Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian reasoning relative to normalized formats (e.g. probabilities, percentages), both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on “transparent” Bayesian problems varies widely, and generally remains rather unimpressive. (...) We suggest there has been an over-focus on this representational facilitator (i.e. transparent problem structures) at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct versus incorrect reasoners depart, and how individual difference might influence this time point. (shrink)

People reject ‘paradoxical’ inferences, such as: Luisa didn't play music; therefore, if Luisa played soccer, then she didn't play music. For some theorists, they are invalid for everyday conditionals, but valid in logic. The theory of mental models implies that they are valid, but unacceptable because the conclusion refers to a possibility inconsistent with the premise. Hence, individuals should accept them if the conclusions refer only to possibilities consistent with the premises: Luisa didn't play soccer; therefore, if Luisa played a (...) game then she didn't play soccer. Two experiments corroborated this prediction for three sorts of ‘paradox’, including a disjunctive paradox. (shrink)

Short abstract (98 words). Reasoning is generally seen as a means to improve knowledge and make better decisions. However, much evidence shows that reasoning often leads to epistemic distortions and poor decisions. This suggests that the function of reasoning should be rethought. Our hypothesis is that the function of reasoning is argumentative. It is to devise and evaluate arguments intended to persuade. Reasoning so conceived is adaptive given humans’ exceptional dependence on communication and vulnerability to misinformation. A wide range of (...) evidence in the psychology of reasoning and decision making can be reinterpreted and better explained in the light of this hypothesis. (shrink)

Groups do better at reasoning tasks than individuals, and, in some cases, do even better than any of their individual members. Here is an illustration. In the standard version of Wason selection task (Wason, 1966), the most commonly studied problem in the psychology of reasoning, only about 10% of participants give the correct solution, even though it can be arrived at by elementary deductive reasoning.1 Such poor performance begs for an explanation, and a great many have been offered. What makes (...) the selection task relevant here is that the difference between individual and group performance is striking. Moshman & Geil for instance (1998, see also Maciejovsky & Budescu, 2007) had participants try and resolve the task either individually or in groups of five or six participants. While, unsurprisingly, only 9% of the participants working on their own found the correct solution, an astonishing 70% of the groups did. Moreover, when groups were formed with participants who had first tried to solve the task individually, 80% of the groups succeeded, including 30% of the groups in which none of the members had succeeded on his or her own. How are such differences between individual and group performance to be explained? (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)

This thesis aims to develop a psychologically plausible account of concepts by integrating key insights from philosophy (on the metaphysical basis for concept possession) and psychology (on the mechanisms underlying concept acquisition). I adopt an approach known as informational atomism, developed by Jerry Fodor. Informational atomism is the conjunction of two theses: (i) informational semantics, according to which conceptual content is constituted exhaustively by nomological mind–world relations; and (ii) conceptual atomism, according to which (lexical) concepts have no internal structure. I (...) argue that informational semantics needs to be supplemented by allowing content-constitutive rules of inference (“meaning postulates”). This is because the content of one important class of concepts, the logical terms, is not plausibly informational. And since, it is argued, no principled distinction can be drawn between logical concepts and the rest, the problem that this raises is a general one. An immediate difficulty is that Quine’s classic arguments against the analytic/synthetic distinction suggest that there can be no principled basis for distinguishing content-constitutive rules from the rest. I show that this concern can be overcome by taking a psychological approach: there is a fact of the matter as to whether or not a particular inference is governed by a mentally-represented inference rule, albeit one that analytic philosophy does not have the resources to determine. I then consider the implications of this approach for concept acquisition. One mechanism underlying concept acquisition is the development of perceptual detectors for the objects that we encounter. I investigate how this might work, by drawing on recent ideas in ethology on ‘learning instincts’, and recent insights into the neurological basis for perceptual learning. What emerges is a view of concept acquisition as involving a complex interplay between innate constraints and environmental input. This supports Fodor’s recent move away from radical concept nativism: concept acquisition requires innate mechanisms, but does not require that concepts themselves be innate. (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)

