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)

Starting from John MacFarlane's recent survey of answers to the question ‘What is assertion?’, I defend an account of assertion that draws on elements of MacFarlane's and Robert Brandom's commitment accounts, Timothy Williamson's knowledge norm account, and my own previous work on the normative status of logic. I defend the knowledge norm from recent attacks. Indicative conditionals, however, pose a problem when read along the lines of Ernest Adams' account, an account supported by much work in the psychology of reasoning. (...) Furthermore, there seems to be no place for degrees of belief in the accounts of belief and assertion given here. Degrees of belief do have a role in decision‐making, but, again, there is much evidence that the orthodox theory of subjective utility maximization is not a good description of what we do in decision‐making and, arguably, neither is it a good normative guide to how we ought to make decisions. (shrink)

We present a unified approach for investigating rational reasoning about basic argument forms involving indicative conditionals, counterfactuals, and basic quantified statements within coherence-based probability logic. After introducing the rationality framework, we present an interactive view on the relation between normative and empirical work. Then, we report a new experiment which shows that people interpret indicative conditionals and counterfactuals by coherent conditional probability assertions and negate conditionals by negating their consequents. The data support the conditional probability interpretation of conditionals and the (...) narrow-scope reading of the negation of conditionals. Finally, we argue that coherent conditional probabilities are important for probabilistic analyses of conditionals, nonmonotonic reasoning, quantified statements, and paradoxes. (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)

Iterated conditionals of the form If p, then if q, r are an important topic in philosophical logic. In recent years, psychologists have gained much knowledge about how people understand simple conditionals, but there are virtually no published psychological studies of iterated conditionals. This paper presents experimental evidence from a study comparing the iterated form, If p, then if q, r with the “imported,” noniterated form, If p and q, then r, using a probability evaluation task and a truth-table task, (...) and taking into account qualitative individual differences. This allows us to critically contrast philosophical and psychological approaches that make diverging predictions regarding the interpretation of these forms. The results strongly support the probabilistic Adams conditional and the “new paradigm” that takes this conditional as a starting point. (shrink)

Iterated conditionals of the form If p, then if q, r are an important topic in philosophical logic. In recent years, psychologists have gained much knowledge about how people understand simple conditionals, but there are virtually no published psychological studies of iterated conditionals. This paper presents experimental evidence from a study comparing the iterated form, If p, then if q, r with the “imported,” noniterated form, If p and q, then r, using a probability evaluation task and a truth‐table task, (...) and taking into account qualitative individual differences. This allows us to critically contrast philosophical and psychological approaches that make diverging predictions regarding the interpretation of these forms. The results strongly support the probabilistic Adams conditional and the “new paradigm” that takes this conditional as a starting point. (shrink)

Given a basic conditional of the form, If A then C, individuals usually list three cases as possible: A and C, not‐A and not‐C, not‐A and C. This result corroborates the theory of mental models. By contrast, individuals often judge that the conditional is true only in the case of A and C, and that cases of not‐A are irrelevant to its truth or falsity. This result corroborates other theories of conditionals. To resolve the discrepancy, we devised two new tasks: (...) the “collective” truth task, in which participants judged whether sets of assertions about a specific individual, such as: If A then C, not‐A, C, could all be true at the same time; and one in which participants judged the truth of conditional predictions about specific future events. The results consistently matched the three possibilities, thereby corroborating the model theory. They also showed a massive violation of the probability calculus in estimates of the probabilities of the four cases in the partition of conditionals (A and C, A and not‐C, not‐A and C, and not‐A and not‐C), which summed to over 200%. (shrink)