## 1. Introduction

According to what is now commonly referred to as “the Equation” in the literature on indicative conditionals, the probability of any indicative conditional equals the probability of its consequent conditional on its antecedent, provided the latter is defined.1 Formally, where “if” is the indicative conditional operator,2

Stalnaker (1970) presented this as an adequacy condition to be met by any semantics for conditionals, meaning that candidate accounts of the truth conditions for conditionals should at least validate (EQ). But, while (EQ) was initially found to have considerable intuitive appeal, Lewis's (1976) so-called triviality arguments convinced the broad philosophical community that (EQ) can be maintained only at the expense of the view that conditionals express propositions, that is, the view that conditionals have classical truth conditions in that they are either true or false.

For a number of theorists, the triviality arguments have been a reason to reject (EQ). However, over the past decade, (EQ) has been subjected to empirical testing by various experimental psychologists, and it has been found, time and again, that people's judged probabilities of conditionals do closely match their judgments of the corresponding conditional probabilities; see, for instance, Hadjichristidis et al. (2001), Evans, Handley, and Over (2003), Oaksford and Chater (2003), Oberauer and Wilhelm (2003), Over and Evans (2003), Evans and Over (2004), Weidenfeld, Oberauer, and Hornig (2005), Evans, Handley, Neilens, and Over (2007), Evans, Handley, Neilens, Bacon, and Over (2010), Oberauer, Geiger, Fischer, and Weidenfeld (2007), Oberauer, Weidenfeld, and Fischer (2007), Over, Hadjichristidis, Evans, Handley, and Sloman (2007), Douven and Verbrugge (2010), Pfeifer and Kleiter (2010), and Politzer, Over, and Baratgin (2010). Given these experimental results, rejecting (EQ) would amount to attributing massive error to people as far as their judgments of the probabilities of conditionals are concerned. In view of this, abandoning the assumption that conditionals express propositions has come to appear the more attractive option to many, even though—it is generally acknowledged—doing so raises some thorny issues, most notably, concerning how conditionals combine with other parts of our language and how we are to account for iterated conditionals.

The present study argues against the broadly shared view that the triviality arguments have shown (EQ) to be incompatible with the view that conditionals express propositions. Specifically, we will point out that these arguments rely on assumptions that entail a generalization of (EQ). Despite the surge of interest among psychologists in the probabilities of conditionals, the said generalized version of (EQ) has so far been ignored by experimentalists. We have, for the first time, tested this version and have obtained data refuting it. In the following, we report these data and argue that, in conjunction with the extant empirical evidence for (EQ), they suggest that (EQ) is tenable even if conditionals express propositions. We start by describing the broader theoretical background of our experimental work, in particular current approaches to the semantics of conditionals, which have raised interest in (EQ) in the first place.