We discuss external and internal graphical and linguistic representational systems. We argue that a cognitive theory of peoples' reasoning performance must account for (a) the logical equivalence of inferences expressed in graphical and linguistic form, and (b) the implementational differences that affect facility of inference. Our theory proposes that graphical representation limit abstraction and thereby aid “processibility”. We discuss the ideas of specificity and abstraction, and their cognitive relevance. Empirical support both comes from tasks which involve the manipulation of external (...) graphics and tasks that do not. For the former, we take Euler's (1772) circles, provide a novel computational reconstruction, show how it captures abstractions, and contrast it with earlier construals and with Johnson‐Laird's (1983) mental models representations. We demonstrate equivalence of the graphical Euler system, and the nongraphical mental models system. For tasks not involving manipulation of external graphics, we discuss text comprehension, and the mental performance of syllogisms. By positing an internal system with the same specificity as Euler's circles, we cover the mental models data, and generate new empirical predictions. Finally, we consider how the architecture of working memory explains why such specific representations are relatively easy to store. (shrink)

In this study on deduction, the authors argue that people reason by imagining the relevant state of affairs, ie building an internal model of it, formulating a tentative conclusion based on this model and then searching for alternative models.

This book represents the first major attempt by any author to provide an integrated account of the evidence for bias in human reasoning across a wide range of disparate psychological literatures. The topics discussed involve both deductive and inductive reasoning as well as statistical judgement and inference. In addition, the author proposes a general theoretical approach to the explanations of bias and considers the practical implications for real world decision making. The theoretical stance of the book is based on a (...) distinction between preconscious heuristic processes which determine the mental representation of 'relevant' features of the problem content, and subsequent analytic reasoning processes which generate inferences and judgements. Phenomena discussed and interpreted within this framework include feature matching biases in propositional reasoning, confirmation bias, biasing and debiasing effects of knowledge on reasoning, and biases in statistical judgement normally attributed to 'availability' and 'representativeness' heuristics. In the final chapter, the practical consequences of bias for real life decision making are considered, together with various issues concerning the problem of 'debiasing'. The major approaches discussed are those involving education and training on the one hand, and the development of intelligent software and interactive decision aids on the other. (shrink)

We discuss external and internal graphical and linguistic representational systems. We argue that a cognitive theory of peoples' reasoning performance must account for (a) the logical equivalence of inferences expressed in graphical and linguistic form; and (b) the implementational differences that affect facility of inference. Our theory proposes that graphical representations limit abstraction and thereby aid processibility. We discuss the ideas of specificity and abstraction, and their cognitive relevance. Empirical support comes from tasks (i) involving and (ii) not involving the (...) manipulation of external graphics. For (i), we take Euler's Circles, provide a novel computational reconstruction, show how it captures abstractions, and contrast it with earlier construals, and with Mental Models' representations. We demonstrate equivalence of the graphical Euler system, and the non-graphical Mental Models system. For (ii), we discuss text comprehension, and the mental performance of syllogisms. By positing an internal system with the same specificity as Euler's Circles we cover the Mental Models data, and generate new empirical predictions. Finally, we consider how the architecture of working memory explains why such specific representations are relatively easy to store. (shrink)

Change in View offers an entirely original approach to the philosophical study of reasoning by identifying principles of reasoning with principles for revising one's beliefs and intentions and not with principles of logic. This crucial observation leads to a number of important and interesting consequences that impinge on psychology and artificial intelligence as well as on various branches of philosophy, from epistemology to ethics and action theory. Gilbert Harman is Professor of Philosophy at Princeton University. A Bradford Book.

The following values have no corresponding Zotero field: PB - University of Illinois Press.

