A conditional sentence is a bi-clausal structure of the form if p (then) q. The conjunction if seems to indicate that a certain kind of relationship holds between the meanings of the two clauses. However, as the passage quoted above demonstrates, the exact nature of this relationship has been a topic of controversy for thousands of years.
An intuitive description of the construction, suggested by the term conditional, is that the if clause describes some condition under which the then clause is claimed to be true. For example, the conditional sentence in (1) claims that the proposition you are my second cousin is true under a certain condition, namely that Atatürk was your great-grandfather.
(1) If Atatürk was your great-grandfather, then you are my second cousin.
Much recent work on the meaning of conditional constructions builds on the similarities between conditionals and modals. The analysis of modality that we sketched in Chapter16 treats modal operators as quantifiers over possible worlds: modals of necessity are universal quantifiers, while modals of possibility are existential quantifiers. The difference between epistemic vs. deontic or other types of modality is the result of restricting this quantification to specific kinds of worlds. For example, we analyzed epistemic must as meaning something like, “In all worlds which are consistent with what I know about the actual world, and in which the normal course of events is followed…”
Conditionals can also be analyzed in terms of possible worlds. One way of evaluating the truth of a conditional statement like (1) is to adopt the following procedure:1 Add the content of the if clause to what is currently known about the actual world. Under those circumstances, would the then clause be true? We might suggest the following paraphrase for sentence (1): “In all possible worlds which are consistent with what I know about the actual world, and in which the normal course of events is followed, and in which Atatürk was your greatgrandfather, you are my second cousin.”
An adequate analysis needs to provide not only a reasonable paraphrase but also an explanation for how this meaning is derived compositionally, addressing questions like the following: What do the individual meanings of the two clauses contribute to the meaning of the sentence as a whole? What does if mean? These questions lead to some very complex issues, to which this chapter can provide only a brief introduction.
It will be easier to talk about conditional sentences if we introduce some standard terminology for referring to the parts of such sentences. We refer to the if clause as the antecedent (also known as the protasis); and to the then clause as the conseqent (or apodosis). The names antecedent and consequent reflect the most basic ordering of these clauses (if p, q), not only in English but (apparently) in all languages.2 But in many languages the opposite order (q if p) is possible as well. Regardless of which comes first in any particular sentence, the antecedent names the condition under which the consequent is claimed to be true.
One factor that makes the analysis of conditional sentences so challenging is that the conditional structure can be used for a variety of different functions, not only in English but in many other languages as well. We introduce the most common of these in §19.2. In §19.3 we focus on “standard” conditionals, i.e. those in which neither the antecedent nor the consequent is asserted or presupposed to be true. In many languages these conditionals may be marked by tense, mood, or other grammatical indicators to show the speaker’s degree of confidence as to how likely the antecedent is to be true.
In §19.4 we will return to the question raised in Chapter 9 as to whether the meaning of English if can be adequately represented or defined in terms of the material implication operator (→) of propositional logic. We will see that, for a number of reasons, this does not seem to be possible. (Of course, that does not mean that the material implication operator is useless for doing natural language semantics; it is an indispensible part of the logical metalanguage. It just means that material implication does not provide a simple translation equivalent for English if.)
We go on in §19.5 to discuss one very influential approach to defining the meaning of if, which takes it to be a marker of restriction for modals or other types of quantifiers. §19.6 discusses some of the special challenges posed by counterfactual conditionals, in which the antecedent is presupposed to be false. Finally, in §19.7 we argue for a distinction between truth-conditional vs. speech act conditionals, and provide some evidence for the claim that speech act conditionals are not part of the propositional content that is being asserted, questioned, etc.
1 This is a version of the “Ramsey Test” from Stalnaker (1968).
2 Greenberg (1963: 84–85); Comrie (1986: 83).
