Hay doble pulsión en el centro de la discusión del razonamiento deductivo. Una conduce aparentemente a la abstracción y dominios arbitrarios, mientras que la otra conduce a la concreción y la dependencia del contenido. El objetivo de esta investigación es diseñar, aplicar y validar un instrumento de evaluación que nos permita corroborar si el razonamiento deductivo maneja reglas lógicas o contenidos. La muestra de estudio se compuso de 80 participantes (edad 18-77 años). El test consta de 60 ítems categorizados en: (...) formalidad, integrabilidad, complejidad y modalidad. Los resultados ponen de manifiesto la fiabilidad del test de razonamiento deductivo con un alpha de Cronbach. 775 y con un índice de validación. 850 para el índice de inteligencia no verbal (INV) del RIAS. Cómo conclusión inferimos que el razonador deductivo no dispone de un cuerpo preciso de reglas generales deductivas, sino que usa colecciones de reglas heurísticas cada vez menos abstractas. (shrink)

The paper offers a solution to the generality problem for a reliabilist epistemology, by developing an “algorithm and parameters” scheme for type-individuating cognitive processes. Algorithms are detailed procedures for mapping inputs to outputs. Parameters are psychological variables that systematically affect processing. The relevant process type for a given token is given by the complete algorithmic characterization of the token, along with the values of all the causally relevant parameters. The typing that results is far removed from the typings of folk (...) psychology, and from much of the epistemology literature. But it is principled and empirically grounded, and shows good prospects for yielding the desired epistemological verdicts. The paper articulates and elaborates the theory, drawing out some of its consequences. Toward the end, the fleshed-out theory is applied to two important case studies: hallucination and cognitive penetration of perception. (shrink)

Perceptual systems respond to proximal stimuli by forming mental representations of distal stimuli. A central goal for the philosophy of perception is to characterize the representations delivered by perceptual systems. It may be that all perceptual representations are in some way proprietarily perceptual and differ from the representational format of thought (Dretske 1981; Carey 2009; Burge 2010; Block ms.). Or it may instead be that perception and cognition always trade in the same code (Prinz 2002; Pylyshyn 2003). This paper rejects (...) both approaches in favor of perceptual pluralism, the thesis that perception delivers a multiplicity of representational formats, some proprietary and some shared with cognition. The argument for perceptual pluralism marshals a wide array of empirical evidence in favor of iconic (i.e., image-like, analog) representations in perception as well as discursive (i.e., language-like, digital) perceptual object representations. (shrink)

The notion of an object file figures prominently in recent work in philosophy and cognitive science. Object files play a role in theories of singular reference, object individuation, perceptual memory, and the development of cognitive capacities. However, the philosophical literature lacks a detailed, empirically informed theory of object files. In this paper, we articulate and defend the multiple-slots view, which specifies both the format and architecture of object files. We argue that object files represent in a non-iconic, propositional format that (...) incorporates discrete symbols for separate features. Moreover, we argue that features of separate categories are stored in separate memory slots within an object file. We supplement this view with a computational framework that characterizes how information about objects is stored and retrieved. (shrink)

ABSTRACTThis paper provides a naturalistic account of inference. We posit that the core of inference is constituted by bare inferential transitions, transitions between discursive mental representations guided by rules built into the architecture of cognitive systems. In further developing the concept of BITs, we provide an account of what Boghossian [2014] calls ‘taking’—that is, the appreciation of the rule that guides an inferential transition. We argue that BITs are sufficient for implicit taking, and then, to analyse explicit taking, we posit (...) rich inferential transitions, which are transitions that the subject is disposed to endorse. (shrink)

According to a classic but nowadays discarded philosophical theory, perceptual experience is a complex of nonconceptual sensory states and full-blown propositional beliefs. This classical dual-component theory of experience is often taken to be obsolete. In particular, there seem to be cases in which perceptual experience and belief conflict: cases of known illusions, wherein subjects have beliefs contrary to the contents of their experiences. Modern dual-component theories reject the belief requirement and instead hold that perceptual experience is a complex of nonconceptual (...) sensory states and some other sort of conceptual state. The most popular modern dual-component theory appeals to sui generis propositional attitudes called ‘perceptual seemings’. This article argues that the classical dual-component theory has the resources to explain known illusions without giving up the claim that the conceptual components of experience are beliefs. The classical dual-component view, though often viewed as outdated and implausible, should be regarded as a serious contender in contemporary debates about the nature of perceptual experience. (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)

