Topological relations such as inside, outside, or intersection are ubiquitous to our spatial thinking. Here, we examined how people reason deductively with topological relations between points, lines, and circles in geometric diagrams. We hypothesized in particular that a counterexample search generally underlies this type of reasoning. We first verified that educated adults without specific math training were able to produce correct diagrammatic representations contained in the premisses of an inference. Our first experiment then revealed that subjects who correctly judged an (...) inference as invalid almost always produced a counterexample to support their answer. Noticeably, even if the counterexample always bore a certain level of similarity to the initial diagram, we observed that an object was more likely to be varied between the two drawings if it was present in the conclusion of the inference. Experiments 2 and 3 then directly probed counterexample search. While participants were asked to evaluate a conclusion on the basis of a given diagram and some premisses, we modulated the difficulty of reaching a counterexample from the diagram. Our results indicate that both decreasing the counterexample density and increasing the counterexample distance impaired reasoning performance. Taken together, our results suggest that a search procedure for counterexamples, which proceeds object‐wise, could underlie diagram‐based geometric reasoning. Transposing points, lines, and circles to our spatial environment, the present study may ultimately provide insights on how humans reason about topological relations between positions, paths, and regions. (shrink)

I discuss two types of evidential problems with the most widely touted experiments in evolutionary psychology, those performed by Leda Cosmides and interpreted by Cosmides and John Tooby. First, and despite Cosmides and Tooby's claims to the contrary, these experiments don't fulfil the standards of evidence of evolutionary biology. Second Cosmides and Tooby claim to have performed a crucial experiment, and to have eliminated rival approaches. Though they claim that their results are consistent with their theory but contradictory to the (...) leading non-evolutionary alternative, Pragmatic Reasoning Schemas theory, I argue that this claim is unsupported. In addition, some of Cosmides and Tooby's interpretations arise from misguided and simplistic understandings of evolutionary biology. While I endorse the incorporation of evolutionary approaches into psychology, I reject the claims of Cosmides and Tooby that a modular approach is the only one supported by evolutionary biology. Lewontin's critical examinations of the applications of adaptationist thinking provide a background of evidentiary standards against which to view the currently fashionable claims of evolutionary psychology. (shrink)

Reasoning is a certain kind of attitude-revision. What kind? The aim of this paper is to introduce and defend a new answer to this question, based on the idea that reasoning is a goodness-fixing kind. Our central claim is that reasoning is a functional kind: it has a constitutive point or aim that fixes the standards for good reasoning. We claim, further, that this aim is to get fitting attitudes. We start by considering recent accounts of reasoning due to Ralph (...) Wedgwood and John Broome, and argue that, while these accounts contain important insights, they are not satisfactory: Wedgwood’s rules out too much, and Broome’s too little. We then introduce and defend our alternative account, discuss some of its implications and attractions, and, finally, consider objections. (shrink)

This paper presents a new theory of modal reasoning, i.e. reasoning about what may or may not be the case, and what must or must not be the case. It postulates that individuals construct models of the premises in which they make explicit only what is true. A conclusion is possible if it holds in at least one model, whereas it is necessary if it holds in all the models. The theory makes three predictions, which are corroborated experimentally. First, conclusions (...) correspond to the true, but not the false, components of possibilities. Second, there is a key interaction: it is easier to infer that a situation is possible as opposed to impossible, whereas it is easier to infer that a situation is not necessary as opposed to necessary. Third, individuals make systematic errors of omission and of commission. We contrast the theory with theories based on formal rules. (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)

The epistemic poverty objection is commonly levelled by externalists against deontological conceptions of epistemic justification. This is that an “oughts” based account of epistemic justification together with “ought” implies “can” must lead us to hold to be justified, epistemic agents who are objectively not truth-conducive cognizers. The epistemic poverty objection has led to a common response from deontologists, namely to embrace accounts of bounded rationality—subjective, practical or regulative accounts rather than objective, absolute or theoretical accounts. But the bounds deontological epistemologists (...) and their opponents entertain rarely include cultural limitations. This paper considers neo-Vygotskian arguments that we must consider such cultural limits in defending deontologism, and thus that any deontologically motivated perspectivism must be in part a cultural perspectivism. The dangers of strong relativism are flagged and an attempt is made to steer a.. (shrink)

