Tuesday, March 12, 2019
Dan Milway discusses Katz's semantic theory
Dan Milway has an interesting project: reading Jerrold Katz's semantic investigations and discussing them for/with/near us. Here are two urls that discusses the preface and chapter 1 of Katz's 1972 Semantic Theory. Other posts are promised. I like these archeological digs into earlier thoughts on still murky matters. I suspect you will too.
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Interesting. I struggled with a not entirely different collection of issues for quite some time and wrote up my conclusions here: http://members.iinet.net.au/~ada/AveryAndrews/Papers/Andrews_NSM_Formal_AJL.pdf (legit download, since the Taylor and Francis one year embargo period for me making it freely available has passed).
ReplyDeleteI think that Katz was right about the nature of the subject, but that his formal technique was a mess, and model theory is really much better for producing a theory of the 'meaning-based properties and relations' of a language, as I like to call them), that you can show to be nontrivial (some sentences will be entailed by some other sentences, some other sentences will not be), at the early stages, at least. In the end, I suspect that proof theory will be required, and algebraic semantics (Godehard Link and others) is a way to have extralogical axioms with the model theory making it relatively easy to make sure that you haven't created contradictions.
My article is trying to find some connections between formal semantics and Anna Wierzbicka's Natural Semantic Metalanguage (NSM); she proposes that meanings are built from a relatively small set of 'primes', about 65 ATM, and we can certainly not some apparent 'laws' that govern them. For example:
If X thinks that Y knows Z, it can't be like this:
X thinks like this: Z is not true
All words and their syntax prime (as of recently, the NSM people do revise as they go), except perhaps for the variables (there are problems there) expressing the idea that knowledge is among other things 'true belief', not attempting to account for the standard justification clause, and also not claiming to be part of a definition (the primes are supposed to be a minimal set, so not interdefinable), just a law that these philosophically important primes seem to obey.
Wrt prior recognition of Katz, I recall Stephen Anderson telling me in what must have been 1972 "Jerry Katz has written his book again, and the first chapter is pretty good". Richard Larson and Gabriel Segal iirc make some acknowledgements to Katz in their _Knowledge of Meaning_, and perhaps Gennaro Chierchia and Sally McConnell-Ginet? I don't have a copy of that here right now. Others ignore him.
Chris Pott's work on conventional implicature might be a beginning of movement beyond topics 11-14, I think issues of discourse and dialog are also becoming important in interesting ways. A weakness of conventional formal logic is that it deals with sentences in isolation, whereas in nature they function in context, for example they might be strong end to end to produce a substantial lie, such as the ones Odysseus told various people on his return to Ithika. These have to be internally consistent, as well as consistent with whatever the local audience could be expected to know about the War etc, and capable of withstanding potentially hostile questioning. DRS theory has a lot to say about what to do about this; I now think, probably with more clarity than a few years ago, that MBRS should really be thought of as properties of discourses and their potential continuations.
Thanks for reading!
DeleteI must say I'm skeptical that model theory is up to the task. I'll admit that I'm nowhere near an expert on model theory and maybe you can tell me I'm wrong here, but I don't see how model theory can distinguish meaningless sentences ("Colourless green ideas sleep furiously") from necessary falsehoods ("every number is expressible as a ratio of integers"), or analytic truths ("Red squares are squares") from necessary synthetic truths ("There are infinitely many primes")
You're right that Katz's formalism (if that's what you mean by "formal technique") is a bit of a mess, but that's perfectly understandable for a new theory. The early formalisms of generative syntax and phonology appear to modern linguists to be a bit messy and hokey, but only because they have since been refined by an entire field of theoreticians. Who knows what Katz's formalism would've looked like if there had been an entire field of linguists developing it.
I think it’s hard to respond to those concerns without knowing how you yourself would go about distinguishing e.g. analytic truths from necessary synthetic truths. It’s not as if the nature (or even existence) of that distinction is settled, leaving only the problem of expressing it in a model-theoretic idiom.
