ABSTRACTOaksford and Chater critiqued the logic programming approach to nonmonotonicity and proposed that a Bayesian probabilistic approach to conditional reasoning provided a more empirically adequate theory. The current paper is a reply to Stenning and van Lambalgen's rejoinder to this earlier paper entitled ‘Logic programming, probability, and two-system accounts of reasoning: a rejoinder to Oaksford and Chater’ in Thinking and Reasoning. It is argued that causation is basic in human cognition and that explaining how abnormality lists are created in LP (...) requires causal models. Each specific rejoinder to the original critique is then addressed. While many areas of agreement are identified, with respect to the key differences, it is concluded the current evidence favours the Bayesian approach, at least for the moment. (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)

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)

Knauff and Gazzo Castañeda (2022) object to using the term “new paradigm” to describe recent developments in the psychology of reasoning. This paper concedes that the Kuhnian term “paradigm” may be queried. What cannot is that the work subsumed under this heading is part of a new, progressive movement that spans the brain and cognitive sciences: Bayesian cognitive science. Sampling algorithms and Bayes nets used to explain biases in JDM can implement the Bayesian new paradigm approach belying any advantages of (...) mental models theory (MMT) at the algorithmic level. Moreover, this paper argues that new versions of MMT lack a computational level theory and questions the grounds for MMTs much-vaunted generality. The paper then examines common ground on the importance of small-scale models/simulations of the world and the importance of argumentation in the social domain rather than individual reasoning. Finally, the paper concludes that although there may be prospects for moving reasoning research forward in a more collective, collaborative manner, many disagreements remain to be resolved. (shrink)

It has been argued that dual process theories are not consistent with Oaksford and Chater’s probabilistic approach to human reasoning (Oaksford and Chater in Psychol Rev 101:608–631, 1994 , 2007 ; Oaksford et al. 2000 ), which has been characterised as a “single-level probabilistic treatment[s]” (Evans 2007 ). In this paper, it is argued that this characterisation conflates levels of computational explanation. The probabilistic approach is a computational level theory which is consistent with theories of general cognitive architecture that invoke (...) a WM system and an LTM system. That is, it is a single function dual process theory which is consistent with dual process theories like Evans’ ( 2007 ) that use probability logic (Adams 1998 ) as an account of analytic processes. This approach contrasts with dual process theories which propose an analytic system that respects standard binary truth functional logic (Heit and Rotello in J Exp Psychol Learn 36:805–812, 2010 ; Klauer et al. in J Exp Psychol Learn 36:298–323, 2010 ; Rips in Psychol Sci 12:29–134, 2001 , 2002 ; Stanovich in Behav Brain Sci 23:645–726, 2000 , 2011 ). The problems noted for this latter approach by both Evans Psychol Bull 128:978–996, ( 2002 , 2007 ) and Oaksford and Chater (Mind Lang 6:1–38, 1991 , 1998 , 2007 ) due to the defeasibility of everyday reasoning are rehearsed. Oaksford and Chater’s ( 2010 ) dual systems implementation of their probabilistic approach is then outlined and its implications discussed. In particular, the nature of cognitive decoupling operations are discussed and a Panglossian probabilistic position developed that can explain both modal and non-modal responses and correlations with IQ in reasoning tasks. It is concluded that a single function probabilistic approach is as compatible with the evidence supporting a dual systems theory. (shrink)

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)

Computational-level models proposed in recent Bayesian cognitive science predict both the “biased” and correct responses on many tasks. So, rather than possessing two reasoning systems, people can generate both possible responses within a single system. Consequently, although an account of why people make one response rather than another is required, dual processes of reasoning may not be.

