This article proposes a new interpretation of mutual information. We examine three extant interpretations of MI by reduction in doubt, by reduction in uncertainty, and by divergence. We argue that the first two are inconsistent with the epistemic value of information assumed in many applications of MI: the greater is the amount of information we acquire, the better is our epistemic position, other things being equal. The third interpretation is consistent with EVI, but it is faced with the problem of (...) measure sensitivity and fails to justify the use of MI in giving definitive answers to questions of information. We propose a fourth interpretation of MI by reduction in expected inaccuracy, where inaccuracy is measured by a strictly proper monotonic scoring rule. It is shown that the answers to questions of information given by MI are definitive whenever this interpretation is appropriate, and that it is appropriate in a wide range of applications with epistemic implications. _1_ Introduction _2_ Formal Analyses of the Three Interpretations _2.1_ Reduction in doubt _2.2_ Reduction in uncertainty _2.3_ Divergence _3_ Inconsistency with Epistemic Value of Information _4_ Problem of Measure Sensitivity _5_ Reduction in Expected Inaccuracy _6_ Resolution of the Problem of Measure Sensitivity _6.1_ Alternative measures of inaccuracy _6.2_ Resolution by strict propriety _6.3_ Range of applications _7_ Global Scoring Rules _8_ Conclusion. (shrink)

We propose a critique ofnormativism, defined as the idea that human thinking reflects a normative system against which it should be measured and judged. We analyze the methodological problems associated with normativism, proposing that it invites the controversial “is-ought” inference, much contested in the philosophical literature. This problem is triggered when there are competing normative accounts (the arbitration problem), as empirical evidence can help arbitrate between descriptive theories, but not between normative systems. Drawing on linguistics as a model, we propose (...) that a clear distinction between normative systems and competence theories is essential, arguing that equating them invites an “is-ought” inference: to wit, supporting normative “ought” theories with empirical “is” evidence. We analyze in detail two research programmes with normativist features – Oaksford and Chater's rational analysis and Stanovich and West's individual differences approach – demonstrating how, in each case, equating norm and competence leads to an is-ought inference. Normativism triggers a host of research biases in the psychology of reasoning and decision making: focusing on untrained participants and novel problems, analyzing psychological processes in terms of their normative correlates, and neglecting philosophically significant paradigms when they do not supply clear standards for normative judgement. For example, in a dual-process framework, normativism can lead to a fallacious “ought-is” inference, in which normative responses are taken as diagnostic of analytic reasoning. We propose that little can be gained from normativism that cannot be achieved by descriptivist computational-level analysis, illustrating our position with Hypothetical Thinking Theory and the theory of the suppositional conditional. We conclude that descriptivism is a viable option, and that theories of higher mental processing would be better off freed from normative considerations. (shrink)

Two experiments using a realistic version of the selection task examined the relationship between participants' probability estimates of finding a counter example and their selections. Experiment 1 used everyday categories in the context of a scenario to determine whether or not the number of instances in a category affected the estimated probability of a counter-example. Experiment 2 modified the scenario in order to alter participants' estimates of finding a specific counter-example. Unlike Kirby 1994a, but consistent with his proposals, both studies (...) showed that probability estimates significantly predicted selection. Overall results point to the value of understanding selections in terms of their subjective expected utility. (shrink)

In this article, we argue for the general importance of normative theories of argument strength. We also provide some evidence based on our recent work on the fallacies as to why Bayesian probability might, in fact, be able to supply such an account. In the remainder of the article we discuss the general characteristics that make a specifically Bayesian approach desirable, and critically evaluate putative flaws of Bayesian probability that have been raised in the argumentation literature.

Normative theories can be useful in developing descriptive theories, as when normative subjective expected utility theory is used to develop descriptive rational choice theory and behavioral game theory. “Ought” questions are also the essence of theories of moral reasoning, a domain of higher mental processing that could not survive without normative considerations.