Despite the accumulation of substantial cognitive science research relevant to education, there remains confusion and controversy in the application of research to educational practice. In support of a more systematic approach, we describe the Knowledge-Learning-Instruction (KLI) framework. KLI promotes the emergence of instructional principles of high potential for generality, while explicitly identifying constraints of and opportunities for detailed analysis of the knowledge students may acquire in courses. Drawing on research across domains of science, math, and language learning, we illustrate the (...) analyses of knowledge, learning, and instructional events that the KLI framework affords. We present a set of three coordinated taxonomies of knowledge, learning, and instruction. For example, we identify three broad classes of learning events (LEs): (a) memory and fluency processes, (b) induction and refinement processes, and (c) understanding and sense-making processes, and we show how these can lead to different knowledge changes and constraints on optimal instructional choices. (shrink)

Closure for justification is the claim that thinkers are justified in believing the logical consequences of their justified beliefs, at least when those consequences are competently deduced. Many have found this principle to be very plausible. Even more attractive is the special case of Closure known as Single-Premise Closure. In this paper, I present a challenge to Single-Premise Closure. The challenge is based on the phenomenon of rational self-doubt – it can be rational to be less than fully confident in (...) one's beliefs and patterns of reasoning. In rough outline, the argument is as follows: Consider a thinker who deduces a conclusion from a justified initial premise via an incredibly long sequence of small competent deductions. Surely, such a thinker should suspect that he has made a mistake somewhere. And surely, given this, he should not believe the conclusion of the deduction even though he has a justified belief in the initial premise. (shrink)

We think of logic as objective. We also think that we are reliable about logic. These views jointly generate a puzzle: How is it that we are reliable about logic? How is it that our logical beliefs match an objective domain of logical fact? This is an instance of a more general challenge to explain our reliability about a priori domains. In this paper, I argue that the nature of this challenge has not been properly understood. I explicate the challenge (...) both in general and for the particular case of logic. I also argue that two seemingly attractive responses – appealing to a faculty of rational insight or to the nature of concept possession – are incapable of answering the challenge. (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)

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)

How do people imagine the possibilities in which an assertion would be true and the possibilities in which it would be false? We argue that the mental representation of the meanings of connectives, such as "and", "or", and "if", specify how to construct the true possibilities for simple assertions containing just a single connective. It follows that the false possibilities are constructed by inference from the true possibilities. We report converging evidence supporting this account from four experiments in which the (...) participants had to list the true and the false possibilities for various sorts of assertion. Their systematic errors, response times, and think-aloud protocols corroborated the theory's predictions. Not even true possibilities are immediately available for complex assertions containing two or more different connectives. The task of listing the true possibilities then becomes difficult, and the task of listing the false possibilities almost impossible. (shrink)

Two experiments examined the role of conditional reasoning in the logical deduction game, Mastermind . An analysis suggested that Modus Tollens (MT) reasoning could be used to determine the code structure, for example, in determining if any of the colours in the code are repeated. Consistent with this analysis, Experiment 1 showed that only MT errors are correlated with the number of hypotheses advanced in Mastermind . A subsequent analysis showed that conditional reasoning such as Affirming the Consequent (AC) and (...) Denying the Antecedent (DA) could lead to particularly damaging inferences only when the code was four different colours. When that was known before play, Experiment 2 showed that AC errors, but not MT errors, were significantly correlated with Mastermind hypotheses advanced. A stepwise multiple regression analysis supported these findings: When the solvers knew they were playing a four-colour code, there was a slight diminution in the variance explained by MT errors, and a significant increase in the variance explained by AC errors. An analysis of the number of different possible codes that could be consistent with hypotheses actually played showed that the number of such codes is far fewer when the code consists of four different colours than when its structure is not known. This analysis suggests that reasoners are therefore unlikely to discover many alternative causes for the feedback given when the code consists of four different colours, and it is under these conditions that humans are most likely to engage in AC reasoning. (shrink)

