Every research project has to be clear about its scope, the boundaries within which it is carried out. The resources of research are limited, certainly in the case of a dissertation project. Some issues, even though relevant for the topic of investigations cannot be dealt with. In this section we will set some boundaries for the research reported here.
In the section on terminological preliminaries it should have become clear that this research is about very specific conditional sentences: those with an explicit antecedent in the form of a subordinated sentence starting with the connective if. But there are also other ways in which the class of conditionals discussed here is restricted. We will not consider conditional sentences with a non-assertive con- sequent, as in (53a) or (53b). We will also exclude Austin conditionals (example (53c)) and anakastic conditionals (example (53d)). These conditionals raise a lot of issues of their own that we cannot deal with here. However, we hope that with the right semantics for questions, imperatives, etc. the approach presented in the following chapters can be easily extended to account for these conditionals.
(53) a. If this has been discussed before then please stop me, but ... (conditional plea)
b. If all Prophecy has been fulfilled, then isn’t the Bible Irrelevant? (con- ditional question)
c. If you are thirsty, there is beer in the fridge. (Austin conditionals) d. If you wanna go to Harlem, you have to take the A-train. (anakastic
conditional)
Furthermore, we will not consider habitual readings of conditionals. That means, we will not deal with conditionals that make statements about general regularities like (54). Indicative conditionals without a modal in the consequent in particular favor habitual readings. For those whose the consequent stands in the present tense and is not marked for the perfect, it has even often been claimed to be the only possible reading. If this is correct, then we have nothing to say about sentences like (54).
(54) If butter is heated, it melts.
There is also another way in which the scope of the theory developed here is limited, except for the class of conditional sentences it considers. The compo- sitional analysis of conditional sentences that will be proposed is not complete. We will only analyze the structure of conditional sentences to the extent that the contribution of the tenses, the perfect and the modals can be distinguished. Predicate structures and reference to individuals will not be distinguished. Even more important, we will not deal with the aspectual classes of the verbal phrases in antecedent and consequent. Although we do propose a semantics for the tenses and the perfect, it will only concern their temporal properties, not their aspec- tual impact. This decision allows us to keep our model simple in that we do not have to introduce event semantics. However, because the topic of the present re- search concerns the temporal properties of conditionals, and aspectual questions are without doubt of relevance for these temporal properties, this is a limitation of the present work that has to be overcome in future work.
Finally, a more methodological caveat. People familiar with the classical liter- ature on the semantics of conditionals may miss a study of the logical properties the theory developed here predicts for conditionals. The discussion in more tra- ditional approaches is concerned with establishing the validity or invalidity of certain logical principles that are considered to characterize conditional reason- ing. However, many of these issues, which play an important role in philosophical discussions, are orthogonal to the more linguistic questions we want to answer here. Thus, even though it is interesting and relevant to investigate how the present approach behaves with respect to these logical properties, this is not our priority here, and therefore has to await future work.
The meaning of the
conditional connective
5.1
Introduction
A large part of the extensive philosophical literature on the semantics of condi- tionals deals exclusively with the meaning of would have conditionals. Addition- ally, philosophers generally describe the semantics of these sentences at a very abstract level, ignoring the semantic impact of tense and modality markers etc. occurring in antecedent and consequent on the semantics. Would have condition- als are treated as constructions made up of a conditional operator ≻ and two sentences representing antecedent and consequent. These sentences are taken to be, if not primitive, then combinations of primitive sentences using the standard connectives ∧, ∨ and ¬ and sometimes also ≻ itself. As explained in the introduc- tion, we want to extend this line of approach with a more serious consideration of the compositional structure of English conditional sentences, to deal in par- ticular with their temporal properties. But this certainly does not mean that all the classical, abstract work on the meaning of would have conditionals is useless. In the ideal case we can take a description of the meaning of would have condi- tionals at this abstract level as a starting point and obtain a linguistically more adequate approach by the introduction of a more complex formal language and the addition of time to the model. The problem with this strategy is that there is not such a thing as the approach to the meaning of would have conditionals at the traditional level of abstraction. Instead there are many different proposals that all have been criticized for various reasons. There is, however, one approach that is particularly popular and has dominated the thinking on the meaning of would have conditionals through the last decades. This is the similarity approach
proposed by Stalnaker (1968) and Lewis (1973). According to this approach, a would have conditional is true if on those models for the antecedent that are most similar to the evaluation world the consequent is true as well. Unfortunately, this approach also comes with certain problems. Hence, we cannot take it unqualified as a starting point for our work. A central criticism is that the description of the similarity relation provided in the original work of Stalnaker and Lewis is too vague. The present chapter will address this problem and try to solve it at the traditional abstract level, before matters become complicated by the introduction of time into the model and a much more complex syntactic analysis of conditional sentences. The goal is first to come up with a convincing description of the se- mantic meaning of would have conditionals at the traditional, abstract level that can then be used as a starting point for the compositional approach developed in the following chapter.
The chapter is structured as follows. We will start by giving a short outline of the basic idea of the similarity approach. Afterwards we will discuss two types of observations brought forward to argue for a more restricted notion of similar- ity than what was originally proposed by Stalnaker and Lewis. In particular, the observations have been used to defend the popular idea that similarity is promi- nently similarity of the past. We will argue that while indeed there is evidence showing that a more restricted notion of similarity is needed, the conclusion that this restrictions has to apply to some notion of pastness is not necessary. Fur- thermore, we will claim that such a purely temporal restriction of similarity is not appropriate to describe the meaning of would have conditionals.
We turn then to another proposal for how to restrict the similarity relation: premise semantics. Premise semantics combines the similarity approach with a different tradition in the history of approaches to the semantics of would have conditionals: cotenability theories. According to premise semantics similarity has to be defined in terms of a certain set of facts of the evaluation world. In the simplest case a world is said to be more similar to the evaluation world, the more of these facts it makes true. Theories of premise semantics can differ in the facts they take to be relevant for similarity and how exactly the impact of these facts on the similarity relation is described. We will focus on one recent proposal in this framework (Veltman 2005) and show how it solves some of the problematic examples for the similarity approach. However, we will also see that it is not able to provide the right restrictions for similarity in general.
After this we will turn our attention to an approach to the meaning of would have conditionals that – at least on first view – diverges from the similarity paradigm. This is the proposal made in Pearl (2000), according to which would have conditionals are interpreted as executing hypothetical surgeries on causal dependencies. We will argue, that while this approach can account for many traditionally hard examples for would have conditionals, it makes the wrong as- sumption that all of these conditionals are based on causal dependencies.
The proposal of Pearl and premise semantics are then combined and turned into a new approach to the meaning of would have conditionals. We will argue that two readings for would have conditionals have to be distinguished. One reading – the ontic reading – can be described by an adapted version of Pearl’s theory. The second reading – the epistemic reading – is based on belief revision. Both readings will be formalized as instantiations of the similarity approach, more particularly, of premise semantics. We will see that the new theory obtained this way allows us to overcome many of the shortcomings of the other approaches discussed in this chapter.