In this paper the arguments for optimal data selection and the contrast class account of negations in the selection task and the conditional inference task are summarised, and contrasted with the matching bias approach. It is argued that the probabilistic contrast class account provides a unified, rational explanation for effects across these tasks. Moreover, there are results that are only explained by the contrast class account that are also discussed. The only major anomaly is the explicit negations effect in the (...) selection task (Evans, Clibbens, & Rood, 1996), which it is argued may not be the result of normal interpretative processes. It is concluded that the effects of negation on human reasoning provide good evidence for the view that human reasoning processes may be rational according to a probabilistic standard. (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)

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)

Hempel's paradox of the ravens has to do with the question of what constitutes confirmation from a logical point of view; Wason 's selection task has been used extensively to investigate how people go about attempting to confirm or disconfirm conditional claims. This paper presents an argument that the paradox is resolved, and that people's typical performance in the selection task can be explained, by consideration of what constitutes an effective strategy for seeking evidence of the tenability of universal or (...) conditional claims in everyday life. (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)

Four experiments are reported which investigated the types of truth tables that people associate with conditional sentences and the kinds of inferences that they will draw from them. The present studies differed from most previous ones in using different types of content in the conditionals, for example promises and warnings. It was found that the type of content had a strong and consistent effect on both truth tables and inferences. It is suggested that this is because in real life conditionals (...) make probabilistic assertions, and that the strength of the probabilistic link is determined by the situation in which the conditional occurs. The implications of these findings for current theories of reasoning are considered and it is concluded that none of them is entirely satisfactory. It is suggested that more linguistically based theories may prove more successful. (shrink)

Jones & Love (J&L) contend that the Bayesian approach should integrate process constraints with abstract computational analysis. We agree, but argue that the fundamentalist/enlightened dichotomy is a false one: Enlightened research is deeply intertwined with the basic, fundamental work upon which it is based.

Collecting information that one expects to be useful is a powerful way to facilitate learning. However, relatively little is known about how people decide which information is worth sampling over the course of learning. We describe several alternative models of how people might decide to collect a piece of information inspired by “active learning” research in machine learning. We additionally provide a theoretical analysis demonstrating the situations under which these models are empirically distinguishable, and we report a novel empirical study (...) that exploits these insights. Our model-based analysis of participants' information gathering decisions reveals that people prefer to select items which resolve uncertainty between two possibilities at a time rather than items that have high uncertainty across all relevant possibilities simultaneously. Rather than adhering to strictly normative or confirmatory conceptions of information search, people appear to prefer a “local” sampling strategy, which may reflect cognitive constraints on the process of information gathering. (shrink)

A Bayesian mind is, at its core, a rational mind. Bayesianism is thus well-suited to predict and explain mental processes that best exemplify our ability to be rational. However, evidence from belief acquisition and change appears to show that we do not acquire and update information in a Bayesian way. Instead, the principles of belief acquisition and updating seem grounded in maintaining a psychological immune system rather than in approximating a Bayesian processor.

We propose that the pragmatic factors that mediate everyday deduction, such as alternative and disabling conditions (e.g. Cummins et al., 1991) and additional requirements (Byrne, 1989) exert their effects on specific inferences because of their perceived relevance to more general principles, which we term SuperPs. Support for this proposal was found first in two causal inference experiments, in which it was shown that specific inferences were mediated by factors that are relevant to a more general principle, while the same inferences (...) were unaffected by factors not relevant to the general principle. These results were extended to deontic inferences in two further experiments. Taken together, these findings show that unstated superordinate principles play a significant role in certain types of reasoning. Questions raised by the findings for the main theoretical approaches are discussed. (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)

We propose a framework for including information‐processing bounds in rational analyses. It is an application of bounded optimality (Russell & Subramanian, 1995) to the challenges of developing theories of mechanism and behavior. The framework is based on the idea that behaviors are generated by cognitive mechanisms that are adapted to the structure of not only the environment but also the mind and brain itself. We call the framework computational rationality to emphasize the incorporation of computational mechanism into the definition of (...) rational action. Theories are specified as optimal program problems, defined by an adaptation environment, a bounded machine, and a utility function. Such theories yield different classes of explanation, depending on the extent to which they emphasize adaptation to bounds, and adaptation to some ecology that differs from the immediate local environment. We illustrate this variation with examples from three domains: visual attention in a linguistic task, manual response ordering, and reasoning. We explore the relation of this framework to existing “levels” approaches to explanation, and to other optimality‐based modeling approaches. (shrink)

