we are just talking at cross purposes.
Plus ca change.