(1) On the merits of extending formal semantics from declaratives to other speech acts: You say that, in a mathematical setting, fruitfulness is assessed either by the production of more theorems or by the exactness of the modelling activity; if I understood you correctly, you say that neither of these obtain the case of formal semantics. Well, I disagree. Obviously, as you pointed out, I believe that formal semantics is a worthwhile enterprise. And it's simply a fact that the formal semantics of declarative sentences is currently a well-developed research program. So why not extend this approach to other speech acts? In fact, that is precisely what formal semanticists have been doing. I claim that the fruitfulness of this approach can be assessed in the same way as a mathematical research program, in particular, in the exactness of the models produced. I would also add a further dimension, also analogous to mathematics: in many cases, it's less important to prove theorems than to coin new definitions (e.g. Dedekind's ideal theory), which serve to unify phenomena that were previously considered separately (e.g. the behavior of primes in certain number fields and the behavior of curves in function fields). This, explanation by unification, is one particular case of a virtue of a mathematical theory, namely its explanatory power. Now, I want to argue that formal semantics do provide us with added explanatory power. In particular, by showing what is common to apparently distinct speech acts (or moods), it allows us to explain a greater variety of phenomena than we could before. — Nagase
I think formal semantics is a worthwhile area of research, but I think you're treating the conditions of adequacy for theories in it as far too much like pure math and far too little like applied mathematics or statistics. The subject matter of formal semantics, when applied to natural languages,
is natural languages. Whether a formal semantics in this case explains anything must be done with reference to the natural language (or natural languages) targeted, not simply extensions of the theory. Let's look at an example.
The Lotka-Volterra equations in mathematical biology, say, are induced by an intuition linking predator-prey species pair abundances to the abundance of the other animal population; predator numbers depend on prey numbers due to resource availability, prey numbers depend on predator numbers due to killing rate.
You could, at this point, say that 'predator prey dynamics can be explained by calculus', but that wouldn't be the whole story. As a model, the Lotka-Volterra equations are terrible. They do not reproduce most phenomena in predator-prey webs, and don't accurately match even the simplified predator-prey dynamics they target. The reality is much messier than those equations suggested.
In the same sense, I believe the extensions of formal semantics from propositions to general speech acts should be checked against language, not just against consistency with previous research in that area. The truth of an account of natural language should be measured by its accord with natural language, not vouchsafed as simply an extension of a theory of a subset of it. It has to be a good model, as well as consistent with the theory, to count as an increase of explanatory power.
I agree that he gives prides of place to communication here (he is pretty explicit on this), and that there is little room in his account of conventions for the more creative aspects of language use as explored by Austin. But I see this as a reason to modify his account, not to reject it outright, perhaps by emphasizing the non-conventional aspects of language use. — Nagase
I don't think an appropriate extension to the project would look to non-conventional aspects of language use, this allows convention to be equated with Lewis' account of conventions for truth-apt (or derivative of truth apt) sentences. "I do" is part of our conventions for marriage, "I love you" is as much performative as declarative and so on. We all understand this because such things are conventions
of language use.
I mean, look at "I do", how would you explain to someone what that means? You'd have to explain the institution of marriage, the legal status of being married, the emotional commitments involved, it makes sense upon a background of sexual relationship and moral norms like fidelity and honesty. You will get a lot more insight into the meaning of "I do" by describing the role it plays in language than by describing a sentential function that maps it to the propositional content of "X assents to marriage with Y at time t in place p". Even if we have filtered out the propositional content, the meaning of "I do" is to be found in the relation of its propositional content to context of its propositional content and an exegesis thereof would care little about whether "I do" itself is truth apt.
Maybe my intuition is the opposite of yours, I see it as much more intuitive to 'feed pragmatics into semantics'.
That is, there are conventions in place which makes us behave as users of a given language. Given that the coordination problem involved is defined in terms of actions and beliefs, and these can only interact with sentences (or utterances of sentences), it makes sense for him to focus on a very coarsed grained view of languages, which focus on the interpretation of sentences. This also chimes in with the idea that semantics feeds sentences into pragmatics, so to speak. — Nagase
Well yes, of course this makes sense, it makes sense in exactly the same way that the Lotka-Volterra equations model real world predator-prey dynamics. They are a toy model to demonstrate a principle relating the feedback between the predator abundance and prey abundance, and when held up to real predator prey dynamics are found sorely lacking in scope. I'm left with the feeling that a narrowly circumscribed model is being mistaken for the real dynamics it targets.
