InSuppose and Tell, Williamson makes a new and original attempt to defend the material conditional account of indicative conditionals. His overarching argument is that this account offers the best explanation of the data concerning how people evaluate and use such conditionals. We argue that Williamson overlooks several important alternative explanations, some of which appear to explain the relevant data at least as well as, or even better than, the material conditional account does. Along the way, we also show that Williamson (...) errs at important junctures about what exactly the relevant data are. (shrink)

The appropriateness, or acceptability, of a conditional does not just ‘go with’ the corresponding conditional probability. A condition of dependence is required as well. In this paper a particular notion of dependence is proposed. It is shown that under both a forward causal and a backward evidential reading of the conditional, this appropriateness condition reduces to conditional probability under some natural circumstances. Because this is in particular the case for the so-called diagnostic reading of the conditional, this analysis might help (...) to explain some of Douven and Verbrugge’s empirical observations. (shrink)

The paper focuses on interpreting ceteris paribus conditions as normal conditions. After discussing six basic problems for the explication of normal conditions and seven interpretations that do not well solve those problems I turn to what I call the epistemic account. According to it the normal is, roughly, the not unexpected. This is developed into a rigorous constructive account of normal conditions, which makes essential use of ranking theory and in particular allows to explain the phenomenon of multiply exceptional conditions. (...) Finally, this static account is extended to a schematic dynamic model of how we may learn about those normal and exceptional conditions. (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)

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)

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)

In this paper, a novel experimental task is developed for testing the highly influential, but experimentally underexplored, possible worlds account of conditionals (Stalnaker, 1968; Lewis, 1973). In Experiment 1, this new task is used to test both indicative and subjunctive conditionals. For indicative conditionals, five competing truth tables are compared, including the previously untested, multi-dimensional possible worlds semantics of Bradley (2012). In Experiment 2, these results are replicated and it is shown that they cannot be accounted for by an alternative (...) hypothesis proposed by our reviewers. In Experiment 3, individual variation in truth assignments of indicative conditionals is investigated via Bayesian mixture models that classify participants as following one of several competing models. As a novelty of this study, it is found that a possible worlds semantics of Lewis and Stalnaker is capable of accounting for participants’ aggregate truth value assignments in this task. Applied to indicative conditionals, we show across three experiments, that the theory both captures participants’ truth values at the aggregate level (Experiments 1 and 2) and that it makes up the largest subgroup in the analysis of individual variation in our experimental paradigm (Experiment 3). (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)

Suppose that two competing norms, N1 and N2, can be identified such that a given person’s response can be interpreted as correct according to N1 but incorrect according to N2. Which of these two norms, if any, should one use to interpret such a response? In this paper we seek to address this fundamental problem by studying individual variation in the interpretation of conditionals by establishing individual profiles of the participants based on their case judgments and reflective attitudes. To investigate (...) the participants’ reflective attitudes we introduce a new experimental paradigm called the Scorekeeping Task. As a case study, we identify the participants who follow the Suppositional Theory of conditionals (N1) versus Inferentialism (N2) and investigate to what extent internally consistent competence models can be reconstructed for the participants on this basis. After extensive empirical investigations, an apparent reasoning error with and-to-if inferences was found in one of these two groups. The implications of this case study for debates on the proper role of normative considerations in psychology are discussed. (shrink)

It is widely held that there are important differences between indicative conditionals (e.g. “If the authors are linguists, they have written a linguistics paper”) and subjunctive conditionals (e.g. “If the authors had been linguists, they would have written a linguistics paper”). A central difference is that indicatives and subjunctives convey different stances towards the truth of their antecedents. Indicatives (often) convey neutrality: for example, about whether the authors in question are linguists. Subjunctives (often) convey the falsity of the antecedent: for (...) example, that the authors in question are not linguists. This paper tests prominent accounts of how these different stances are conveyed: whether by presupposition or conversational implicature. Experiment 1 tests the presupposition account by investigating whether the stances project – remain constant – when embedded under operators like negations, possibility modals, and interrogatives, a key characteristic of presuppositions. Experiment 2 tests the conversational-implicature account by investigating whether the stances can be cancelled without producing a contradiction, a key characteristic of implicatures. The results provide evidence that both stances – neutrality about the antecedent in indicatives and the falsity of the antecedent in subjunctives – are conveyed by conversational implicatures. (shrink)

