It is commonly believed that the role of context cannot be ignored in the analysis of conditionals, and counterfactuals in particular. On truth conditional accounts involving possible worlds semantics, conditionals have been analysed as expressions of relative necessity: “If A, then B” is true at some world w if B is true at all the A-worlds deemed relevant to the evaluation of the conditional at w. A drawback of this approach is that for the evaluation of conditionals with the same (...) antecedents at some world, the same worlds are deemed as relevant for all occasions of utterance. But surely this is inadequate, if shifts of contexts between occasions are to be accounted for. Both the linguistic and logical implications of this defect are discussed, and in order to overcome it a modification of David Lewis’ ordering semantics for counterfactuals is developed for a modified language. I follow Lewis by letting contexts determine comparative similarity assignments, and show that the addition of syntactic context parameters (context indices) to the language gives the freedom required to switch between sets of relevant antecedent worlds from occasion to occasion by choosing the corresponding similarity assignment accordingly. Thus an account that extends Lewis’ analysis of a language containing a single counterfactual connective > to a language containing infinitely many counterfactual connectives >_c, each indexed by a different context name c, overcomes the limitations of traditional analyses. Finally it is also shown that these traditional accounts can be recovered from the modified account if certain contextual restrictions are in place. -/- . (shrink)

In my article, I present a new version of a probabilistic truth prescribing semantics for natural language indicative conditionals. The proposed truth conditions can be paraphrased as follows: an indicative conditional is true if the corresponding conditional probability is high and the antecedent is positively probabilistically relevant for the consequent or the probability of the antecedent of the conditional equals 0. In the paper, the truth conditions are defended and some of the logical properties of the proposed semantics are described.

The chapter is devoted to the probability and acceptability of indicative conditionals. Focusing on three influential theses, the Equation, Adams’ thesis, and the qualitative version of Adams’ thesis, Sikorski argues that none of them is well supported by the available empirical evidence. In the most controversial case of the Equation, the results of many studies which support it are, at least to some degree, undermined by some recent experimental findings. Sikorski discusses the Ramsey Test, and Lewis’s triviality proof, with special (...) attention dedicated to the popular ways of blocking it. Sikorski concludes that the role of the three theses in future studies of conditionals should be re-thought, and he presents alternative proposals. (shrink)

The Ramsey Test is considered to be the default test for the acceptability of indicative conditionals. I will argue that it is incompatible with some of the recent developments in conceptualizing conditionals, namely the growing empirical evidence for the _Relevance Hypothesis_. According to the hypothesis, one of the necessary conditions of acceptability for an indicative conditional is its antecedent being positively probabilistically relevant for the consequent. The source of the idea is _Evidential Support Theory_ presented in Douven (2008). I will (...) defend the hypothesis against alleged counterexamples, and show that it is supported by growing empirical evidence. Finally, I will present a version of the Ramsey test which incorporates the relevance condition and therefore is consistent with growing empirical evidence for the relevance hypothesis. (shrink)

In this study we investigate the influence of reason-relation readings of indicative conditionals and ‘and’/‘but’/‘therefore’ sentences on various cognitive assessments. According to the Frege-Grice tradition, a dissociation is expected. Specifically, differences in the reason-relation reading of these sentences should affect participants’ evaluations of their acceptability but not of their truth value. In two experiments we tested this assumption by introducing a relevance manipulation into the truth-table task as well as in other tasks assessing the participants’ acceptability and probability evaluations. Across (...) the two experiments a strong dissociation was found. The reason-relation reading of all four sentences strongly affected their probability and acceptability evaluations, but hardly affected their respective truth evaluations. Implications of this result for recent work on indicative conditionals are discussed. (shrink)

This paper examines precursors and consequents of perceived relevance of a proposition A for a proposition C. In Experiment 1, we test Spohn's assumption that ∆P = P − P is a good predictor of ratings of perceived relevance and reason relations, and we examine whether it is a better predictor than the difference measure − P). In Experiment 2, we examine the effects of relevance on probabilistic coherence in Cruz, Baratgin, Oaksford, and Over's uncertain “and-to-if” inferences. The results suggest (...) that ∆P predicts perceived relevance and reason relations better than the difference measure and that participants are either less probabilistically coherent in “and-to-if” inferences than initially assumed or that they do not follow P = P. Results are discussed in light of recent results suggesting that the Equation may not hold under conditions of irrelevance or negative relevance. (shrink)