Two experiments investigated inferences based on suppositions. In Experiment 1, the subjects decided whether suppositions about individuals' veracity were consistent with their assertions—for example, whether the supposition “Ann is telling the truth and Beth is telling a lie”, is consistent with the premises: “Ann asserts: I am telling the truth and Beth is telling the truth. Beth asserts: Ann is telling the truth”. It showed that these inferences are more difficult than ones based on factual premises: “Ann asserts: I live (...) in Dublin and Beth lives in Dublin”. There was no difference between problems about truthtellers and liars, who always told the truth or always lied, and normals, who sometimes told the truth and sometimes lied. In Experiment 2, the subjects made inferences about factual matters set in three contexts: a truth-inducing context in which friends confided their personality characteristics, a lie-inducing context in which business rivals advertised their products, and a neutral context in which computers printed their program characteristics. Given the supposition that the individuals were lying, it was more difficult to make inferences in a truth-inducing context than in the other two contexts. We discuss the implications of our results for everyday reasoning from suppositions, and for theories of reasoning based on models or inference rules. (shrink)

We propose that people typically reason about realistic situations using neither content-free syntactic inference rules nor representations of specific experiences. Rather, people reason using knowledge structures that we term pragmatic reasoning schemas, which are generalized sets of rules defined in relation to classes of goals. Three experiments examined the impact of a “permission schema” on deductive reasoning. Experiment 1 demonstrated that by evoking the permission schema it is possible to facilitate performance in Wason's selection paradigm for subjects who have had (...) no experience with the specific content of the problems. Experiment 2 showed that a selection problem worded in terms of an abstract permission elicited better performance than one worded in terms of a concrete but arbitrary situation, providing evidence for an abstract permission schema that is free of domain-specific content. Experiment 3 provided evidence that evocation of a permission schema affects not only tasks requiring procedural knowledge, but also a linguistic rephrasing task requiring declarative knowledge. In particular, statements in the form if p then q were rephrased into the form p only if q with greater frequency for permission than for arbitrary statements, and rephrasings of permission statements produced a pattern of introduction of modals totally unlike that observed for arbitrary conditional statements. Other pragmatic schemas, such as “causal” and “evidence” schemas can account for both linguistic and reasoning phenomena that alternative hypotheses fail to explain. (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)

This paper is about syllogistic reasoning, i.e., reasoning from such pairs of premises as, All the chefs are musicians; some of the musicians are painters. We present a computer model that implements the latest account of syllogisms, which is based on the theory of mental models. We also report four experiments that were designed to test this account. Experiments 1 and 2 examined the strategies revealed by the participants' use of paper and pencil as aids to reasoning. Experiment 3 used (...) a new technique to externalize thinking. The participants had to refute, if possible, putative conclusions by constructing external models that were examples of the premises but counterexamples of the conclusions. Experiment 4 used the same techniques to examine the participants' strategies as they drew their own conclusions from syllogistic premises. The results of the experiments showed that individuals not trained in logic can construct counterexamples, that they use similar operations to those implemented in the computer model, but that they rely on a much greater variety of interpretations of premises and of search strategies than the computer model does. We re‐evaluates current theories of syllogistic reasoning in the light of these results. (shrink)

In this book, Newell makes the case for unified theories by setting forth a candidate.

"[Goodbye, Descartes] is certain to attract attention and controversy..a fascinating journey to the edges of logical thinking and beyond." -Publishers Weekly Critical Acclaim for Keith Devlin's Previous Book Mathematics: The Science of Patterns "A book such as this belongs in the personal library of everyone interested in learning about some of the most subtle and profound works of the human spirit." -American Scientist "Devlin's very attractive book is a well-written attempt to explain mathematics to educated nonmathematicians. the basic ideas are (...) presented in a clear, concise, and easily understood manner. Highly recommended." -Choice "[Devlin] has found an interesting way of exhibiting how mathematics is unified. the author's presentation is a tour de force." -Mathematical Reviews A Selection of the Newbridge Library of Science and Reader's Subscription. (shrink)

The following values have no corresponding Zotero field: PB - Lawrence Erlbaum Associates Inc Mahwah, NJ.