Oaksford and Chater (1994) proposed to analyse the Wason selection task as an inductive instead of a deductive task. Applying Bayesian statistics, they concluded that the cards that participants tend to select are those with the highest expected information gain. Therefore, their choices seem rational from the perspective of optimal data selection. We tested a central prediction from the theory in three experiments: card selection frequencies should be sensitive to the subjective probability of occurrence for individual cards. In Experiment 1, (...) expected frequencies of the p- and the q-card were manipulated independently by concepts referring to large vs. small sets. Although the manipulation had an effect on card selection frequencies, there was only a weak correlation between the predicted and the observed patterns. In the second experiment, relative frequencies of individual cards were manipulated more directly by explicit frequency information. In addition, participants estimated probabilities for the four logical cases and of the conditional statement itself. The experimental manipulations strongly affected the probability estimates, but were completely unrelated to card selections. This result was replicated in a third experiment. We conclude that our data provide little support for optimal data selection theory. (shrink)

Rational choice theory enjoys unprecedented popularity and influence in the behavioral and social sciences, but it generates intractable problems when applied to socially interactive decisions. In individual decisions, instrumental rationality is defined in terms of expected utility maximization. This becomes problematic in interactive decisions, when individuals have only partial control over the outcomes, because expected utility maximization is undefined in the absence of assumptions about how the other participants will behave. Game theory therefore incorporates not only rationality but also common (...) knowledge assumptions, enabling players to anticipate their co-players' strategies. Under these assumptions, disparate anomalies emerge. Instrumental rationality, conventionally interpreted, fails to explain intuitively obvious features of human interaction, yields predictions starkly at variance with experimental findings, and breaks down completely in certain cases. In particular, focal point selection in pure coordination games is inexplicable, though it is easily achieved in practice; the intuitively compelling payoff-dominance principle lacks rational justification; rationality in social dilemmas is self-defeating; a key solution concept for cooperative coalition games is frequently inapplicable; and rational choice in certain sequential games generates contradictions. In experiments, human players behave more cooperatively and receive higher payoffs than strict rationality would permit. Orthodox conceptions of rationality are evidently internally deficient and inadequate for explaining human interaction. Psychological game theory, based on nonstandard assumptions, is required to solve these problems, and some suggestions along these lines have already been put forward. Key Words: backward induction; Centipede game; common knowledge; cooperation; epistemic reasoning; game theory; payoff dominance; pure coordination game; rational choice theory; social dilemma. (shrink)

This paper addresses the apparent mismatch between the normative and descriptive literatures in the cognitive science of conditional reasoning. Descriptive psychological theories still regard material implication as the normative theory of the conditional. However, over the last 20 years in the philosophy of language and logic the idea that material implication can account for everyday indicative conditionals has been subject to severe criticism. The majority view is now apparently in favour of a subjective conditional probability interpretation. A comparative model fitting (...) exercise is presented that shows that a conditional probability model can explain as much of the data on abstract indicative conditional reasoning tasks as psychological theories that supplement material implication with various rationally unjustified processing assumptions. Consequently, when people are asked to solve laboratory reasoning tasks, they can be seen as simply generalising their everyday probabilistic reasoning strategies to this novel context. (shrink)

The authors outline a theory of conditionals of the form If A then C and If A then possibly C. The 2 sorts of conditional have separate core meanings that refer to sets of possibilities. Knowledge, pragmatics, and semantics can modulate these meanings. Modulation can add information about temporal and other relations between antecedent and consequent. It can also prevent the construction of possibilities to yield 10 distinct sets of possibilities to which conditionals can refer. The mental representation of a (...) conditional normally makes explicit only the possibilities in which its antecedent is true, yielding other possibilities implicitly. Reasoners tend to focus on the explicit possibilities. The theory predicts the major phenomena of understanding and reasoning with conditionals. (shrink)

It is a commonplace that contemplation of an imaginary particular may have cognitive and motivational effects that differ from those evoked by an abstract description of an otherwise similar state of affairs. In his Treatise on Human Nature, Hume ([1739] 1978) writes forcefully of this.