The Cognitive Reflection Test is a widely used measure of the degree to which individuals override an intuitive response and engage in reflection. For both theoretical and practical reasons, it is widely taken to assess an important component of rational thought. In this paper, I will argue that while doing well on the CRT requires valuable cognitive capacities and dispositions, doing badly does not always indicate a lack of such capacities and dispositions. The CRT, I argue, offers respondents implicit (but (...) misleading) testimony: some of those who do badly do so due to a stronger disposition to defer to testimony. Since deference is not irrational, those who do badly need not be irrational, not even in part. (shrink)

Both scientists and children make important structural discoveries, yet their computational underpinnings are not well understood. Structure discovery has previously been formalized as probabilistic inference about the right structural form—where form could be a tree, ring, chain, grid, etc.. Although this approach can learn intuitive organizations, including a tree for animals and a ring for the color circle, it assumes a strong inductive bias that considers only these particular forms, and each form is explicitly provided as initial knowledge. Here we (...) introduce a new computational model of how organizing structure can be discovered, utilizing a broad hypothesis space with a preference for sparse connectivity. Given that the inductive bias is more general, the model's initial knowledge shows little qualitative resemblance to some of the discoveries it supports. As a consequence, the model can also learn complex structures for domains that lack intuitive description, as well as predict human property induction judgments without explicit structural forms. By allowing form to emerge from sparsity, our approach clarifies how both the richness and flexibility of human conceptual organization can coexist. (shrink)

Dual-process theories of conditional reasoning predict that relationships among four basic logical forms, and to intellectual ability and thinking predictions, are most evident when conflict arises between experiential and analytic processing (e.g., Stanovich & West, 2000). To test these predictions, 210 undergraduates were presented with conditionals for which the consequents were either weakly or strongly associated with alternative antecedents (i.e., WA and SA problems, respectively). Consistent with predictions, modus ponens inferences were not related to inferences on the uncertain forms (affirmation (...) of the consequent, denial of the antecedent). On WA problems, modus tollens, affirmation of the consequent, and denial of the antecedent were related to each other and to verbal ability. Modus ponens was linked to verbal ability only when disabling conditions were activated. In accord with the predictions of Stanovich and West (2000), on most problems, thinking dispositions predicted variance in inferences independently from verbal ability. We argue that a largely automatic experiential processing system governs performance on modus ponens, unless disablers are activated. Consciously controlled analytic processing predominates on the uncertain forms and, under some conditions, on modus tollens. (shrink)

This paper addresses a common challenge with computational cognitive models: identifying parameter values that are both theoretically plausible and generate predictions that match well with empirical data. While computational models can offer deep explanations of cognition, they are computationally complex and often out of reach of traditional parameter fitting methods. Weak methodology may lead to premature rejection of valid models or to acceptance of models that might otherwise be falsified. Mathematically robust fitting methods are, therefore, essential to the progress of (...) computational modeling in cognitive science. In this article, we investigate the capability and role of modern fitting methods—including Bayesian optimization and approximate Bayesian computation—and contrast them to some more commonly used methods: grid search and Nelder–Mead optimization. Our investigation consists of a reanalysis of the fitting of two previous computational models: an Adaptive Control of Thought—Rational model of skill acquisition and a computational rationality model of visual search. The results contrast the efficiency and informativeness of the methods. A key advantage of the Bayesian methods is the ability to estimate the uncertainty of fitted parameter values. We conclude that approximate Bayesian computation is (a) efficient, (b) informative, and (c) offers a path to reproducible results. (shrink)