Johnson-Laird and Byrne present a theory of conditional inference based upon the manipulation of mental models. In the present paper, the theory is critically examined with regard to its ability to account for psychological data, principally with respect to the rate at which people draw the four basic inferences of modus ponens, denial of the antecedent, affirmation of the consequent and modus tollens. It is argued first that the theory is unclear in its definition and in particular with regard to (...) predictions of problem difficulty. Clarification and specification of principles are consequently provided here. Next, it is argued that there are a number of phenomena in the conditional reasoning literature for which the theory cannot account in its present form. Specifically, the relatively frequency of DA and AC inferences on affirmative conditionals is not as predicted by the theory, differences occur between inferences on if then and only if rules beyond the capacity of the theory to explain and there is no account of the “negative conclusion bias” observed when negated components are introduced into the rules. A number of revisions to the mental model theory of conditional reasoning are proposed in order to account for these findings. (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)

In this paper we investigate the locus of believability effects in syllogistic reasoning. We identify three points in the reasoning process at which such effects could occur: the initial interpretation of premises, the examination of alternative representations of them (in all of which any valid conclusion must be true), and the “filtering” of putative conclusions. The effect of beliefs at the first of these loci is well established. In this paper we report three experiments that examine whether beliefs have an (...) effect at the other two loci. In experiments 1 and 2 subjects drew their own conclusions from syllogisms that suggested believable or unbelievable ones. In the third experiment they evaluated conclusions that were presented to them. The data show that beliefs both affect the examination of alternative models and act as a filter on putative conclusions. We conclude by showing how some types of problem and some problem contents make the existence of alternative models more obvious than others. (shrink)

Beyond modularityattempts a synthesis of Fodor's anticonstructivist nativism and Piaget's antinativist constructivism. Contra Fodor, I argue that: (1) the study of cognitive development is essential to cognitive science, (2) the module/central processing dichotomy is too rigid, and (3) the mind does not begin with prespecified modules; rather, development involves a gradual process of “modularization.” Contra Piaget, I argue that: (1) development rarely involves stagelike domain-general change and (2) domainspecific predispositions give development a small but significant kickstart by focusing the infant's (...) attention on proprietary inputs. Development does not stop at efficient learning. A fundamental aspect of human development (“representational redescription”) is the hypothesized process by which information that isina cognitive system becomes progressively explicit knowledgetothat system. Development thus involves two complementary processes of progressive modularization and progressive “explicitation.” Empirical findings on the child as linguist, physicist, mathematician, psychologist, and notator are discussed in support of the theoretical framework. Each chapter concentrates first on the initial state of the infant mind/brain and on subsequent domain-specific learning in infancy and early childhood. It then goes on to explore data on older children's problem solving and theory building, with particular focus on evolving cognitive flexibility. Emphasis is placed throughout on the status of representations underlying different capacities and on the multiple levels at which knowledge is stored and accessible. Finally, consideration is given to the need for more formal developmental models, and a comparison is made between representational redescription and connectionist simulations of development. In conclusion, I consider what is special about human cognition by speculating on the status of representations underlying the structure of behavior in other species. (shrink)

I have been supposing that for the theory of reasoning, explicit belief is an all-or-nothing matter, I have assumed that, as far as principles of reasoning are concerned, one either believes something explicitly or one does not; in other words an appropriate "representation" is either in one's "memory" or not. The principles of reasoning are principles for modifying such all-or-nothing representations. This is not to deny that in some ways belief is a matter of degree. For one thing implicit belief (...) is certainly a matter of degree, since it is a matter of how easily and automatically one can infer something from what one believes explicitly. Furthermore, explicit belief is a matter of degree in the sense that one believes some things more strongly than others. Sometimes one is only somewhat inclined to believe something, sometimes one is not sure what to believe, sometimes one is inclined to disbelieve something, sometimes one is quite confident something is not so, and so forth. (shrink)

Lance Rips describes a unified theory of natural deductive reasoning and fashions a working model of deduction, with strong experimental support, that is capable of playing a central role in mental life.