The aim is to motivate theoretically a relevance approach to conditionals in a comparative discussion of the main alternatives. In particular, it will be argued that a relevance approach to conditionals is better motivated than the suppositional theory currently enjoying wide endorsement. In the course of this discussion, an argument will be presented for why failures of the epistemic relevance of the antecedent for the consequent should be counted as genuine semantic defects. Furthermore, strategies for dealing with compositionality and the (...) perceived objective purport of indicative conditionals will be put forward. (shrink)

Ranking theory is a formal epistemology that has been developed in over 600 pages in Spohn's recent book The Laws of Belief, which aims to provide a normative account of the dynamics of beliefs that presents an alternative to current probabilistic approaches. It has long been received in the AI community, but it has not yet found application in experimental psychology. The purpose of this paper is to derive clear, quantitative predictions by exploiting a parallel between ranking theory and a (...) statistical model called logistic regression. This approach is illustrated by the development of a model for the conditional inference task using Spohn's ranking theoretic approach to conditionals. (shrink)

Is evidential support transitive? The answer is negative when evidential support is understood as confirmation so that X evidentially supports Y if and only if p(Y | X) > p(Y). I call evidential support so understood “support” (for short) and set out three alternative ways of understanding evidential support: support-t (support plus a sufficiently high probability), support-t* (support plus a substantial degree of support), and support-tt* (support plus both a sufficiently high probability and a substantial degree of support). I also (...) set out two screening-off conditions (under which support is transitive): SOC1 and SOC2. It has already been shown that support-t is non-transitive in the general case (where it is not required that SOC1 holds and it is not required that SOC2 holds), in the special case where SOC1 holds, and in the special case where SOC2 holds. I introduce two rather weak adequacy conditions on support measures and argue that on any support measure meeting those conditions it follows that neither support-t* nor support-tt* is transitive in the general case, in the special case where SOC1 holds, or in the special case where SOC2 holds. I then relate some of the results to Douven’s evidential support theory of conditionals along with a few rival theories. (shrink)

This paper outlines an account of concessive conditionals that rests on two main ideas. One is that the logical form of a sentence as used in a given context is determined by the content expressed by the sentence in that context. The other is that a coherent distinction can be drawn between a reading of ‘if’ according to which a conditional is true when its consequent holds on the supposition that its antecedent holds, and a stronger reading according to which (...) a conditional is true when its antecedent supports its consequent. As we will suggest, the logical form of concessive conditionals can be elucidated by relying on this distinction. (shrink)

According to the Bayesian paradigm in the psychology of reasoning, the norms by which everyday human cognition is best evaluated are probabilistic rather than logical in character. Recently, the Bayesian paradigm has been applied to the domain of argumentation, where the fundamental norms are traditionally assumed to be logical. Here, we present a major generalisation of extant Bayesian approaches to argumentation that (i)utilizes a new class of Bayesian learning methods that are better suited to modelling dynamic and conditional inferences than (...) standard Bayesian conditionalization, (ii) is able to characterise the special value of logically valid argument schemes in uncertain reasoning contexts, (iii) greatly extends the range of inferences and argumentative phenomena that can be adequately described in a Bayesian framework, and (iv) undermines some influential theoretical motivations for dual function models of human cognition. We conclude that the probabilistic norms given by the Bayesian approach to rationality are not necessarily at odds with the norms given by classical logic. Rather, the Bayesian theory of argumentation can be seen as justifying and enriching the argumentative norms of classical logic. (shrink)

The new Bayesian paradigm in the psychology of reasoning aims to integrate the study of human reasoning, decision making, and rationality. It is supported by two findings. One, most people judge the probability of the indicative conditional, P(if A then B), to be the conditional probability, P(B|A), as implied by the Ramsey test. Two, they judge if A then B to be void when A is false. Their three-valued response table used to be called ‘defective’, but should be termed the (...) de Finetti table. We show how to study general de Finetti truth tables for negations, conjunctions, disjunctions, and conditionals. (shrink)

More than a decade of research has found strong evidence for P(if A, then C) = P(C|A) (“the Equation”). We argue, however, that this hypothesis provides an overly simplified picture due to its inability to account for relevance. We manipulated relevance in the evaluation of the probability and acceptability of indicative conditionals and found that relevance moderates the effect of P(C|A). This corroborates the Default and Penalty Hypothesis put forward in this paper. Finally, the probability and acceptability of concessive conditionals (...) (“Even if A, then still C”) were investigated and it was found that the Equation provides a better account of concessive conditionals than of indicatives across relevance manipulations. (shrink)