An experiment is reported which tests for positive confirmation bias in a setting in which individuals choose what information to buy, prior to making a decision. The design – an adaptation of Wason's selection task – reveals the use that subjects make of information after buying it. Strong evidence of positive confirmation bias, in both information acquisition and information use, is found; and this bias is found to be robust to experience. It is suggested that the bias results from a (...) pattern of reasoning which, although producing sub-optimal decisions, is internally coherent and which is self-reinforcing. (shrink)

Knauff and Gazzo Castañeda (this issue) critique the "new paradigm" – a framework that replaces logic with probabilities – on the grounds that there existed no "old” paradigm for it to supplant. Their position is supported by the large numbers of theories that theorists developed to explain the Wason selection task, syllogisms, and other tasks. We propose some measures to inhibit such facile theorizing, which threatens the viability of cognitive science. We show that robust results exist contrary to the new (...) paradigm, and that it is unable to account for other results. (shrink)

This paper describes Peirce's systems of logic diagrams, focusing on the so-called ''existential'' graphs, which are equivalent to the first-order predicate calculus. It analyses their implications for the nature of mental representations, particularly mental models with which they have many characteristics in common. The graphs are intended to be iconic, i.e., to have a structure analogous to the structure of what they represent. They have emergent logical consequences and a single graph can capture all the different ways in which a (...) possibility can occur. Mental models share these properties. But, as the graphs show, certain aspects of propositions cannot be represented in an iconic or visualisable way. They include negation, and the representation of possibilities qua possibilities, which both require representations that do not depend on a perceptual modality. Peirce took his graphs to reveal the fundamental operations of reasoning, and the paper concludes with an analysis of different hypotheses about these operations. (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)

Utility maximization is a key element of a number of theoretical approaches to explaining human behavior. Among these approaches are rational analysis, ideal observer theory, and signal detection theory. While some examples of these approaches define the utility maximization problem with little reference to the bounds imposed by the organism, others start with, and emphasize approaches in which bounds imposed by the information processing architecture are considered as an explicit part of the utility maximization problem. These latter approaches are the (...) topic of this issue of the journal. (shrink)

It is known that, on average, people adapt their choice of memory strategy to the subjective utility of interaction. What is not known is whether an individual's choices are boundedly optimal. Two experiments are reported that test the hypothesis that an individual's decisions about the distribution of remembering between internal and external resources are boundedly optimal where optimality is defined relative to experience, cognitive constraints, and reward. The theory makes predictions that are tested against data, not fitted to it. The (...) experiments use a no-choice/choice utility learning paradigm where the no-choice phase is used to elicit a profile of each participant's performance across the strategy space and the choice phase is used to test predicted choices within this space. They show that the majority of individuals select strategies that are boundedly optimal. Further, individual differences in what people choose to do are successfully predicted by the analysis. Two issues are discussed: the performance of the minority of participants who did not find boundedly optimal adaptations, and the possibility that individuals anticipate what, with practice, will become a bounded optimal strategy, rather than what is boundedly optimal during training. (shrink)

Almaatouq et al.'s prescription for more integrative experimental designs is welcome but does not address an equally important problem: Lack of adequate theories. We highlight two features theories ought to satisfy: “Well-specified” and “grounded.” We discuss the importance of these features, some positive exemplars, and the complementarity between the target article's prescriptions and improved theorizing.

The new paradigm in the psychology of reasoning draws on Bayesian formal frameworks, and some advocates of the new paradigm think of these formal frameworks as providing a computational-level theory of rational human inference. I argue that Bayesian theories should not be seen as providing a computational-level theory of rational human inference, where by “Bayesian theories” I mean theories that claim that all rational credal states are probabilistically coherent and that rational adjustments of degrees of belief in the light of (...) new evidence must be in accordance with some sort of conditionalization. The problems with the view I am criticizing can best be seen when we look at chains of inferences, rather than single-step inferences. Chains of inferences have been neglected almost entirely within the new paradigm. (shrink)