On the negation of indicative conditionals∗

A debated aspect of the analysis of indicative conditionals of the form “if A then C” concerns whether they have as their negation the conjunction “A and not C” or the conditional negation “if A then not C”. We argue that neither theory is adequate, but that both forms of negation can be pragmatically retrieved from a Kratzer-style analysis of conditionals in which the negation of “if A then C” is equivalent to the weak negation “if A possibly not C”. This paper lays out the relevant pragmatic hypotheses and presents the results of one experimental study intended to test those predictions. 1 Negating conditionals By an indicative conditional sentence, we mean an if-then sentence in which both the antecedent and the consequent are in the indicative mood, as in the following examples: (1) If John was in Paris, then Mary was in New York. (2) If John visits Paris tomorrow, then Mary will be pleased. (3) If this figure is a rectangle, then it is a square. The question we are investigating is how the insertion of a sentential negation operator (such as “it is not the case that”) is understood, and more specifically how the denial of such sentences is expressed (as in a response starting by “No,...”), depending on the sentence and on the context. A large part of the recent literature on the negation of conditionals has been focused on the opposition between two families of theories: on the one hand accounts based on the material conditional analysis, predicting the negation of “if A then C” to be the conjunction “A and not C” (see [6], [8], [10], [9]), and on the other suppositional theories predicting the negation to be the conditional negation “if A then not C” (including possible-world theories [20], trivalent theories [15], [1], and probabilistic theories [2], [4], [16], [5]). Several experiments have been conducted in recent years by psychologists of reasoning to advance this debate (viz. [7], [3], [11]), indicating a preference for conditional negation, but with systematic exceptions (for example, [7] report differences depending on whether the conditional sentence is in the past tense, or the future tense). ∗This is an abridged version of a more extended paper in preparation. The full version, in particular, also includes the results of another experimental study. We are indebted to Jean Baratgin, David Over, Philippe Schlenker, and Benjamin Spector for valuable discussions, and to Robert Stalnaker for helpful comments and criticisms. We also thank Jean-Louis Stilgenbauer for his technical assistance in the experiment, and the ANR project BETAFDOC (“Beyond Degrees of Truth, Degrees of Confidence”) for support. 1Suppositional theories are all inspired from Ramsey’s remarks in[18], who already concluded, from what has since been called the Ramsey Test: “in a sense If p, q and If p,¬q are contradictories”. Proceedings of the 19th Amsterdam Colloquium Maria Aloni, Michael Franke & Floris Roelofsen (eds.) 10 Our claim is that the debate has been unduly restricted to that opposition. In particular, most accounts of the psychology of conditionals have ignored a third family of accounts, predicting the negation of a conditional sentence to be equivalent to “if A, possibly not C’ (viz. [13], [12], [14] and other analyses in the family of strict conditionals, without the uniqueness assumption). In our view, this modal negation is the baseline negation for all indicative conditionals, but the other two kinds of negations are pragmatically recoverable from it based on additional features of the context and on constraints regarding the information shared between the participants in a conversation. In what follows we first give a more precise operationalized version of those hypotheses, and then present the result of one experimental study in which they were tested.