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)

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.

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)

Cognitive scientists have revealed systematic errors in human reasoning. There is disagreement about what these errors indicate about human rationality, but one upshot seems clear: human reasoning does not seem to fit traditional views of human rationality. This concern about rationality has made its way through various fields and has recently caught the attention of philosophers. The concern is that if philosophers are prone to systematic errors in reasoning, then the integrity of philosophy would be threatened. In this paper, I (...) present some of the more famous work in cognitive science that has marshaled this concern. Then I present reasons to think that those with training in philosophy will be less prone to certain systematic errors in reasoning. The suggestion is that if philosophers could be shown to be less prone to such errors, then the worries about the integrity of philosophy could be constrained. Then I present evidence that, according to performance on the CRT (Frederick 2005), those who have benefited from training and selection in philosophy are indeed less prone to one kind of systematic error: irrationally arbitrating between intuitive and reflective responses. Nonetheless, philosophers are not entirely immune to this systematic error, and their proclivity for this error is statistically related to their responses to a variety of philosophical questions. So, while the evidence herein puts constraints on the worries about the integrity of philosophy, it by no means eliminates these worries. The conclusion, then, is that the present evidence offers prima facie reasons to ascribe a mitigated privilege to philosophers' ability to rationally arbitrate between intuitive and reflective responses. (shrink)

Yama (2001) has presented an ingenious series of experiments in which he attempts to separate two accounts in the literature of the cause of "matching bias" in conditional reasoning. One account is that the bias arises from the way in which people process negations and the other is that it is due to the larger set sizes associated with negative propositions, rather than negation per se . Yama's experiments show influences of both negation and set size, from which he concludes (...) that both factors contribute to the matching bias that is normally observed. In this note, it is argued that this conclusion is at odds with other findings in the literature, particularly those investigating implicit negation as the cause of the bias. Introducing explicit negations has been shown to remove matching bias completely and not partially, as Yama's account must predict. A possible reconciliation is proposed in terms of subtle contextual differences introduced by Yama's experiments. (shrink)

Searching for information is critical in many situations. In medicine, for instance, careful choice of a diagnostic test can help narrow down the range of plausible diseases that the patient might have. In a probabilistic framework, test selection is often modeled by assuming that people's goal is to reduce uncertainty about possible states of the world. In cognitive science, psychology, and medical decision making, Shannon entropy is the most prominent and most widely used model to formalize probabilistic uncertainty and the (...) reduction thereof. However, a variety of alternative entropy metrics (Hartley, Quadratic, Tsallis, Rényi, and more) are popular in the social and the natural sciences, computer science, and philosophy of science. Particular entropy measures have been predominant in particular research areas, and it is often an open issue whether these divergences emerge from different theoretical and practical goals or are merely due to historical accident. Cutting across disciplinary boundaries, we show that several entropy and entropy reduction measures arise as special cases in a unified formalism, the Sharma–Mittal framework. Using mathematical results, computer simulations, and analyses of published behavioral data, we discuss four key questions: How do various entropy models relate to each other? What insights can be obtained by considering diverse entropy models within a unified framework? What is the psychological plausibility of different entropy models? What new questions and insights for research on human information acquisition follow? Our work provides several new pathways for theoretical and empirical research, reconciling apparently conflicting approaches and empirical findings within a comprehensive and unified information‐theoretic formalism. (shrink)

Cummins (this issue) puts the case for an innate module for deontic reasoning. We argue that this case is not persuasive. First, we claim that Cummins’evolutionary arguments are neutral regarding whether deontic reasoning is learned or innate. Second, we argue that task differences between deontic and indicative reasoning explain many of the phenomena that Cummins takes as evidence for a deontic module. Third, we argue against the suggestion that deontic reasoning is superior to indicative reasoning, either in adults or children. (...) Finally, we re‐evaluate Cummins’interpretation of differences in children's performance on deontic and indicative versions of Wason's selection task. (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)

It has been reported as a robust effect that people are likely to select a matching case in the Wason selection task. For example, they usually select the 5 case, in the Wason selection task with the conditional "if an E, then a not-5". This was explained by the matching bias account that people are likely to regard a matching case as relevant to the truth of the conditional (Evans, 1998). However, because a positive concept usually constructs a smaller set (...) than its negative one does (a rarity assumption), it is more effective to get information on the truth of the conditional in a positive set than in a negative set. Thus the optimal data selection account can also explain the effect. The set size of Q and matching by introducing negation were manipulated independently in four experiments. From the results it was inferred that the so-called matching bias was an amalgam of two different cognitive components-relevance judgement by matching and optimal data selection. (shrink)

We respond to Morris and Richardson 's claim that Pickering and Chater's arguments about the lack of a relation between cognitive science and folk psychology are flawed. We note that possible controversies about the appropriate uses for the two terms do not affect our arguments. We then address their claim that computational explanation of knowledge-rich processes has proved possible in the domains of problem solving, scientific discovery, and reasoning. We argue that, in all cases, computational explanation is only possible for (...) aspects of those processes that do not make reference to general knowledge. We conclude that consideration of the issues raised by Morris and Richardson reinforces our original claim that there are two fundamentally distinct projects for understanding the mind, one based on justification, and the other on computational explanation, and that these apply to non-overlapping aspects of mental life. (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)