Recent studies indicate that indicative conditionals like "If people wear masks, the spread of Covid-19 will be diminished" require a probabilistic dependency between their antecedents and consequents to be acceptable (Skovgaard-Olsen et al., 2016). But it is easy to make the slip from this claim to the thesis that indicative conditionals are acceptable only if this probabilistic dependency results from a causal relation between antecedent and consequent. According to Pearl (2009), understanding a causal relation involves multiple, hierarchically organized conceptual dimensions: (...) prediction, intervention, and counterfactual dependence. In a series of experiments, we test the hypothesis that these conceptual dimensions are differentially encoded in indicative and counterfactual conditionals. If this hypothesis holds, then there are limits as to how much of a causal relation is captured by indicative conditionals alone. Our results show that the acceptance of indicative and counterfactual conditionals can become dissociated. Furthermore, it is found that the acceptance of both is needed for accepting a causal relation between two co-occurring events. The implications that these findings have for the hypothesis above, and for recent debates at the intersection of the psychology of reasoning and causal judgment, are critically discussed. Our findings are consistent with viewing indicative conditionals as answering predictive queries requiring evidential relevance (even in the absence of direct causal relations). Counterfactual conditionals in contrast target causal relevance, specifically. Finally, we discuss the implications our results have for the yet unsolved question of how reasoners succeed in constructing causal models from verbal descriptions. (shrink)

Based on the new experimental evidence, we argue that a link between a conditional antecedent and the consequent is semantically expressed rather than pragmatically conveyed. In our paper, we focus on particular kinds of links which conditionals may convey in a context. For instance, a conditional ‘If p, q’ may convey a thought equivalent to ‘p will cause q’, ‘p is the best explanation for q’, ‘q follows from p’, etcetera. The traditional theoretical literature on conditionals seems to imply that (...) these specific links are generated pragmatically and are akin to conversational implicatures. In order to test this hypothesis, we used a well-recognized linguistic test from ‘reinforceability’, which serves to distinguish between a semantic and pragmatic level of meaning, and we designed an experimental study based on that test. The outcome of our study is that specific links conveyed by conditionals exhibit features of semantic entailments rather than conversational implicatures. This result accords with some of the recent findings in empirical investigations on conditionals. In the final part of our paper, we discuss various accounts of conditionals which can accommodate the results of our study. (shrink)

This paper explores the connective ‘because’, based on the idea that ‘CbecauseA’ implies the acceptance/truth of the antecedentAas well as of the consequentC, and additionally that the antecedent makes a difference for the consequent. To capture this idea of difference-making a ‘relevantized’ version of the Ramsey Test for conditionals is employed that takes the antecedent to be relevant to the consequent in the following sense: a conditional is true/accepted in a state$$\sigma $$σjust in case (i) the consequent is true/accepted when$$\sigma (...) $$σis revised by the antecedentand(ii) the consequent fails to be true/accepted when$$\sigma $$σis revised by the antecedent’s negation. To extend this to a semantics for ‘because’, we add that (iii) the antecedent and (iv) the consequent are accepted/true in the state$$\sigma $$σ. We get metaphysical or doxastic interpretations of these clauses, depending on what we mean by a model and a state. We introduce several semantics known from suppositional conditionals, which we reinterpret for difference-making conditionals and ‘because’. We present a minimal logic for ‘because’ sentences and show how it can be extended in ways that parallel the hierarchy of extensions of the logic of suppositional conditionals. We establish correspondence results between axioms for ‘because’ and properties of states, and prove that the specified logics are sound with respect to the semantics. (shrink)

This paper investigates the implicative conditional, a connective intended to describe the logical behavior of an empirically defined class of natural language conditionals, also named implicative conditionals, which excludes concessive and some other conditionals. The implicative conditional strengthens the strict conditional with the possibility of the antecedent and of the contradictory of the consequent. $${p\Rightarrow q}$$ p ⇒ q is thus defined as $${\lnot } \Diamond {(p \wedge \lnot q) \wedge } \Diamond {p \wedge } \Diamond {\lnot q}$$ ¬ ◊ (...) ( p ∧ ¬ q ) ∧ ◊ p ∧ ◊ ¬ q. We explore the logical properties of this conditional in a reflexive normal Kripke semantics, provide an axiomatic system and prove it to be sound and complete for our semantics. The implicative conditional validates transitivity and contraposition, which we take to be integral parts of reasoning and communication. But it only validates restricted versions of strengthening the antecedent, right weakening, simplification, and rational monotonicity. Apparent counterexamples to some of these properties are explained as due to contextual factors. Finally, the implicative conditional avoids the paradoxes of material and strict implication, and validates some connexive principles such as Aristotle’s theses and weak Boethius’ thesis, as well as some highly entrenched principles of conditionals, such as conjunction of consequents, disjunction of antecedents, modus ponens, cautious monotonicity and cut. (shrink)

Decision theorists tend to treat indicative conditionals with reservation, because they can easily lead a deliberating agent astray. However, many indicatives can be very helpful in contexts of deliberation, so denying them all a role in such contexts seems to be overkill. We show that a recently revived inferential view on conditionals provides a straightforward explanation of why some indicatives are unassertable in contexts of deliberation and hints at a way of telling "deliberationally useless" and "deliberationally useful" conditionals apart.

