We discuss O&C's probabilistic approach from a probability logical point of view. Specifically, we comment on subjective probability, the indispensability of logic, the Ramsey test, the consequence relation, human nonmonotonic reasoning, intervals, generalized quantifiers, and rational analysis.

The two main psychological theories of the ordinary conditional were designed to account for inferences made from assumptions, but few premises in everyday life can be simply assumed true. Useful premises usually have a probability that is less than certainty. But what is the probability of the ordinary conditional and how is it determined? We argue that people use a two stage Ramsey test that we specify to make probability judgements about indicative conditionals in natural language, and we describe experiments (...) that support this conclusion. Our account can explain why most people give the conditional probability as the probability of the conditional, but also why some give the conjunctive probability. We discuss how our psychological work is related to the analysis of ordinary indicative conditionals in philosophical logic. (shrink)

Modus ponens is the argument from premises of the form If A, then B and A to the conclusion B. Nearly all participants agree that the modus ponens conclusion logically follows when the argument appears in this Basic form. However, adding a further premise can lower participants’ rate of agreement—an effect called suppression. We propose a theory of suppression that draws on contemporary ideas about conditional sentences in linguistics and philosophy. Semantically, the theory assumes that people interpret an indicative conditional (...) as a context-sensitive strict conditional: true if and only if its consequent is true in each of a contextually determined set of situations in which its antecedent is true. Pragmatically, the theory claims that context changes in response to new assertions, including new conditional premises. Thus, the conclusion of a modus ponens argument may no longer be accepted in the changed context. Psychologically, the theory describes people as capable of reasoning about broad classes of possible situations, ordered by typicality, without having to reason about individual possible worlds. The theory accounts for the main suppression phenomena, and it generates some novel predictions that new experiments confirm. (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)

Causal reasoning is one of our most central cognitive competencies, enabling us to adapt to our world. Causal knowledge allows us to predict future events, or diagnose the causes of observed facts. We plan actions and solve problems using knowledge about cause-effect relations. Without our ability to discover and empirically test causal theories, we would not have made progress in various empirical sciences. In the past decades, the important role of causal knowledge has been discovered in many areas of cognitive (...) psychology. Despite the ubiquity of causal reasoning, textbooks of cognitive psychology have neglected this growing field. The goal of The Oxford Handbook of Causal Reasoning is to fill this gap. The handbook brings together the leading researchers in the field of causal reasoning and offers state-of-the-art presentations of theories and research. It provides introductions of competing theories of causal reasoning, and discusses its role in various cognitive functions and domains. The final section presents research from neighboring fields. 1. Causal Reasoning: An Introduction Michael R. Waldmann Part I: Theories of Causal Cognition 2. Associative Accounts of Causal Cognition Mike E. Le Pelley, Oren Griffiths, and Tom Beesley 3. Rules of Causal Judgment: Mapping Statistical Information Onto Causal Beliefs José C. Perales, Andrés Catena, Antonio Cándido, and Antonio Maldonado 4. The Inferential Reasoning Theory of Causal Learning: Toward a Multi- Process Propositional Account Yannick Boddez, Jan De Houwer, and Tom Beckers 5. Causal Invariance as an Essential Constraint for Creating a Causal Representation of the World: Generalizing the Invariance of Causal Power Patricia W. Cheng and Hongjing Lu 6. The Acquisition and Use of Causal Structure Knowledge Benjamin Margolin Rottman 7. Formalizing Prior Knowledge in Causal Induction Thomas L. Griffiths 8. Causal Mechanisms Samuel G. B. Johnson and Woo-kyoung Ahn 9. Force Dynamics and Causation Phillip Wolff and Robert Thorstad 10. Mental Models and Causation P. N. Johnson- Laird and Sangeet S. Khemlani 11. Pseudocontingencies Klaus Fiedler and Florian Kutzner 12. Singular Causation David Danks 13. Cognitive Neuroscience of Causal Reasoning Joachim T. Operskalski and Aron K. Barbey Part II: Basic Cognitive Functions 14. Visual Impressions of Causality Peter White 15. Goal-Directed Actions Bernhard Hommel 16. Planning and Control Magda Osman 17. Reinforcement Learning and Causal Models Samuel J. Gershman 18. Causation and the Probability of Causal Conditionals David E. Over 19. Causal Models and Conditional Reasoning Mike Oaksford and Nick Chater 20. Concepts as Causal Models: Categorization Bob Rehder 21. Concepts as Causal Models: Induction Bob Rehder 22. Causal Explanation Tania Lombrozo and Nadya Vasilyeva 23. Diagnostic Reasoning Björn Meder and Ralf Mayrhofer 24. Inferring Causal Relations by Analogy Keith J. Holyoak and Hee-Seung Lee 25. Causal Argument Ulrike Hahn, Roland Bluhm, and Frank Zenker 26. Causality in Decision- Making York Hagmayer and Philip M. Fernbach Part III: Domains of Causal Reasoning 27. Intuitive Theories Tobias Gerstenberg and Joshua B. Tenenbaum 28. Space, Time, and Causality Marc J. Buehner 29. Causation in Legal and Moral Reasoning David A. Lagnado and Tobias Gerstenberg 30. The Role of Causal Knowledge in Reasoning About Mental Disorders Woo-kyoung Ahn, Nancy S. Kim, and Matthew S. Lebowitz 31. Causality and Causal Reasoning in Natural Language Torgrim Solstad and Oliver Bott 32. Social Attribution and Explanation Denis Hilton Part IV: Development, Phylogeny, and Culture 33. The Development of Causal Reasoning Paul Muentener and Elizabeth Bonawitz 34. Causal Reasoning in Non-Human Animals Christian Schloegl and Julia Fischer 35. Causal Cognition and Culture Andrea Bender, Sieghard Beller, and Douglas L. Medin. (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)