DeleteThere are certainly some notions of analytic truth, necessary truth etc. that can be distinguished and explicated in model-theoretic terms. For example, you can distinguish sentences true in all models (possible candidates for logical/analytic truths) from sentences denoting propositions that are true in all possible worlds within some particular model (possible candidates for necessary truths).
Similarly, necessary falsehoods can be taken to denote propositions false in all worlds in a model of interest, while meaningless sentences might e.g. fail to compose owing to type mismatches or certain functions being partial.
Well, let's go with the usual way the distinction is framed: Analytic sentences/propositions are those whose truth depends solely on the meaning and arrangement of their constituents. Synthetic sentences/proposition are those whose truth depends on how their meanings relate to the world.
DeleteOf course, If one assumes, as it seems that most formal semanticists do, that expressions only have meaning insofar as they are related to the world, then this distinction is non-sensical. Hence my skepticism about model theory's ability to explain the distinction. Again if you (plural) know of work that demonstrates that my skepticism is unfounded, I'd be happy to check it out.
So my problem with analytic/synthetic as defined is that it depends on a prior understanding of what meaning is, which I lack. But I do (think I) understand the idea of being able to imagine situations where a sentence would be true and where it wouldn't, which is what model theory addresses.
DeleteI don't consider myself to be any kind of philosopher, but I don't think I'm worse at it than the average person who gets interested in linguistics, and is good enough at linguistics to get into a graduate program, which is the level that semantics needs to be aimed at, to start with, at least.
I don't think you need an understanding of what meaning is to engage with the analytic/synthetic distinction, or other non-reference meaning-related notions. In my opinion, you only need an intuitive grasp of meaning, the kind of grasp that allows one to say that the notion of synonymy is part of the notion of meaning while the notion of rhyme is not. That kind of intuitive grasp plus a sense of curiosity is plenty to start developing a scientific theory of meaning.
DeleteMy intuitive grasp of meaning is sufficient to distinguish semantics from phonology, but not to distinguish analytic/synthetic from other kinds of necessary/nonnecessary truth. Which doesn't mean that it wouldn't now be possible to base something good on Katzian theory, but I think it would require a combination of experimental tests showing the existence of a kind of fast calculation of semantic properties and relations that was different from the slower processes involved in some other kinds of reasoning, together with a mathematical characerization of how these deductions work, including presumably proofs of decideability. Recent work on 'natural deduction' might be useful in this respect.
DeleteAnother point is that when formal semantics got going, proof theory was considerably less developed than it is today, and far less accessible. Things are different now, and, furthermore, we have different expectations of a 20 year old (generative grammar in 1975) than of a 64 year old.
It also requires explanation, I think, that although deductive approaches, not only Katz, but also generative semantics (eg George Lakoff's Natural Logic screed from c. 1970, iirc) are much closer in spirit to generative grammar, and were for that reason the first to be considered, model theory was what got generally accepted as the way to proceed. The reason, I think, is that it is intrinsically easier, and requires less in the way of arbitrary decisions to get started.
Alex D says some of what I would want to say, better than I would probably have said it, but here are a few other points:
ReplyDelete1) model theory can be regarded as a Marr level 1 description of entailment, whereby entailment and allied notations are mathematically defined, but not in a 'constructive' way that necessarily supports recursive enumerability or decideability of the relationships.
2) a proof-theoretical account, including Katz's, does entail recursive enumerability at least, thereby plausibly attaining Marr's level 2, but a good reason for not leaping straight into that as Katz did is that there are very many different ways of setting such systems up, while model theory suffers from this problem to a lesser degree (I conjecture, because it doesn't require speculations about how the properties relations can be detected).
3) I think that it is possible that Katz's approach could be an early approximation to a description of a psychologically real, fast and decideable sublogic for calculating some MBPRs more or less instantly in real time, but it would be a long path to demonstrate anything like (when I suggested something along these lines to the ANU computational logic people, the general reaction was that I was bonkers).
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ReplyDeleteI've posted the next part here. This post covers the first half of Chapter 2
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