Rational analysis (Anderson 1990, 1991a) is an empiricalprogram of attempting to explain why the cognitive system isadaptive, with respect to its goals and the structure of itsenvironment. We argue that rational analysis has two importantimplications for philosophical debate concerning rationality. First,rational analysis provides a model for the relationship betweenformal principles of rationality (such as probability or decisiontheory) and everyday rationality, in the sense of successfulthought and action in daily life. Second, applying the program ofrational analysis to research on human reasoning (...) leads to a radicalreinterpretation of empirical results which are typically viewed asdemonstrating human irrationality. (shrink)

Argumentation is pervasive in everyday life. Understanding what makes a strong argument is therefore of both theoretical and practical interest. One factor that seems intuitively important to the strength of an argument is the reliability of the source providing it. Whilst traditional approaches to argument evaluation are silent on this issue, the Bayesian approach to argumentation (Hahn & Oaksford, 2007) is able to capture important aspects of source reliability. In particular, the Bayesian approach predicts that argument content and source reliability (...) should interact to determine argument strength. In this paper, we outline the approach and then demonstrate the importance of source reliability in two empirical studies. These experiments show the multiplicative relationship between the content and the source of the argument predicted by the Bayesian framework. (shrink)

I consider the role of cognitive modeling in cognitive science. Modeling, and the computers that enable it, are central to the field, but the role of modeling is often misunderstood. Models are not intended to capture fully the processes they attempt to elucidate. Rather, they are explorations of ideas about the nature of cognitive processes. In these explorations, simplification is essential—through simplification, the implications of the central ideas become more transparent. This is not to say that simplification has no downsides; (...) it does, and these are discussed. I then consider several contemporary frameworks for cognitive modeling, stressing the idea that each framework is useful in its own particular ways. Increases in computer power (by a factor of about 4 million) since 1958 have enabled new modeling paradigms to emerge, but these also depend on new ways of thinking. Will new paradigms emerge again with the next 1,000‐fold increase? (shrink)

The Bayesian model has been used in psychology as the standard reference for the study of probability revision. In the first part of this paper we show that this traditional choice restricts the scope of the experimental investigation of revision to a stable universe. This is the case of a situation that, technically, is known as focusing. We argue that it is essential for a better understanding of human probability revision to consider another situation called updating (Katsuno & Mendelzon, 1992), (...) in which the universe is evolving. In that case the structure of the universe has definitely been transformed and the revision message conveys information on the resulting universe. The second part of the paper presents four experiments based on the Monty Hall puzzle that aim to show that updating is a natural frame for individuals to revise their beliefs. (shrink)

Part I Introduction The specific problem adressed in this thesis is: what is the rational use of theory and experiment in the process of scientific discovery, in theory and in the practice of drug research for Parkinson’s disease? The thesis aims to answer the following specific questions: what is: 1) the structure of a theory?; 2) the process of scientific reasoning?; 3) the route between theory and experiment? In the first part I further discuss issues about rationality in science as (...) introduction to part II, and I present an overview of my case-study of neuropharmacology, for which I interviewed researchers from the Groningen Pharmacy Department, as an introduction to part III. Part II Discovery In this part I discuss three theoretical models of scientific discovery according to studies in the fields of Logic, Cognition, and Computation. In those fields the structure of a theory is respectively explicated as: a set of sentences; a set of associated memory chunks; and as a computer program that can generate the observed data. Rationality in discovery is characterized by: finding axioms that imply observation sentences; heuristic search for a hypothesis, as part of problem solving, by applying memory chunks and production rules that represent skill; and finding the shortest program that generates the data, respectively. I further argue that reasoning in discovery includes logical fallacies, which are neccesary to introduce new hypotheses. I also argue that, while human subjects often make errors in hypothesis evaluation tasks from a logical perspective, these evaluations are rational given a probabilistic interpretation. Part III Neuropharmacology In this last part I discusses my case-study and a model of discovery in a practice of drug research for Parkinson’s disease. I discuss the dopamine theory of Parkinson’s disease and model its structure as a qualitative differential equation. Then I discuss the use and reasons for particular experiments to both test a drug and explore the function of the brain. I describe different kinds of problems in drug research leading to a discovery. Based on that description I distinguish three kinds of reasoning tasks in discovery, inference to: the best explanation, the best prediction and the best intervention. I further demonstrate how a part of reasoning in neuropharmacology can be computationally modeled as qualitative reasoning, and aided by a computer supported discovery system. (shrink)

