The Probabilities of Conditionals Revisited

Abstract

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 of the conditional given the antecedent of the conditional. Philosophers widely agree in their assessment that the triviality arguments of Lewis and others have conclusively shown the Equation to be tenable only at the expense of the view that indicative conditionals express propositions. This study challenges the correctness of that assessment by presenting data that cast doubt on an assumption underlying all triviality arguments.

Logic, probability, and human reasoning

“…Some studies support the Equation, although to varying degrees [54,[75][76][77][78][79][80], and others do not [81,82]. It may fail because of ignorance of the probability calculus: a recent study reports that the judgments of only a minority of well-educated individuals corroborated it and only for some sorts of conditional [83].…”

“…Basic conditionals -those unaffected by modulation -refer to the three possibilities above. They are analogous to the truth table for material implication (see Table 1 in main text) and that analogy has misled many theorists into supposing that the model theory treats basic conditionals as material implications (e.g., [23,71,75,79]). On the contrary, it implies that a basic conditional, 'if A then C', is true only if all three situations in its fully explicit models are possible:…”

Experimental Approaches to the Study of Conditionals

“…van Fraassen presents the belief-state-sensitivity of the conditional as a possibility, but recently empirical results have been found to be in support of the hypothesis that this possibility actually obtains. Douven and verbrugge (2013) present evidence showing that people do not in general obey the generalized version of the Equation according to which the conditional probability of "If A then C" given some condition B equals the conditional probability of C given the conjunction of A and B. This is exactly what we would expect to find on the assumption that van Fraassen is right.…”

“…6 Johnson-laird and Byrne do not quite put it this way, but the circumstances under which a basic conditional is true (Johnson-laird and Byrne 2002, 650) are exactly those under which the corresponding material conditional is true. 7 See Hadjichristidis et al (2001), Evans, Handley, and over (2003), oberauer and Wilhelm (2003, over (2004), Weidenfeld, oberauer, andHornig (2005), Evans et al (2007), oaksford and Chater (2007), oberauer Fischer (2007), over et al (2007), gauffroy and Barrioullet (2009), verbrugge (2010, 2013), Pfeifer and Kleiter (2010), Politzer, over, and Baratgin (2010), Fugard et al (2011), and over, Douven, and verbrugge (2013). 8 In fact, there was also a control group of participants who were not shown the patches but only received a description of the soritical series.…”

Dynamic inference and everyday conditional reasoning in the new paradigm

“…Recall that the reasonableness of MP relies on the probability that "S assigns to the car starting given S learns that the key is turned being greater than or equal to the probability S assigns to the probability of the car starting assuming the key was turned." This is because, on the subjective 1 We thank Igor Douven for pointing out that if probability conditionals cannot be regarded as propositions, then this notation can only be interpreted as a pseudo-probability (see Douven & Verbrugge, 2013).…”