This paper proposes a new interpretation of mutual information (MI). 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 (EVI) 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. (shrink)

The phenomenon known as matching bias consists of a tendency to see cases as relevant in logical reasoning tasks when the lexical content of a case matches that of a propositional rule, normally a conditional, which applies to that case. Matching is demonstrated by use of the negations paradigm that is by using conditionals in which the presence and absence of negative components is systematically varied. The phenomenon was first published in 1972 and the present paper reviews the history of (...) research and theorising on the problem in the subsequent 25 years. Theories of matching bias considered include those based on several broad frameworks including the heuristic-analytic theory, the mental models theory, the theory of optimal data selection, and relevance theory as well as the specific processing-negations account. The ability of these theories to account for a range of phenomena is considered, including the effects of linguistic form, realistic content, and explicit negation on the matching bias effect. Of particular importance are recent findings showing that the bias is observable on a wider range of linguistic forms than has generally been thought, and that it is almost entirely dependent on the use of implicit negation in the logical cases to which rules are applied. The reasons for the general suppression of matching when realistic content is used are, however, unclear and a need for further research is identified here. It is concluded that matching bias is a highly robust effect which is closely connected with the problem of understanding implicit negation. Most of the theories in the literature are unable to account for at least some of the major phenomena discovered in research on the bias. The accounts that fare best are those that posit local effects of negation, including the heuristic-analytic and processing negations theories. (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)

Conditionals somehow express conditional beliefs. However, conditional belief is a bi-propositional attitude that is generally not truth-evaluable, in contrast to unconditional belief. Therefore, this article opts for an expressivistic semantics for conditionals, grounds this semantics in the arguably most adequate account of conditional belief, that is, ranking theory, and dismisses probability theory for that purpose, because probabilities cannot represent belief. Various expressive options are then explained in terms of ranking theory, with the intention to set out a general interpretive scheme (...) that is able to account for the most variegated usage of conditionals. The Ramsey test is only the first option. Relevance is another, familiar, but little understood item, which comes in several versions. This article adds a further family of expressive options, which is able to subsume also counterfactuals and causal conditionals, and indicates at the end how this family allows for partial recovery of truth conditions for conditionals. (shrink)

Social cognition is the capacity to understand and interact with others. The mainstream account of social cognition is mindreading, the view that we humans understanding others by interpreting their behavior in terms of mental states. Recently theorists from philosophy, psychology, and neuroscience have challenged the mindreading account, arguing for a more deflationary account of social cognition. In this paper I examine a deflationary account of social cognition, embodied simulation, which is inspired by recent neuroscientific findings. I argue that embodied simulation (...) fails to present an adequate alternative to mindreading accounts of social cognition. I defend a philosophically and empirically plausible two-systems account of social cognition, which holds that even very young children are capable of mindreading. (shrink)

In this article, 41 models of covariation detection from 2 × 2 contingency tables were evaluated against past data in the literature and against data from new experiments. A new model was also included based on a limiting case of the normative phi‐coefficient under an extreme rarity assumption, which has been shown to be an important factor in covariation detection (McKenzie & Mikkelsen, 2007) and data selection (Hattori, 2002; Oaksford & Chater, 1994, 2003). The results were supportive of the new (...) model. To investigate its explanatory adequacy, a rational analysis using two computer simulations was conducted. These simulations revealed the environmental conditions and the memory restrictions under which the new model best approximates the normative model of covariation detection in these tasks. They thus demonstrated the adaptive rationality of the new model. (shrink)

Participants attempted to solve a modified version of Wason's selection task. Variables were: sizes of the sets referenced by a specified assertion, form of the assertion, thematic content of the assertion, and the need for sampling or not. In Experiment 1, participants were given enough information to determine the truth or falsity of the specified assertion with certainty; in Experiment 2, they had to rely on sampling and could not determine the assertion's truth or falsity with certainty. Performance was better (...) in Experiment 1 than in Experiment 2, but in both cases much better than what is typically obtained with the conventional selection task. The results support the hypothesis that performance of the selection task is sensitive to the sizes of the sets involved, add credence to the conclusion that framing the task in a thematically meaningful way can facilitate performance, and demonstrate that facilitation does not require deontic reasoning or a well-known convention being involved. The relationship between expressed confidence and level of performance is consistent with other studies showing the former to be a good predictor of the latter. (shrink)

A hallmark of intelligent behavior is rationality – the disposition and ability to think analytically to make decisions that maximize expected utility or follow the laws of probability. However, the question remains as to whether rationality and intelligence are empirically distinct, as does the question of what cognitive mechanisms underlie individual differences in rationality. In a sample of 331 participants, we assessed the relationship between rationality and intelligence. There was a common ability underpinning performance on some, but not all, rationality (...) tests. Latent factors representing rationality and general intelligence were strongly correlated (r =.54), but their correlation fell well short of unity. Rationality correlated significantly with fluid intelligence (r =.56), working memory capacity (r =.44), and attention control (r =.49). Attention control fully accounted for the relationship between working memory capacity and rationality, and partially accounted for the relationship between fluid intelligence and rationality. We conclude by speculating about factors rationality tests may tap that other cognitive ability tests miss, and outline directions for further research. (shrink)