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

This paper explores an idea of Stoic descent that is largely neglected nowadays, the idea that an argument is valid when the conditional formed by the conjunction of its premises as antecedent and its conclusion as consequent is true. As it will be argued, once some basic features of our naıve understanding of validity are properly spelled out, and a suitable account of conditionals is adopted, the equivalence between valid arguments and true conditionals makes perfect sense. The account of validity (...) outlined here, which displays one coherent way to articulate the Stoic intuition, accords with standard formal treatments of deductive validity and encompasses an independently grounded characterization of inductive validity. (shrink)

The question I am addressing in this paper is the following: how is it possible to empirically test, or confirm, counterfactuals? After motivating this question in Section 1, I will look at two approaches to counterfactuals, and at how counterfactuals can be empirically tested, or confirmed, if at all, on these accounts in Section 2. I will then digress into the philosophy of probability in Section 3. The reason for this digression is that I want to use the way observable (...) absolute and relative frequencies, two empirical notions, are used to empirically test, or confirm, hypotheses about objective chances, a metaphysical notion, as a role-model. Specifically, I want to use this probabilistic account of the testing of chance hypotheses as a role-model for the account of the testing of counterfactuals, another metaphysical notion, that I will present in Sections 4 to 8. I will conclude by comparing my proposal to one non-probabilistic and one probabilistic alternative in Section 9. (shrink)

This note is a sequel to Huber. It is shown that obeying a normative principle relating counterfactual conditionals and conditional beliefs, viz. the royal rule, is a necessary and sufficient means to attaining a cognitive end that relates true beliefs in purely factual, non-modal propositions and true beliefs in purely modal propositions. Along the way I will sketch my idealism about alethic or metaphysical modality.

This paper explores trivalent truth conditions for indicative conditionals, examining the “defective” truth table proposed by de Finetti and Reichenbach. On their approach, a conditional takes the value of its consequent whenever its antecedent is true, and the value Indeterminate otherwise. Here we deal with the problem of selecting an adequate notion of validity for this conditional. We show that all standard validity schemes based on de Finetti’s table come with some problems, and highlight two ways out of the predicament: (...) one pairs de Finetti’s conditional with validity as the preservation of non-false values, but at the expense of Modus Ponens; the other modifies de Finetti’s table to restore Modus Ponens. In Part I of this paper, we present both alternatives, with specific attention to a variant of de Finetti’s table proposed by Cooper and Cantwell. In Part II, we give an in-depth treatment of the proof theory of the resulting logics, DF/TT and CC/TT: both are connexive logics, but with significantly different algebraic properties. (shrink)

In previous published research (“Conditionals and Inferential Connections: A Hypothetical Inferential Theory,” Cognitive Psychology, 2018), we investigated experimentally what role the presence and strength of an inferential connection between a conditional’s antecedent and consequent plays in how people process that conditional. Our analysis showed the strength of that connection to be strongly predictive of whether participants evaluated the conditional as true, false, or neither true nor false. In this article, we re-analyse the data from our previous research, now focussing on (...) the semantics of conditionals rather than on how they are processed. Specifically, we use those data to compare the main extant semantics with each other and with inferentialism, a semantics according to which the truth of a conditional requires the presence of an inferential connection between the conditional’s component parts. (shrink)

This paper develops a probabilistic analysis of conditionals which hinges on a quantitative measure of evidential support. In order to spell out the interpreta- tion of ‘if’ suggested, we will compare it with two more familiar interpretations, the suppositional interpretation and the strict interpretation, within a formal framework which rests on fairly uncontroversial assumptions. As it will emerge, each of the three interpretations considered exhibits specific logical features that deserve separate consideration.

This paper outlines an account of conditionals, the evidential account, which rests on the idea that a conditional is true just in case its antecedent supports its consequent. As we will show, the evidential account exhibits some distinctive logical features that deserve careful consideration. On the one hand, it departs from the material reading of ‘if then’ exactly in the way we would like it to depart from that reading. On the other, it significantly differs from the non-material accounts which (...) hinge on the Ramsey Test, advocated by Adams, Stalnaker, Lewis, and others. (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)

Habilitation thesis in psychology. The book consists of a collection of reasoning studies. The experimental investigations will take us from people’s reasoning about probabilities, entailments, pragmatic factors, argumentation, and causality to morality. An overarching theme of the book is norm pluralism and individual differences in rationality research.