Studies of categorical induction typically examine how belief in a premise (e.g., Falcons have an ulnar artery) projects on to a conclusion (e.g., Robins have an ulnar artery). We study induction in cases in which the premise is uncertain (e.g., There is an 80% chance that falcons have an ulnar artery). Jeffrey's rule is a normative model for updating beliefs in the face of uncertain evidence. In three studies we tested the descriptive validity of Jeffrey's rule and a related probability (...) theorem, the rule of total probability. Although these rules provided good approximations to mean judgments in some cases, the results from regression and correlation analyses suggest that participants focus on the parts of these rules that are associated with the highest overall probability. We relate our findings to rational models of judgment. (shrink)

In two experiments, we investigated how people interpret and reason with realistic conditionals in the form of inducements (i.e., promises and threats) and advice (i.e., tips and warnings). We found that inducements and advice differed with respect to the degree to which the speaker was perceived to have (a) control over the consequent, (b) a stake in the outcome, and (c) an obligation to ensure that the outcome occurs. Inducements and advice also differed with respect to perceived sufficiency and necessity, (...) as well as the degree to which these statements were perceived to be effective in changing the behaviour described in the antecedent of the conditional. Multiple regression analyses indicated that perceived control over the consequent, necessity, and sufficiency emerged as the best predictors of (a) the degree to which statements were perceived to be effective in changing the behaviour of the addressee, and (b) inference patterns on a conditional arguments task. (shrink)

The appeal to expert opinion is an argument form that uses the verdict of an expert to support a position or hypothesis. A previous scheme-based treatment of the argument form is formalized within a Bayesian network that is able to capture the critical aspects of the argument form, including the central considerations of the expert's expertise and trustworthiness. We propose this as an appropriate normative framework for the argument form, enabling the development and testing of quantitative predictions as to how (...) people evaluate this argument, suggesting that such an approach might be beneficial to argumentation research generally. We subsequently present two experiments as an example of the potential for future research in this vein, demonstrating that participants' quantitative ratings of the convincingness of a proposition that has been supported with an appeal to expert opinion were broadly consistent with the predictions of the Bayesian model. (shrink)

The explanation of the suppression of Modus Ponens inferences within the framework of linguistic pragmatics and of plausible reasoning (i.e., deduction from uncertain premises) is defended. First, this approach is expounded, and then it is shown that the results of the first experiment of Byrne, Espino, and Santamar a (1999) support the uncertainty explanation but fail to support their counterexample explanation. Second, two experiments are presented. In the first one, aimed to refute one objection regarding the conclusions observed, the additional (...) conditional premise ( if N, C ) was replaced with a statement of uncertainty ( it is not certain that N ); the answers produced by the participants remained qualitatively and quantitatively similar in both conditions. In the second experiment, a fine-grained analysis of the responses to and justifications for an evaluation task was performed. The results of both experiments strongly supported the uncertainty explanation. (shrink)

Participants acting as mock jurors made inferences about whether a person was a suspect in a murder based on an expert's testimony about the presence of objects at the crime scene and the disclosure that the testimony was true or false. Experiment 1 showed that participants made more correct inferences, and made inferences more quickly, when the truth or falsity of the expert's testimony was disclosed immediately after the testimony rather than when the disclosure was delayed. Experiment 2 showed no (...) advantage for prior disclosure over immediate disclosure. Experiment 3 showed that the pattern of inferences when there was no disclosure mirrored the pattern when it was disclosed that the expert's testimony was true rather than false. Participants made more correct inferences from true conjunctions than disjunctions, and from false disjunctions than conjunctions. We discuss the implications for theories of the mental representations and cognitive processes that underlie human reasoning. (shrink)

Recent research (e.g., Evans & Over, 2004) has provided support for the hypothesis that people evaluate the probability of conditional statements of the form if p then q as the conditional probability of q given p , P( q / p ). The present paper extends this approach to pragmatic conditionals in the form of inducements (i.e., promises and threats) and advice (i.e., tips and warnings). In so doing, we demonstrate a distinction between the truth status of these conditionals and (...) their effectiveness as speech acts. Specifically, while probability judgements of the truth of conditional inducements and advice are highly correlated with estimates of P( q / p ), their perceived effectiveness in changing behaviour instead varies as a function of the conditional probability of q given not-p , P( q / ∼p ). Finally, we show that the conditional probability approach can be extended to predicting inference rates on a conditional reasoning task. (shrink)

For most of its history, the psychology of reasoning was dominated by binary extensional logic. The so-called “new paradigm” instead puts subjective degrees of belief center stage, often represented as probabilities. We argue that the “new paradigm” is too vaguely defined and therefore does not allow a clear decision about what falls within its scope and what does not. We also show that there was not one settled theoretical “old” paradigm, before the new developments emerged, and that the alleged new (...) paradigm is less revolutionary as the term suggests. A more veridical view is that current progress is developing in continuities where rival research programs can thrive or fail in the face of new experimental findings. The article closes with some topics where more connections between competing research programs are likely to promote progress in our understanding of human reasoning. (shrink)