Research from ethology and evolutionary biology indicates the following about the evolution of reasoning capacity. First, solving problems of social competition and cooperation have direct impact on survival rates and reproductive success. Second, the social structure that evolved from this pressure is the dominance hierarchy. Third, primates that live in large groups with complex dominance hierarchies also show greater neocortical development, and concomitantly greater cognitive capacity. These facts suggest that the necessity of reasoning effectively about dominance hierarchies left an indelible (...) mark on primate reasoning architectures, including that of humans. In order to survive in a dominance hierarchy, an individual must be capable of (a) making rank discriminations, (b) recognizing what is forbidden and what is permitted based one's rank, and (c) deciding whether to engage in or refriin from activities that will allow one to move up in rank. The first problem is closely tied to the capacity for transitive reasoning, while the second and third are intimately related to the capacity for deontic reasoning. I argue that the human capacity for these types of reasoning have evolutionary roots that reach deeper into our ancestral past than the emergence of the hominid line, and the operation of these evolutionarily primitive reasoning systems can be seen in the development of human reasoning and domain-specific effects in adult reasoning. (shrink)

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)

Cognition is both empowered and limited by representations. The matrix lens model explicates tasks that are based on frequency counts, conditional probabilities, and binary contingencies in a general fashion. Based on a structural analysis of such tasks, the model links several problems and semantic domains and provides a new perspective on representational accounts of cognition that recognizes representational isomorphs as opportunities, rather than as problems. The shared structural construct of a 2 × 2 matrix supports a set of generic tasks (...) and semantic mappings that provide a unifying framework for understanding problems and defining scientific measures. Our model's key explanatory mechanism is the adoption of particular perspectives on a 2 × 2 matrix that categorizes the frequency counts of cases by some condition, treatment, risk, or outcome factor. By the selective steps of filtering, framing, and focusing on specific aspects, the measures used in various semantic domains negotiate distinct trade-offs between abstraction and specialization. As a consequence, the transparent communication of such measures must explicate the perspectives encapsulated in their derivation. To demonstrate the explanatory scope of our model, we use it to clarify theoretical debates on biases and facilitation effects in Bayesian reasoning and to integrate the scientific measures from various semantic domains within a unifying framework. A better understanding of problem structures, representational transparency, and the role of perspectives in the scientific process yields both theoretical insights and practical applications. (shrink)

This study investigated the cognitive processes involved in inductive reasoning. Sixteen undergraduates solved quadratic function–finding problems and provided concurrent verbal protocols. Three fundamental areas of inductive activity were identified: Data Gathering, Pattern Finding, and Hypothesis Generation. These activities are evident in three different strategies that they used to successfully find functions. In all three strategies, Pattern Finding played a critical role not previously identified in the literature. In the most common strategy, called the Pursuit strategy, participants created new quantities from (...) x and y, detected patterns in these quantities, and expressed these patterns in terms of x. These expressions were then built into full hypotheses. The processes involved in this strategy are instantiated in an ACT‐based model that simulates both successful and unsuccessful performance. The protocols and the model suggest that numerical knowledge is essential to the detection of patterns and, therefore, to higher‐order problem solving. (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)

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)

In this response, we clarify several misunderstandings of the understanding/acceptance principle and defend our specific operationalization of that principle. We reiterate the importance of addressing the problem of rational task construal and we elaborate the notion of computational limitations contained in our target article. Our concept of thinking dispositions as variable intentional-level styles of epistemic and behavioral regulation is explained, as is its relation to the rationality debate. Many of the suggestions of the commentators for elaborating two-process models are easily (...) integrated into our generic dual-process account. We further explicate how we view the relation between System 1 and System 2 and evolutionary and normative rationality. We clarify our attempt to fuse the contributions of the cognitive ecologists with the insights of the original heuristics and biases researchers. (shrink)

This paper reviews the largely psychological literature surrounding apparent failures of human rationality (sometimes referred to as 'the Rationality Wars') and locates it with respect to concepts and issues within more traditional epistemological inquiry. The goal is to bridge the gap between these two large and typically disconnected literatures – concerning rationality and the psychology of human reasoning, on the one hand, and epistemological theories of justified or rational belief, on the other – and to do so in such as (...) way as to expose interesting points of contact and convergence between them. (shrink)