Ranking theory is one of the salient formal representations of doxastic states. It differs from others in being able to represent belief in a proposition (= taking it to be true), to also represent degrees of belief (i.e. beliefs as more or less firm), and thus to generally account for the dynamics of these beliefs. It does so on the basis of fundamental and compelling rationality postulates and is hence one way of explicating the rational structure of doxastic states. Thereby (...) it provides foundations for accounts of defeasible or nonmonotonic reasoning. It has widespread applications in philosophy, it proves to be most useful in Artificial Intelligence, and it has started to find applications as a model of reasoning in psychology. (shrink)

An organizing theme of the dissertation is the issue of how to make philosophical theories useful for scientific purposes. An argument for the contention is presented that it doesn’t suffice merely to theoretically motivate one’s theories, and make them compatible with existing data, but that philosophers having this aim should ideally contribute to identifying unique and hard to vary predictions of their theories. This methodological recommendation is applied to the ranking-theoretic approach to conditionals, which emphasizes the epistemic relevance and the (...) expression of reason relations as part of the semantics of the natural language conditional. As a first step, this approach is theoretically motivated in a comparative discussion of other alternatives in psychology of reasoning, like the suppositional theory of conditionals, and novel approaches to the problems of compositionality and accounting for the objective purport of indicative conditionals are presented. In a second step, a formal model is formulated, which allows us to derive quantitative predictions from the ranking-theoretic approach, and it is investigated which novel avenues of empirical research that this model opens up for. Finally, a treatment is given of the problem of logical omniscience as it concerns the issue of whether ranking theory (and other similar approaches) makes too idealized assumptions about rationality to allow for interesting applications in psychology of reasoning. Building on the work of Robert Brandom, a novel solution to this problem is presented, which both opens up for new perspectives in psychology of reasoning and appears to be capable of satisfying a range of constraints on bridge principles between logic and norms of reasoning, which would otherwise stand in a tension. (shrink)

This dissertation is devoted to empirically contrasting the Suppositional Theory of conditionals, which holds that indicative conditionals serve the purpose of engaging in hypothetical thought, and Inferentialism, which holds that indicative conditionals express reason relations. Throughout a series of experiments, probabilistic and truth-conditional variants of Inferentialism are investigated using new stimulus materials, which manipulate previously overlooked relevance conditions. These studies are some of the first published studies to directly investigate the central claims of Inferentialism empirically. In contrast, the Suppositional Theory (...) of conditionals has an impressive track record through more than a decade of intensive testing. The evidence for the Suppositional Theory encompasses three sources. Firstly, direct investigations of the probability of indicative conditionals, which substantiate “the Equation” (P(if A, then C) = P(C|A)). Secondly, the pattern of results known as “the defective truth table” effect, which corroborates the de Finetti truth table. And thirdly, indirect evidence from the uncertain and-to-if inference task. Through four studies each of these sources of evidence are scrutinized anew under the application of novel stimulus materials that factorially combine all permutations of prior and relevance levels of two conjoined sentences. The results indicate that the Equation only holds under positive relevance (P(C|A) – P(C|¬A) > 0) for indicative conditionals. In the case of irrelevance (P(C|A) – P(C|¬A) = 0), or negative relevance (P(C|A) – P(C|¬A) < 0), the strong relationship between P(if A, then C) and P(C|A) is disrupted. This finding suggests that participants tend to view natural language conditionals as defective under irrelevance and negative relevance (Chapter 2). Furthermore, most of the participants turn out only to be probabilistically coherent above chance levels for the uncertain and-to-if inference in the positive relevance condition, when applying the Equation (Chapter 3). Finally, the results on the truth table task indicate that the de Finetti truth table is at most descriptive for about a third of the participants (Chapter 4). Conversely, strong evidence for a probabilistic implementation of Inferentialism could be obtained from assessments of P(if A, then C) across relevance levels (Chapter 2) and the participants’ performance on the uncertain-and-to-if inference task (Chapter 3). Yet the results from the truth table task suggest that these findings could not be extended to truth-conditional Inferentialism (Chapter 4). On the contrary, strong dissociations could be found between the presence of an effect of the reason relation reading on the probability and acceptability evaluations of indicative conditionals (and connate sentences), and the lack of an effect of the reason relation reading on the truth evaluation of the same sentences. A bird’s eye view on these surprising results is taken in the final chapter and it is discussed which perspectives these results open up for future research. (shrink)

In this paper, new evidence is presented for the assumption that the reason-relation reading of indicative conditionals ('if A, then C') reflects a conventional implicature. In four experiments, it is investigated whether relevance effects found for the probability assessment of indicative conditionals (Skovgaard-Olsen, Singmann, and Klauer, 2016a) can be classified as being produced by a) a conversational implicature, b) a (probabilistic) presupposition failure, or c) a conventional implicature. After considering several alternative hypotheses and the accumulating evidence from other studies as (...) well, we conclude that the evidence is most consistent with the Relevance Effect being the outcome of a conventional implicature. This finding indicates that the reason-relation reading is part of the semantic content of indicative conditionals, albeit not part of their primary truth-conditional content. (shrink)