Prominent evolutionary psychologists have argued that our innate psychological endowment consists of numerous domainspecific cognitive resources, rather than a few domaingeneral ones. In the light of some conceptual clarification, we examine the central inprinciple arguments that evolutionary psychologists mount against domaingeneral cognition. We conclude (a) that the fundamental logic of Darwinism, as advanced within evolutionary psychology, does not entail that the innate mind consists exclusively, or even massively, of domainspecific features, and (b) that a mixed innate cognitive economy of domainspecific (...) and domaingeneral resources remains a genuine conceptual possibility. However, an examination of evolutionary psychology's 'grain problem' reveals that there is no way of establishing a principled and robust distinction between domainspecific and domaingeneral features. Nevertheless, we show that evolutionary psychologists can and do live with this grain problem without their whole enterprise being undermined. (shrink)

Individual differences on a variety of framing and conjunction problems were examined in light of Slovic and Tversky's (1974) understanding/acceptance principle-that more reflective and skilled reasoners are more likely to affirm the axioms that define normative reasoning and to endorse the task construals of informed experts. The predictions derived from the principle were confirmed for the much discussed framing effect in the Disease Problem and for the conjunction fallacy on the Linda Problem. Subjects of higher cognitive ability were disproportionately likely (...) to avoid each fallacy. Other framing problems produced much more modest levels of empirical support. It is conjectured that the varying patterns of individual differences are best explained by two-process theories of reasoning (e.g. Evans, 1984, 1996; Sloman, 1996) conjoined with the assumption that the two processes differentially reflect interactional and analytic intelligence. (shrink)

Verbs such as enjoy in the student enjoyed the book exhibit logical metonymy: enjoy is interpreted as enjoy reading. Theoreticalwork [Computational Linguistics 17 (4) (1991) 409; The Generative Lexicon, MIT Press, Cambridge, MA, 1995] predicts that this interpretation can be influenced by intra‐sentential context, e.g., by the subject of enjoy. In this article, we test this prediction using a completion experiment and find that the interpretation of a metonymic verb is influenced by the semantic role of its subject. We present (...) a Bayesian model that accounts for the interpretation of logical metonymy and achieves a good fit on our experimental data. We show that the parameters of the model can be estimated from completion data or from corpus data. (shrink)

According to Aristotle, humans are the rational animal. The borderline between rationality and irrationality is fundamental to many aspects of human life including the law, mental health, and language interpretation. But what is it to be rational? One answer, deeply embedded in the Western intellectual tradition since ancient Greece, is that rationality concerns reasoning according to the rules of logic – the formal theory that specifies the inferential connections that hold with certainty between propositions. Piaget viewed logical reasoning as defining (...) the end-point of cognitive development; and contemporary psychology of reasoning has focussed on comparing human reasoning against logical standards. (shrink)

Four experiments investigated the effects of probability manipulations on the indicative four card selection task (Wason, 1966, 1968). All looked at the effects of high and low probability antecedents (p) and consequents (q) on participants' data selections when determining the truth or falsity of a conditional rule, if p then q . Experiments 1 and 2 also manipulated believability. In Experiment 1, 128 participants performed the task using rules with varied contents pretested for probability of occurrence. Probabilistic effects were observed (...) which were partly consistent with some probabilistic accounts but not with non-probabilistic approaches to selection task performance. No effects of believability were observed, a finding replicated in Experiment 2 which used 80 participants with standardised and familiar contents. Some effects in this experiment appeared inconsistent with existing probabilistic approaches. To avoid possible effects of content, Experiments 3 (48 participants) and 4 (20 participants) used abstract material. Both experiments revealed probabilistic effects. In the Discussion we examine the compatibility of these results with the various models of selection task performance. (shrink)

