Introduction

Conditional sentences are sentences of the form “if A, (then) C”, as in the following examples:

(1) If this figure is a square, then it is a rectangle.

(2) If John comes to the party, Mary will be pleased.

(3) If John had come to the party, Mary would have been pleased.

In such sentences, the if-clause A is called the antecedent (sometimes protasis) of the conditional, and the then-clause C is called the consequent (or apodosis, see Carroll, 1894). Traditionally, conditional sentences have been taken to express hypothetical judgments, as opposed to categorical judgments (see the table of judgments in Kant, 1781), in that the speaker who expresses a sentence of the form “if A, C” does not assert C, but makes a weaker commitment, namely that C holds under the hypothesis expressed by A. For instance, in saying (1), the speaker expresses something weaker than if she had asserted this figure is a rectangle, and similarly with (2) and (3).

The expression of conditionality in language does not necessarily involve explicit if–then constructions, as the following examples show:

(4)

1. a. Kiss my dog and you'll get fleas.

2. b. If you kiss my dog, then you'll get fleas.

(5)

1. a. No Hitler, no A-bomb.

2. b. If there had been no Hitler, there would have been no A-bomb.

(6)

1. a. Unless you talk to Vito, you'll be in trouble.

2. b. If you don't talk to Vito, you'll be in trouble.

However, all such sentences can be rephrased by means of an if-clause, as shown by the paraphrase given below them, and in this chapter we will focus on the semantic analysis of conditional sentences expressed with if.

From a typological point of view, at least three different kinds of conditional sentences are usually distinguished on semantic grounds, namely indicative conditionals, counterfactual conditionals (sometimes called subjunctive conditionals, although, as we will see below, the two notions are not exactly coextensional), and relevance conditionals (also known as biscuit conditionals, based on Austin's example reproduced below). An illustration of the indicative–counterfactual distinction is given by (2) vs. (3) above. In (2), the speaker entertains as an open possibility that John comes to the party.