Friday, January 04, 2008
Scalar Implicatures and Speakers' Knowledge
'Grammar (which includes semantics and syntax) is a computational system that delivers, say, pairs of phonetic representations and interpreted logical forms. The output of the computational system is passed onto the conceptual/pragmatic system that employs it for concrete communication. The computational system of grammar and the conceptual/pragmatic system are separate units and work in a modular way: each unit is blind to the inner workings of the other. Things like agreement or c-command belong to grammar; things like relevance or conversational maxims belong to the conceptual/pragmatic system.'
(Chierchia 2004: 39)
Chierchia has focused on scalar implicature in an attempt to undermine this natural picture. He writes:
'I will argue that pragmatic computations and grammar-driven ones are "interspersed." Implicatures are not computed after truth conditions of (root) sentences have been figured out; they are computed phrase by phrase in tandem with the truth conditions (or whatever computational semantics computes).
He's offered essentially two sets of considerations in favor of this alternative picture:
1. The Gricean account both under- and over-generates scalar implicatures.
2. Adopting a picture according to which scalar implicatures are computed phrase by phrase in the grammar enables one to explain so-called 'intervention effects' on negative polarity items (NPIs); that is, it helps one explain why NPIs are blocked in certain environments which, by the lights of our best existing theories of NPI-licensing, should allow an NPI.
I'm going to leave the second argument aside here, and concentrate on the first. Let's focus on the following example:
(1) George ate some of the fries or the apple pie.
(1a) George ate some (but not all) of the fries or the apple pie.
(1b) It is not the case that George ate all of the fries or the apple pie.
(Chierchia 2004: 46. The example has been changed following Russell 2006.)
Now, intuitively (1) implicates (1a). But, Chierchia argues, if scalar implicatures are determined globally, that is, after the truth conditions of (1) have been computed, it seems like we can't explain how that's so. Rather, Griceans should expect a hearer to reason as follows:
"The speaker said 'George ate some of the fries or the apple pie, and could as easily have said 'George ate all of the fries or the apple pie', which is stronger. Because she is co-operative, she makes the strongest statement possible, so 'George ate all of the fries or the apple pie' can't be true."
(Based on Russell 2006: 361)
It seems, then, that the Gricean predicates that (1) implicates (1b). As Chierchia puts it, 'negation, in the globalist view, seems to wind up in the wrong place: it is expected to take scope over the whole disjunction, whereas we would want it to negate just the [first] disjunct of the alternative'. And this is problematic, since the suggestion that (1) implicates (1b) seems plain wrong, for (1b) entails (1c):
(1c) George did not eat the apple pie.
In his 2006, Benjamin Russell has tried to respond to both of Chierchia's arguments against the Gricean. Here's his line of response to Chierchia's discussion of constructions like (1).
Firstly, he suggests, following Horn and Soames, that in a case like (1), Gricean reasoning shouldn't license one to conclude that a stronger statement would be false: just that the speaker isn't in a position to make it. So, for instance, the reasoning about should really go as follows:
"The speaker said 'George ate some of the fries or the apple pie, and could as easily have said 'George ate all of the fries or the apple pie', which is stronger. Because she is co-operative, she makes the strongest statement possible, so she can't know that 'George ate all of the fries or the apple pie' is true."
(Russell 2006: 370)
So (1) doesn't implicate (1a), but rather (2):
(2) ~K (to be read: the speaker does not know that) George ate all the fries or the apple pie.
And (2) doesn't entail the problematic (1c), but rather the following unproblematic epistemic facts about the speaker:
(2a) ~K George ate all of the fries
(2b) ~K George ate the apple pie.
Russell then asks how we are to account for the fact that (2b) cannot be strengthened to the 'obviously undesirable' (3):
(3) K ~(George ate all the apple pie).
He suggest that '[t]his can be explained in Gricean terms: a sentence's scalar implicatures cannot be strengthened if this leads to contradiction with another of its basic implicatures' (2006: 371). Hence, since (1) has as a basic implicature
(4) ~K George ate some of the fries,
we cannot strengthen (2b) to (3). Of course, (4) doesn't by itself contradict (3), but Russell offers the following proof that it nonetheless suffices to block strengthening to (3) in this case. Recall our target sentence and its basic implicature:
(1) George ate some of the fries or the apple pie.
(4) ~K George ate some of the fries.
From (1) we have,
(a) K (George ate some of the fries or the apple pie).
(b) K ((~George ate the apple pie) -> George ate some of the fries).
Assuming that K distributes, we arrive at
(c) (K ~George ate the apple pie) -> (K George ate some of the fries)
So by contraposition,
(d) (~K George ate some of the fries) -> (~K ~George ate the apple pie)
Therefore, given (4) we arrive at:
(e) ~K ~George ate the apple pie,
which directly contradicts (3). This is why (2b) cannot be strengthened to (3). (Russell 2006: 371)
I'm sympathetic to Russell's stance on these issues, but I'm worried about the appeal to a distribution axiom for K in this proof, and the step from (a) to (b). First of all, all the usual suspects that have been touted as counterexamples to closure are going to be worries for distribution:
i. K (I will visit San Antonio this coming weekend -> I will not have a fatal heart attack this Friday)
ii. K I will visit San Antonio this coming weekend -> K I will not have a fatal heart attack this Friday
I have hands -> K I am not a handless brain in a vat being fed experiences of an external world
i. K (I have hands -> I am not a handless brain in a vat being fed experiences of an external world)
i. K (That is a zebra -> it is not a mule cleverly painted to look just like a zebra)
ii. K That is a zebra -> K it is not a mule cleverly painted to look just like a zebra,
and so on. And notice that the step from (a) to (b) actually requires the closure of K under known (or perhaps obvious) logical consequence. (Well, there are other principles one could appeal to here, I guess. But that won't seriously affect my main point, which I'm happy to make just with respect to the distribution axiom.)
But more worryingly in my view, the assumptions that knowledge distributes over the conditional and that it obeys a closure principle that will license the step from (a) to (b) lead to tension with the kind of examples that have moved even friends of closure like Hawthorne to Chisholm the principle:
'...the principle is not especially intuitive as it stands. If at t, I know that p and know that entails q, I may still have to do something--namely perform a deductive inference--in order to come to know that q. Until I perform that inference, I do not know that q. At any rate, that seems to be the natural view of the matter.'
(Hawthorne 2004: 32. Author's footnotes suppressed)
In fact, Hawthorne argues that even building in the requirement that the subject actually perform the inference in question isn't enough to render closure plausible. But let's stick there for now. The K in Russell's proof is to be read as something like 'it is known to the speaker that'. It seems to be a worry for Russell's response to Chierchia that it forces us to assume that this operator is obeys the strongest, least plausible version of epistemic closure and a distribution axiom. For it seems that even friends of epistemic closure will find these principles hard to stomach. The upshot is, I suggest, that Russell's Gricean response to Chierchia isn't very satisfactory, assuming as it does some very strong, controversial principles governing the operator 'it is known to the speaker that'.
Chierchia, F. 2004. Scalar Implicatures, Polarity Phenomena, and the Syntax/Pragmatics Interface. In A. Belletti, ed. 2004. Structures and Beyond. Oxford: Oxford.
Hawthorne, J. 2004. Knowledge and Lotteries. Oxford: Oxford.
Russell, B. 2006. Against Grammatical Computation of Scalar Implicatures. Journal of Semantics 23: 361-82.