Taking a Darwinian approach, we propose that people reason to detect free-riders on the Wason Selection task with the sharing-rule; If one receives the resource, one is an in-group member (standard), or If one is an in-group member, one receives the resource (switched). As predicted, taking the resource-provider's perspective, both undergraduates and children (11 to 12 years old) checked for the existence of out-group members taking undeserved resource. Changing the perspective to that of the resource-recipient did not alter the selection (...) pattern in undergraduates, although the prediction was that another type of free-riding -failure to share by resource-provider- would be checked as well. However, by removing confounding factors in the materials, both undergraduates and children checked for both types of free-riding, which fully supports the prediction. These results indicate that the sharing-rule elicits a thematic content effect that cannot be explained by preceding deontic reasoning theories. (shrink)

A working assumption that processes of natural and cultural evolution have tailored the mind to fit the demands and structure of its environment begs the question: how are we to characterize the structure of cognitive environments? Decision problems faced by real organisms are not like simple multiple-choice examination papers. For example, some individual problems may occur much more frequently than others, whilst some may carry much more weight than others. Such considerations are not taken into account when (i) the performance (...) of candidate cognitive mechanisms is assessed by employing a simple accuracy metric that is insensitive to the structure of the decision-maker's environment, and (ii) reason is defined as the adherence to internalist prescriptions of classical rationality. Here we explore the impact of frequency and significance structure on the performance of a range of candidate decision-making mechanisms. We show that the character of this impact is complex, since structured environments demand that decision-makers trade off general performance against performance on important subsets of test items. As a result, environment structure obviates internalist criteria of rationality. Failing to appreciate the role of environment structure in shaping cognition can lead to mischaracterising adaptive behavior as irrational. (shrink)

Wason’s selection task is a paramount experimental problem in the study of human reasoning, often connected with the celebrated ravens paradox in the philosophical literature. Various normative accounts of the selection task rely on a Bayesian approach. Some claim vindication of participants’ rationality. Others don’t, thus following Wason’s original intuition that observed responses are mistaken. In this article we argue that despite claims to the contrary, all these accounts actually speak to the same effect: Wason was right. First, we provide (...) a new accuracy-based analysis of the selection task that includes the existing proposals as special cases. We then show on this basis that none can actually vindicate participants’ rationality. We conclude that all normative renditions considered eventually concur: all in all, Bayesians should follow Wason in the selection task. (shrink)

This paper addresses the apparent mismatch between the normative and descriptive literatures in the cognitive science of conditional reasoning. Descriptive psychological theories still regard material implication as the normative theory of the conditional. However, over the last 20 years in the philosophy of language and logic the idea that material implication can account for everyday indicative conditionals has been subject to severe criticism. The majority view is now apparently in favour of a subjective conditional probability interpretation. A comparative model fitting (...) exercise is presented that shows that a conditional probability model can explain as much of the data on abstract indicative conditional reasoning tasks as psychological theories that supplement material implication with various rationally unjustified processing assumptions. Consequently, when people are asked to solve laboratory reasoning tasks, they can be seen as simply generalising their everyday probabilistic reasoning strategies to this novel context. (shrink)

Severity of Test (SoT) is an alternative to Popper's logical falsification that solves a number of problems of the logical view. It was presented by Popper himself in 1963. SoT is a less sophisticated probabilistic model of hypothesis testing than Oaksford & Chater's (O&C's) information gain model, but it has a number of striking similarities. Moreover, it captures the intuition of everyday hypothesis testing.

This commentary focuses on the parts of psychological game theory dealing with preference, as illustrated by team reasoning, and supports the conclusion that these theoretical notions do not contribute above and beyond existing theory in understanding social interaction. In particular, psychology and games are already bridged by a comprehensive, formal, and inherently psychological theory, interdependence theory (Kelley & Thibaut 1978; Kelley et al. 2003), which has been demonstrated to account for a wide variety of social interaction phenomena.