This study examines the problem of belief revision, defined as deciding which of several initially accepted sentences to disbelieve, when new information presents a logical inconsistency with the initial set. In the first three experiments, the initial sentence set included a conditional sentence, a non‐conditional (ground) sentence, and an inferred conclusion drawn from the first two. The new information contradicted the inferred conclusion. Results indicated that conditional sentences were more readily abandoned than ground sentences, even when either choice would lead (...) to a consistent belief state, and that this preference was more pronounced when problems used natural language cover stories rather than symbols. The pattern of belief revision choices differed depending on whether the contradicted conclusion from the initial belief set had been a modus ponens or modus tollens inference. Two additional experiments examined alternative model‐theoretic definitions of minimal change to a belief state, using problems that contained multiple models of the initial belief state and of the new information that provided the contradiction. The results indicated that people did not follow any of four formal definitions of minimal change on these problems. The new information and the contradiction it offered was not, for example, used to select a particular model of the initial belief state as a way of reconciling the contradiction. The preferred revision was to retain only those initial sentences that had the same, unambiguous truth value within and across both the initial and new information sets. The study and results are presented in the context of certain logic‐based formalizations of belief revision, syntactic and model‐theoretic representations of belief states, and performance models of human deduction. Principles by which some types of sentences might be more “entrenched” than others in the face of contradiction are also discussed from the perspective of induction and theory revision. (shrink)

Most theories of deduction have assumed that linguistic processes transduce from language into an internal representation and back again, and that non-linguistic processes are central to deduction itself. In this article it is proposed that for deduction tasks for which the necessary information is provided verbally, the heart of deduction for untrained participants involves repeatedly reencoding the problem, a type of behavior referred to here as verbal reasoning. It is shown that model theory accounts of behavior on most deduction tasks (...) are consistent with verbal reasoning and that verbal reasoning can account for detailed behavior in a single task; a computational model of syllogistic reasoning—VR—based on linguistic mechanisms is presented. VR models all of the standard phenomena, makes a number of accurate novel predictions, and fits the behavior of individual participants with an accuracy that rivals their own test–retest reliability. (shrink)

The mental model theory postulates that reasoners build models of the situations described in premises. A conclusion is possible if it holds in at least one model of the premises; it is probable if it holds in most of the models; and it is necessary if it holds in all of the models. The theory also postulates that reasoners represent as little information as possible in explicit models and, in particular, that they represent only information about what is true. One (...) unexpected consequence of this assumption is that there should be a category of illusory inferences: they will have conclusions that seem obvious, but that are wholly erroneous. Experiment 1 established the existence of such illusory inferences about probabilities. Overall, 88% of the intelligent adult subjects chose as more probable an outcome that was impossible for at least one of the illusory problems. Experiment 2 corroborated the phenomenon and showed that illusory inferences include a wide variety of problems. Finally, the paper argues that current theories based on formal rules of inference are unlikely to be able to explain the illusions. (shrink)

In this paper, the theory of syllogistic reasoning proposed by Johnson-Laird is shown to be inadequate and an alternative theory is put forward. Protocols of people attempting to solve syllogistic problems and explaining to another person how they reached their conclusions were obtained. Two main groups of subjects were identified. One group represented the relationship between classes in a spatial manner that was supplemented by a verbal representation. The other group used a primarily verbal representation. A detailed theory of the (...) processes for both groups is given. (shrink)

This article outlines a theory of naive probability. According to the theory, individuals who are unfamiliar with the probability calculus can infer the probabilities of events in an extensional way: They construct mental models of what is true in the various possibilities. Each model represents an equiprobable alternative unless individuals have beliefs to the contrary, in which case some models will have higher probabilities than others. The probability of an event depends on the proportion of models in which it occurs. (...) The theory predicts several phenomena of reasoning about absolute probabilities, including typical biases. It correctly predicts certain cognitive illusions in inferences about relative probabilities. It accommodates reasoning based on numerical premises, and it explains how naive reasoners can infer posterior probabilities without relying on Bayes's theorem. Finally, it dispels some common misconceptions of probabilistic reasoning. (shrink)