• Questions: “what sort of thing is meaning?”, “how is it compositional?”.

  • Contrast with Katz “semantic markerese” [logical language?].

  • Translating to Markerese doesn’t require understanding truth conditions, but “semantics with no treatment of truth conditions is not semantics”.

  • Not about social use of language: “possible languages as abstract semantic systems” and “psychological and sociological facts whereby one of these systems is used by a population” are totally separate things. [But we have no example of the former divorced from the latter. All languages arise in social context, so presumably the actual form that meaning takes, the fact that it’s approximately context free, the fact that meaning is compositional all arise from social factors.]

  • This is in the model-theoretic tradition, but offers “a simpler way to do essentially the same thing”.

  • Underlying syntactic formalism is categorial grammar [“transformational” just means categories have ordering info?]

  • “A meaning for a sentence is something that determines the conditions under which the sentence is true or false. It determines the truth-value of the sentence in various possible states of affairs, at various times, at various places, for various speakers, and so on.”

  • It follows that the intension of a sentence is a fn from indices to truth values, names: indices -> things, nouns, indices -> sets.

  • Rather than fns of possible worlds (a la Carnap), take these indices to be coordinates: “packages of miscellaneous factors relevant to determining extensions”—includes not just id of possible world, but speaker location in place, time, bindings to indexicals, etc.

  • “Intensions are designed to do part of what meanings do. Yet they are not meanings, for there are differences in meaning unaccompanied by differences in intension.” (Tautologies, etc.) [Is it obvious that tautologies all have the same intension under a sufficiently rich system of coordinates? Not as given in the paper, but if the speaker’s beliefs are part of the coordinate system, different prior beliefs should distinguish different tautologies based on what the listener has computed so far. In general it’s a little weird in these truth-conditional approaches that uncertainty is not part of the state for purposes of predictaion, since speakers and listeners obviously don’t have access to deductive closure over even those parts of the world they observe. And once you have machinery for assigning binary truth values to indices, you’re almost all the way to a full probabilistic treatment.]

  • What is a “thing”? Russell’s paradoxes exclude things like “all sets”, “intensions”. This paper doesn’t treat with semantic metalanguages.

  • An adj is a function from nouns to compound nouns. NOT: from sets of things to sets of things. Consider that Maoist and Communist might pick out the same set of things, but alleged Maoist and alleged Communist different sets. [But then do we believe in compositionality at all? Intension of a constituent is determined by interactions among all the words in the constituent. The treatment here is superficially compositional, but if alleged can freely do different things to different nouns then you haven’t given up any expressive power.]

  • More generally, the intension of a type (x/y..z) is a function from y..z-intensions to x-intensions. [What? If “Communist” and “Maoist” have the same extension in every index, they have the same intension (in “coordinate” sense). So does this defn of intension also carry lexical information?]

  • We’ve said so far that “meaning” needs to be more than intension, at least to distinguish between tautologies. So say “meaning” has something to do with structure as well: “Semantically interpreted phrase markers minus their terminal nodes”. [So no pair of sentences with different syntax can have the same meaning?]

  • Truth of an utterance is defined w/r/t a particular occasion, specified by a set of indices.

  • Various notions stronger than truth are defined based on structural equivalence.

  • Usual CCG observation that once we have made the category part of the meaning of the word, a grammar just specifies a way to encode meanings. Grammar just provides ordering information on top of types.

  • Discussions of how ti implement various other syntactic theories in this framework. [???]

  • L analyzes DPs as S/(S/N). What are you doing?

  • Ah—to force quantifiers to scope in the right order. This seems like a weird conflation of a purely syntactic phenomenon with a semantic one.

  • [Skipping details of discussion—an alternative analysis is offered that looks more normal]

  • Non-declarative sentences: treat as paraphrases of the corresponding performative. [Yes!]

  • Self-referential sentences generate situations where paraphrase is not truth-preserving.

Final thoughts

One thing that really surprises me is the casualness with which L allows the intension of alleged Maoist to be determined by a combination of the words alleged and Maoist, and not by some regular combination of their intensions. This distinction goes to the heart of why compositionality is hard to pin down, and it’s not resolved satisfactorily here. On one hand, it is indeed obviously the case that [[alleged Maoist]] is not just [[alleged]] AND [[Maoist]]. On the other hand, if you allow modifiers to be arbitrary functions from the phrases they modify to other intensions, you can assign any possible sequence of meanings to any possible sequence of sentences—you’ve removed the possibility of making any meaningful statement about compositionality in your language. If we really believe that meaning is compositional, it has to be generated by some mechanism stronger than intersection but weaker than the version presented here; the interesting question is how much weaker.

On the subject of overpowered mechanisms: The notion that two utterances should be regarded as having the same meaning only if they generate it via the same tree-shaped computation seems initially like it’s too restrictive. But once it becomes clear that in this account “paraphrases” are generated by transformation of some underlying deep structure rather than with new computations, it again becomes arbitrarily powerful unless you’re willing to put some restrictions on the form of the transformational grammar. But in any case this seems like a lot of machinery to introduce just to give different tautologies different meanings, when you can resolve everything by putting the set of conclusions available to the listener into the coordinate system.

The account of non-declarative sentences seems correct.