Green, Over, and Pyne's (1997) paper (hereafter referred to as ''GOP") seems to provide a novel approach to examining probabilistic effects in Wason's selection task. However, in this comment, it is argued that their chosen experimental paradigm confounds most of their results. The task demands of the externalisation procedure (Green, 1995) enforce a correlation between card selections and the probability of finding a counterexample, which was the main finding of GOP's experiments. Consequently GOP cannot argue that their data support Kirby's (...) (1994) proposal that people's normal strategy in the selection task is to seek falsifying evidence. Despite this methodological problem, effects of the probability of the antecedent ( p ) of a conditional rule, if p then q , predicted by Kirby (1994) and by Oaksford and Chater (1994) were observed, although they were inconsistent between Experiments 1 and 2. Moreover, the probability estimates that GOP collected, which are not vulnerable to that methodological criticism, do support the idea that when P ( p ) > P ( q ), participants revise P ( p ) down as suggested by Oaksford and Chater (1994). (shrink)

Two experiments are reported that employed think-aloud methods to test predictions concerning relevance effects and rationalisation processes derivable from Evans' (1996) heuristic-analytic theory of the selection task. Evans' account proposes that card selections are triggered by relevance-determining heuristics, with analytic processing serving merely to rationalise heuristically cued decisions. As such, selected cards should be associated with more references to both their facing and their hidden sides than rejected cards, which are not subjected to analytic rationalisation. Experiment 1 used a standard (...) selection-task paradigm, with negative components permuted through abstract conditional rules. Support was found for all heuristic-analytic predictions. This evidence was shown to be robust in Experiment 2, where "select - don't select" decisions were enforced for all cards. Both experiments also clarify the role played by secondary heuristics in cueing the consideration of hidden card values during rationalisation. We suggest that whilst Evans' heuristic-analytic model and Oaksford and Chater's (e.g., 2003) optimal data selection model can provide compelling accounts of our protocol findings, the mental models theory fares less well as an explanation of our full dataset. (shrink)

Knauff and Gazzo Castañeda (2022) criticise the use of the term “new paradigm” in the psychology of reasoning and raise important issues about how to advance research in the field. In this commentary I argue that for the latter it would be helpful to clarify further the concepts that reasoning theories rely on, and to strengthen the links between the theories and the empirical observations that would and would not be compatible with them.

We review the various explanations that have been offered toaccount for subjects'' behaviour in Wason ''s famous selection task. Weargue that one element that is lacking is a good understanding ofsubjects'' semantics for the key expressions involved, and anunderstanding of how this semantics is affected by the demands the taskputs upon the subject''s cognitive system. We make novel proposals inthese terms for explaining the major content effects of deonticmaterials. Throughout we illustrate with excerpts from tutorialdialogues which motivate the kinds of (...) analysis proposed. Our long termgoal is an integration of the various insights about conditionalreasoning on offer from different cognitive science methodologies. Thepurpose of this paper is to try to draw the attention of logicians andsemanticists to this area, since we believe that empirical investigationof the cognitive processes involved could benefit from semanticanalyses. (shrink)

The article covers such issues as the relevance of the theory of perception as a multi-level information processing, the methodological role of the concept of representation and the relation of neurodynamic structures to subjective experience. The author critically reviews the philosophical presumptions underlying the various concepts of “local rationality,” the core of which is constituted by the belief that large ethnic cultures generate or are based on their own rationality and their own logic. Three statements are successively considered: thinking is (...) based on the inherent rules of rationality, logic is an extract of rationality, and types of rationality are geographically consistent with large ethnocultural communities. Empirical arguments are presented that demonstrate equivocality of the first two theses. In particular, firstly, it is shown that the genuine rationality of thinking lies not in following the rules that are immanent to it, but in the development of thinking and, more broadly, cognitive operations towards optimization of certain indicators of the cognitive or motor system that are important for survival and adaptation. In addition, this rationality is multivariate, and the choice between variants is often weakly determined or even random. Thus, the first statement turns out to be refuted. Secondly, by reference to the well-known experiments, it is shown that most people do not explicitly follow some declared logical rules in solving even logical or mathematical problems, and yet there is reason to consider their behavior rational. The third thesis, as shown with some limited empirical material, appears to be partially confirmed. Nevertheless, the demonstration of the doubtfulness of the first two theses makes the conclusion that different nations have different logics insufficiently substantiated. (shrink)