Samuels and Stich explore the debate over the extent to which ordinary human reasoning and decision making is rational. One prominent cluster of views, often associated with the heuristics and biases tradition in psychology, maintains that human reasoning is, in important respects, normatively problematic or irrational. Samuels and Stich start by sketching some key experimental findings from this tradition and describe a range of pessimistic claims about the rationality of ordinary people that these and related findings are sometimes taken to (...) support. Such pessimistic interpretations of the experimental findings have not gone unchallenged however: Samuels and Stich outline some of the research on reasoning that has been done by evolutionary psychologists and sketch a cluster of more optimistic theses about ordinary reasoning that such psychologists defend. Although Samuels and Stich think that the most dire pronouncements made by writers in the heuristics and biases tradition are unwarranted, they also maintain that the situation is rather more pessimistic than sometimes suggested by evolutionary psychologists. They conclude by defending this “middle way” and sketch a family of “dual processing” theories of reasoning which, they argue, offer some support for the moderate interpretation they advocate. (shrink)

There is an Aristotelian thesis that can be considered controversial. That is the thesis related to a denied conditional with only one propositional variable and in which, in addition, one of its clauses is also denied. While the thesis is not a tautology, people tend to accept it as true. Pfeifer’s approach can account for this fact. However, I try to show that this problem can also be explained from other alternative frameworks, in particular, from that of the mental models (...) theory, that of López-Astorga based on the pragmatic phenomenon of conditional perfection, and that of the mental logic theory. Likewise, I indicate the difficulties regarding Aristotle’s thesis of the mental models theory and López-Astorga’s proposal, and conclude that the account of the mental logic theory is the strongest alternative to Pfeifer’s explanation and that what is clearly obvious is that conditional should not be materially interpreted. (shrink)

We address the way verb-based and rule-content knowledge are combined in understanding institutional deontics. Study 1 showed that the institutional regulations used in our studies were readily categorised into one of two content groups: rights or duties. Participants perceived rights as benefiting the addressees identified by the rule, whereas they perceived duties as benefiting the collective that imposed the rule. Studies 2, 3, and 4 showed that rule content had clear effects on perceptions of violations and relevance of cases for (...) explaining the rule, even when controlling for deontic verb, phrasing of the action permitted by a right, or the formality of the deontic verb. These effects are incompatible with a simple pragmatic disambiguation approach to pragmatic modulation, as they often induce permissibility judgments that contradict the core semantic meanings of the deontic verbs. Other ways of reconciling verb meaning with rule content should be considered in a fuller the.. (shrink)

Individual differences in performance on a variety of selection tasks were examined in three studies employing over 800 participants. Nondeontic tasks were solved disproportionately by individuals of higher cognitive ability. In contrast, responses on two deontic tasks that have shown robust performance facilitationthe Drinking-age Problem and the Sears Problem-were unrelated to cognitive ability. Performance on deontic and nondeontic tasks was consistently associated. Individuals in the correct/correct cell of the bivariate performance matrix were over-represented. That is, individuals giving the modal response (...) on a nondeontic task (P and Q) were significantly less likely to give the modal response on a deontic task (P and not-Q) than were individuals who made the non-modal P and not-Q selection on nondeontic problems. The implications of the results are discussed within the heuristic-analytic framework of Evans (1996; Evans & Over, 1996) and the optimal data selection model of Oaksford and Chater (1994). (shrink)

What counts as human rationality: reasoning processes that embody content-independent formal theories, such as propositional logic, or reasoning processes that are well designed for solving important adaptive problems? Most theories of human reasoning have been based on content-independent formal rationality, whereas adaptive reasoning, ecological or evolutionary, has been little explored. We elaborate and test an evolutionary approach, Cosmides' social contract theory, using the Wason selection task. In the first part, we disentangle the theoretical concept of a “social contract” from that (...) of a “cheater-detection algorithm”. We demonstrate that the fact that a rule is perceived as a social contract — or a conditional permission or obligation, as Cheng and Holyoak proposed — is not sufficient to elicit Cosmides' striking results, which we replicated. The crucial issue is not semantic, but pragmatic: whether a person is cued into the perspective of a party who can be cheated. In the second part, we distinguish between social contracts with bilateral and unilateral cheating options. Perspective change in contracts with bilateral cheating options turns P & not-Q responses into not-P & Q responses. The results strongly support social contract theory, contradict availability theory, and cannot be accounted for by pragmatic reasoning schema theory, which lacks the pragmatic concepts of perspectives and cheating detection. (shrink)