Continuity: C[\eta] = Union of i \in C: i[\eta]
Introspection: C[\eta] \subseteq C
I will say right away that something seems wrong with Continuity: it doesn't apply to modal operators, or any sentences containing modal operators, since you can't evaluate a modal operator at a world (you could consider the world as a singleton, but that would involve copying the world parameter into the i parameter--far from trivial! Surely it is more accurate to say that Continuity simply false for modal operators).
Problems with Introspection simply involve accommodation. If we have it that accommodation is our only means of expanding C, that might be a bit odd: there doesn't seem to be a good reason to hold that assertions must always reduce C. Someone who holds that must lump all violations of Introspection over onto the pragmatics (I say this on the assumption that accommodation is a pragmatic phenomenon---I've never seen anyone deny that)...and that just seems ad hoc.
Now that I'm done ranting about our criteria for "STATIC-NESS" vs "DYNAMIC-NESS," onto the substance of Dever's comments. In DPL, like for Heim, the effect of an indefinite NP is to "open a new file"--that is, to add one member to Dom(F). Dever characterizes this as a "variable reset":
"The points from which states are built are no longer simple possible worlds--the conception that lay behind much...previous discussion. States are instead assignment functions, mapping variables to objects from a given domain.
[variable reset formula]...For example, updating a state consisting of a single assignment function \f on a tautological existential quantification Ex(x=x) will result in an enlarged state containing all x-variants of \f." (40-41)
I only sorta understand Dever's variable reset formula, but as far as I can tell it is the same as Heim's: even if all I say is the tautological "a thing is self-identical," at a context, the indefinite must (on pain of infelicity) be bearing a novel index, and so the file is updated with that new index--even though the card has no nontrivial information on it yet. This is taken to be a violation of Introspection because the points under discussion--I guess they are assignment-world pairs--expand rather than contract as a result of the semantic processing of my utterance.
The next part is interesting, since Dever goes through a bit of an epicycle regarding the importance of this move:
"[T]he violation of Introspection can appear, on examination, rather shallow. Introspection fails only for the existential quantifier [for Heim, read: indefinite NP], due to the value reset. The value reset occurs only as an artifact of the formal system, via the decision to make the very same variables available for anaphoric reuse. Were we instead to require that every quantifier, and hence every anaphoric sequence, had to be modeled by a novel variable, there would be no need for value resetting, hence no need for non-Introspective behavior. Each variable could, discourse initial, be associated with a maximal range of available assignments, and all update could proceed Introspectively." (pg 41)
There is a lot going on here. First, it isn't quite right, as far as I can tell, that in Heim's system an indefinite acts as a value reset--rather, it telegraphs the presence at LF of a novel index. So no resetting happens at all. As Dever will go on to say, the choice between the two ways of setting things up is quite trivial from a technical point of view. However, it is NOT true that Heim's system is Introspective, since the effect of an indefinite NP is to expand Dom(F).
Dever then suggests that making the semantics introspective in the way he suggests--by having all indefinite NPs bear a novel index--is a move would come at some cost:
"...But this proposal misses an important fact. The existentials are playing not just the semantic role of value resetting, but the broadly pragmatic role of providing a peg for discourse reference. If all variables begin maximally reset, then there is no remaining semantic function for the existential quantifier--any existential quantification of a variable would have to be the first occurrence of the variable, and the existential will simply reaffirm the maximally reset status of the variable. But if there is no semantic function for the existential, we lack DPL's semantic explanation of the role of existentials in licensing subsequent anaphora...
In addition to the truth-determining assignment functions, we need a dynamically developing collection of discourse reference pegs. The role of the existential then is not to reset...the assignments to a variable, but rather to expand the collection of pegs, and hence make available anaphoric connections. Adherence to STATIC is bought at the price of richer informational structure.
" (pg 42, emph. added)
The [translated into Heim-style] suggestion is that IF we adopt this patch to save Introspection, we strip indefinite NPs of any semantic function at all. Here's how this might be right: the occurrence of an indefinite NP telegraphs the presence of a novel index, but novel indices might appear on e.g. deictic pronouns as well; it is not the case that the semantic effect of novel index introduction is accomplished solely by indefinites. Moreover, such an introduction only has indirect effects on truth-conditions. However, I'm kind of suspicious of everything that's going on here: Heim's thesis is that indefinites are free variables. Surely it wouldn't be right to say that variables have no semantic value, or have no effects on truth-conditions; they are an essential ingredient in any semantics, static or otherwise.
So it seems that the question is still this: should we associate to
(1) I lost ten marbles and found nine of them.
and
(2) I lost ten marbles and found all but one.
...the same semantic value? Why not?--as long as we add that there is more to their effect on context than just their semantic value (in the sense of their truth-conditions)? We can add that the "further effect" is systematic and can be given a recursive treatment, and that a system which accounts for it can also (because of its added richness) account for all the strictly-speaking-semantic stuff too.
Perhaps the "why not" is answered by donkey sentence and bound-disjunct sentences. The minimal pairs differ not only in their felicity, but in their truth-conditions.
(3) If I get a platypus or an echidna for Christmas, my sister will want one too.
(4) If I get a monotreme for Christmas, my sister will want one too.
(5) If Andy is turning left or right, Jack is too.
(6) If Andy is turning, Jack is too.
(7) You may take a red card or a black card.
(8) You may take a card.
(9) Always, when I want to use the shower or the oven, my roommate wants to use it too.
[\neq whenever I either want to use the shower or the oven, my roommate wants to use the shower or the oven, too.]
This is an interesting thing because it differs somewhat from donkey data. For the donkey sentence, the problem was that it didn't seem possible to give the right truth-conditions for the donkey sentence using existentials; I assume this can be treated as a failure of compositionality in that the appearance of the indefinites in the sentence don't lend themselves to a compositional derivation of the truth-conditions for a donkey sentence on the traditional semantics for "a/an." However, the donkey sentence doesn't lend itself well to minimal pairs, since there doesn't seem to BE another way of saying what the donkey sentence says.
Anyway, if these minimal pairs go through, it seems to show that a disjunction cannot be analyzed as the union of its disjuncts. What I would like to do is to figure out exactly why this is so, and how it differs in the strength of its implications--as I think it does--from similar conclusions (such as embeddings of disjunctions in belief contexts). From the point of view of Dever's interests, though, what should we conclude?
If a "peg" can act as either an existential (when unbound) or a variable (when bound), then it certainly has semantic effects. Those semantic effects can be assimilated in the interpretation rules and a novelty-felicity condition, as Heim does. But this doesn't seem to me to diminish the semantic role of a peg, at all; as interpreters of speech, we couldn't know what the LF of an utterance was--and therefore, we couldn't even begin interpreting it--unless we knew which indices were novel. We know because of the placement of indefinites. Punkt!
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