To conclude this section, we have seen some interesting aspects of when-conditional constructions. Most of these were briefly stated and no solutions were proposed. The point of this section was to get straight on the data and see what kind of problems and facts one as to think when trying to account for when-conditionals.
I have proposed an hypothesis that will be used in the next section. It could turn out to be false, but it seems to be a correct approximation for the time being. As I have argued at length in previous sections, the ‘oddness’ of when-constructions should be model through world knowledge. In the next section, I will propose an analysis that models this idea by using possible worlds as epistemic possibilities and where the growth of knowledge is worlds elimination.27 In other word, the ‘odd’ sentences that have been considered
ungrammatical will be analyzed as sentences in which there are no worlds that can make them true.
The dynamic setting that will be presented is not meant to be the final chapter of the when-conditional story. Most of the problems related to what has been called the ‘proportion problem’ will be left unexplained. However, as one should see in the next section, the system proposed allows one to see what is going on exactly and thus is a proper logical system to conduct further research on ‘when’.
7
Toward a Dynamic Setting for
When-Conditionals
This section is dedicated to the presentation of a logic extending Groenendijk and Stokhof’s Dynamic Predicate Logic (DPL) [24]. The basic idea behind this logic (that we will call DUQ1 for brevity), is to formalize the claims that had been advanced so
far concerning the individual-level/stage-level predicates distinction, the nature of when- conditionals and the nature of a case, (a situation or an event).
Like other dynamic systems, the meaning of a sentence in DUQ is not thought as lying in its truth conditions, but rather in the way it changes the information of the interpreter. The meaning of a sentence is viewed as the change an utterance of it brings about, and the meanings of non-sentential expressions consist in their contributions to this change: meaning is information change potential. As in [25], we shall distinguish two types of information: the information about the world (or factual information) and the information about the discourse.
The former is what matters the most in information exchange type of discourse. In other words, the prime purpose of the type of discourse we will be interested in is to get as best informed as possible as to know what is the world like. As in Update Semantics, ([67], [66]), information about the world will be represented as a set of possible worlds; the worlds that, given the information available, might still be the real one. Partiality of information about the world is accounted for by representing it as a set of alternative possibilities. In a nutshell, gaining information about the world amounts to eliminate worlds which were still considered possible. Hence, an agent know which world is the real one if and only if he has gained completeinformation about the world.
The second type of information, discourse information, is modeled with possible assign- ments. Assignments are used as usual, i.e. as total functions from the set of variables to the domain. To get better informed with respect to the discourse consists in eliminating possible assignments. Of course, discourse information can provide information about the world, as in [25], by the elimination of the last assignment left with respect to some world, this world gets eliminated. We will assume that the reader has basic acquaintance with both DPL and Update Semantics throughout this section.
7.1
Some Preliminaries to DUQ
It is sometimes useful to explain the reader what the logic is intended to do and how it does it before presenting it. The ideas behind DUQ is to account for the oddity of individual-level predicates in when-conditionals and Q-adverbs constructions. As we have discussed throughout this thesis, the oddity is not due to a grammatical difference, but rather caused by our world knowledge. That sentences like (1) are odd, has nothing to
do with their grammar, it has to do with the fact that it describes something that is unlikely to happen in the actual world.
(1) When Alice is tall, she can reach the cookie jar.
This is something we can model in Update Semantics using some of the insights presented in [67].
DUQ does not make use of any variables ranging over eventualities (or spatiotemporal locations). It is thus closer in spirit to Montague ([48]) than to Davidson ([15]). We have presented some arguments in the last section to prefer the former to the later. A consequence is that it makes the system slightly more complicated. We have to somehow construct the eventualities in the semantics. In order to avoid extreme complexity, we will assume a very naive conception of time. In the minimal DUQ presented here, time is thought as a finite set of time intervals on which we can define a successor and a predecessor function. We shall discuss later some ways of extending the system in order to have a more accurate conception of time.
We have seen in the previous section that tenses play an important role in making ‘when’ conditional. This is not going to be modeled here. The version of DUQ that will be presented here is minimal in a lot of respects and only after the presentation of the system, I shall discuss some possible extensions of it. Some are straightforward and has been left-out for ease of presentation. Some are more difficult to implement as I shall point out.
Finally, we have seen in the last section that when-conditionals have a strange relation with Q-adverbs and we have seen that the proportion problem is related to this. I have proposed an hypothesis: semantically, there are always two quantifications involved in when-conditional constructions. This will be modeled in DUQ and what the hypothesis involves should, by the same token, become clearer.