Nevertheless, I don't want to throw the baby out with the bath water, sentences and truth apt expressions are an excellent playground for philosophical theories about how language interfaces with the world, sufficiently simple to allow the development of precise formalisms which nevertheless have quite general scope.
(3) Lewis's account is entirely focused on declaratives: Correct, though he does offer an extension, even in "Languages and Language" (this is one of the objections he answers), which is similar in spirit to the one in "General Semantics". Incidentally, in "General Semantics", the mood of a sentence is not simply associated with the sentence, but it is built in into its structure as one of the nodes in the phrase marker. Given that the performative is actually the root of the phrase marker, one could identify the performative with the whole tree; then the sentence radical will be the root of a subtree of the phrase marker, and will thus be indeed embedded into the performative. So I think Lewis's terminology is apt here. — Nagase
It's embedded in 'the sentence' when 'the sentence' is treated as containing a mood operator. The convention to put the mood operator at the beginning of the parse tree's terminal nodes rather than as an operator
on a parse tree of a sentence is really arbitrary here. To say it is embedded in the sentence is to say the mood is part of the sentence content, but the possibility of 'falsehood' of the mood in Lewis' sense shows that this isn't the case. {command, "Go to bed"} is false when I'm not commanding someone to go to bed, despite saying so. If I utter the speech act {command, "Go to bed"} how am I to make sense of the fact that I was, say, joking with my friend, solely through the 'falsehood' of the speech act? There are far more ways not to be a thing than to be a thing.
You might rejoinder that this would simply be a different speech act {joke, "Go to bed"} but I could make precisely the same kind of argument towards that. Regardless of this, Lewis is leveraging our folk-theory of language to do such parsing, which is little more than an invitation to understand ""Go to bed", Sally joked" as {joke, "Go to bed"} with "Sally" as an indexical. In that regard it's hardly an 'account' of language use at all, it is little more than a procedure to mathematise expressions into a far more comfortable formal set+function form than the nuanced messiness of their original utterance.
Another rejoinder here references Chomsky's innateness hypothesis with regard to grammar
s, which you've leveraged elsewhere. I'm quite happy to grant that this provides some insights about the possible grammars for languages, but I don't think it's particularly relevant to including mood terms/indexicals in the parse tree considering one is a mental state or pro-attitude and one is a sentence or proposition. To be sure, command can be modelled as being in a grammatical imperative mood, but Lewis does seem to interpret the truth conditions of these moods as when their corresponding mental state occurs during the utterance. Do you really understand anything more about imperatives by attaching them as indexical prefixes to a parse tree or as an operator on a parse tree? It seems to me, again, the focus here isn't really on understanding imperatives, it's on providing a procedure to mathematise imperative expressions All the 'explanatory power' in the account
for understanding natural language is given by folk-theoretic categorisation of speech acts into sentences with a grammatical mood or the structure of parse trees on those sentences. Once one has recognised an imperative, it will be represented thusly... how do we understand imperatives to make these constructions? Beyond the scope of these papers.
Carlo Rovelli makes an example in one of his talks about simple harmonic motion and pendulums, that we do not care about the 'love stories of bacteria' inside the pendulum when modelling it as a simple harmonic oscillator. What we do care about is, well, how the whole thing moves. Of course, simple harmonic motion would go on forever, and the real pendulum stops which is unanticipated from the theory and invites an extension (including a damping term). In this manner, the real world shouts "No!" to our simple model.
How does the real world shout "No!" to a formal semantics for a (subset of) natural language?
Perhaps a more precise form of this question: let us grant that all speech acts are to be understood as derivatives of declaratives, how does this 'derivativeness' show up in either the use or acquisition of language?
Edit: for clarification, I don't mean this in a vulgar verificationist sense, I mean how does natural language inspire formal semantics and how can a formal semantics be checked for adequacy beyond internal consistency and 'philosophical fruitfulness = being part of the hard core of a research program"