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

The theory of mental models and its computer implementations have led to crucial experiments showing that no standard logic—the sentential calculus and all logics that include it—can underlie human reasoning. The theory replaces the logical concept of validity (the conclusion is true in all cases in which the premises are true) with necessity (conclusions describe no more than possibilities to which the premises refer). Many inferences are both necessary and valid. But experiments show that individuals make necessary inferences that are (...) invalid, e.g., Few people ate steak or sole; therefore, few people ate steak. Other crucial experiments show that individuals reject inferences that are not necessary but valid, e.g., He had the anesthetic or felt pain, but not both; therefore, he had the anesthetic or felt pain, or both. Nothing in logic can justify the rejection of a valid inference: a denial of its conclusion is inconsistent with its premises, and inconsistencies yield valid inferences of any conclusions whatsoever including the one denied. So inconsistencies are catastrophic in logic. In contrast, the model theory treats all inferences as defeasible (nonmonotonic), and inconsistencies have the null model, which yields only the null model in conjunction with any other premises. So inconsistences are local. Which allows truth values in natural languages to be much richer than those that occur in the semantics of standard logics; and individuals verify assertions on the basis of both facts and possibilities that did not occur. (shrink)

ABSTRACTThree experiments examined how people reason about what is possible or necessary when a conditional is true. Participants were asked to indicate whether it was necessary, possible or impossible for a specific instance to conform to one of the truth-table cases, given the truth of the conditional. It was found that most participants, inconsistently, judged the pq case as necessary but the ¬pq or ¬p¬q cases as possible. Logically, these two kinds of judgments are contradictory. Moreover, a true conditional doesn’t (...) imply that a specific instance under the conditional must be pq. Therefore, people demonstrate a necessity illusion for pq cases which contradicts their commitment to the possibility of ¬pq or ¬p¬q cases. Existing accounts of conditionals are unable to explain the contradiction and the necessity illusion. We propose an inference dissociation account and explore the theoretical implications of this necessity illusion. (shrink)

This paper replies to Politzer’s (2007) criticisms of the mental model theory of conditionals. It argues that the theory provides a correct account of negation of conditionals, that it does not provide a truth-functional account of their meaning, though it predicts that certain interpretations of conditionals yield acceptable versions of the ‘paradoxes’ of material implication, and that it postulates three main strategies for estimating the probabilities of conditionals.

It is unclear how an argumentative environment would select for better reasoning given three general findings. First, argument rationality typically fails to persuade poor reasoners. Second, reasoned argumentation competes with more persuasive and less rational arguments for limited cognitive resources. Third, those poor at reasoning fail to distinguish between valid and invalid arguments. Reasoning, therefore, is poorly designed for argument.

Recent studies have shown that deductive reasoning skills are related to mathematical abilities. Nevertheless, so far the links between mathematical abilities and these two forms of deductive inference have not been investigated in a single study. It is also unclear whether these inference forms are related to both basic maths skills and mathematical reasoning, and whether these relationships still hold if the effects of fluid intelligence are controlled. We conducted a study with 87 adult participants. The results showed that transitive (...) reasoning skills were related to performance on a number line task, and conditional inferences were related to arithmetic skills. Additionally, both types of deductive inference were related to mathematical reasoning skills, although transitive and conditional reasoning ability were unrelated. Our results also highlighted the important role that ordering abilities play in mathematical reasoning, extending findings regarding the role of ordering abilities in basic maths skills. These results have implications for the theories of mathematical and deductive reasoning, and they could inspire the development of novel educational interventions. (shrink)

The theory of mental models postulates that meaning and knowledge can modulate the interpretation of conditionals. The theory's computer implementation implied that certain conditionals should be true or false without the need for evidence. Three experiments corroborated this prediction. In Experiment 1, nearly 500 participants evaluated 24 conditionals as true or false, and they justified their judgments by completing sentences of the form, It is impossible that A and ___ appropriately. In Experiment 2, participants evaluated 16 conditionals and provided their (...) own justifications, which tended to be explanations rather than logical justifications. In Experiment 3, the participants also evaluated as possible or impossible each of the four cases in the partitions of 16 conditionals: A and C, A and not-C, not-A and C, not-A and not-C. These evaluations corroborated the model theory. We consider the implications of these results for theories of reasoning based on logic, probabilistic logic, and suppositions. (shrink)

Mercier & Sperber (M&S) argue for their argumentative theory in terms of communicative abilities. Insights can be gained by extending the discussion beyond human reasoning to rodent and robot navigation. The selection of arguments and conclusions that are mutually reinforcing can be cast as a form of abductive reasoning that I argue underlies the construction of cognitive maps in navigation tasks.