Inferences about spatial, temporal, and other relations are ubiquitous. This article presents a novel model-based theory of such reasoning. The theory depends on 5 principles. The structure of mental models is iconic as far as possible. The logical consequences of relations emerge from models constructed from the meanings of the relations and from knowledge. Individuals tend to construct only a single, typical model. They spontaneously develop their own strategies for relational reasoning. Regardless of strategy, the difficulty of an inference depends (...) on the process of integration of the information from separate premises, the number of entities that have to be integrated to form a model, and the depth of the relation. The article describes computer implementations of the theory and presents experimental results corroborating its main principle. (shrink)

We present a meta-analytic review on the processing of negations in conditional reasoning about affirmation problems (Modus Ponens: “MP”, Affirmation of the Consequent “AC”) and denial problems (Denial of the Antecedent “DA”, and Modus Tollens “MT”). Findings correct previous generalisations about the phenomena. First, the effects of negation in the part of the conditional about which an inference is made, are not constrained to denial problems. These inferential-negation effects are also observed on AC. Second, there generally are reliable effects of (...) a negation in the clause referred to by the categorical premise, and these referred-negation effects are constrained to the logically fallacious AC and DA inferences. All findings are presented and discussed in relation to contemporary mental model (MM) and mental logic (ML) theories. It is argued that a double-negation elimination hypothesis provides a sufficient explanation of inferential-negation effects within both MM theory and ML theory, if the latter is extended by a validating search for counter examples. Both MM and ML theories adhere to a processing scheme that allows them to incorporate an account of referred-negation effects based on the thesis that counter-example frequency is modulated by the scope of a contrast class delineated by a false affirmative. We conclude that MM and ML theories provide adequate processing schemes to accommodate for the explanatory hypotheses, at least in principle. In practice, both approaches remain equivocal as regards the connectivity and interactivity with long-term memory knowledge invoked in generating, manipulating, and testing the mental representations of negative state of affairs. (shrink)

Four experiments examined the strategies that individuals develop in sentential reasoning. They led to the discovery of five different strategies. According to the theory proposed in the paper, each of the strategies depends on component tactics, which all normal adults possess, and which are based on mental models. Reasoners vary their use of tactics in ways that have no deterministic account. This variation leads different individuals to assemble different strategies, which include the construction of incremental diagrams corresponding to mental models, (...) and the pursuit of the consequences of a single model step by step. Moreover, the difficulty of a problem (i.e., the number of mental models required by the premises) predisposes reasoners towards certain strategies. Likewise, the sentential connectives in the premises also bias reasoners towards certain strategies, e.g., conditional premises tend to elicit reasoning step by step whereas disjunctive premises tend to elicit incremental diagrams. (shrink)

We are reliable about logic in the sense that we by-and-large believe logical truths and disbelieve logical falsehoods. Given that logic is an objective subject matter, it is difficult to provide a satisfying explanation of our reliability. This generates a significant epistemological challenge, analogous to the well-known Benacerraf-Field problem for mathematical Platonism. One initially plausible way to answer the challenge is to appeal to evolution by natural selection. The central idea is that being able to correctly deductively reason conferred a (...) heritable survival advantage upon our ancestors. However, there are several arguments that purport to show that evolutionary accounts cannot even in principle explain how it is that we are reliable about logic. In this paper, I address these arguments. I show that there is no general reason to think that evolutionary accounts are incapable of explaining our reliability about logic. (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)

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)

Reasoning research has focussed mainly on the type of cognitive processes involved when representing premises and when producing conclusions. But less is known about the factors that guide these representational and inferential processes. What premises are actually taken as input in reasoning? And what conclusions are intended? In this paper it is argued that considerations of relevance are helpful for addressing these issues as a pragmatic analysis of two sorts of tasks is carried out, Wason’s 2-4-6 problem and a conditional (...) reasoning problem . Study 1 indicates that the way this task is communicated may encourage participants to consider misleading information as highly relevant for solving it. Two experiments go on to show that when the relevance of misleading information is contextually diminished, participants are more efficient at providing the correct solution. Study 2 compares the production rate of two sorts of conclusions: logically valid but weakly relevant conclusions and invalid but relevant and pragmatically justified conclusions. This study shows that the relevance of conclusions determines to a large extent whether or not they will be produced. (shrink)

Tarski’s conceptual analysis of the notion of logical consequence is one of the pinnacles of the process of defining the metamathematical foundations of mathematics in the tradition of his predecessors Euclid, Frege, Russell and Hilbert, and his contemporaries Carnap, Gödel, Gentzen and Turing. However, he also notes that in defining the concept of consequence “efforts were made to adhere to the common usage of the language of every day life.” This paper addresses the issue of what relationship Tarski’s analysis, and (...) Béziau’s further generalization of it in universal logic, have to reasoning in the everyday lives of ordinary people from the cognitive processes of children through to those of specialists in the empirical and deductive sciences. It surveys a selection of relevant research in a range of disciplines providing theoretical and empirical studies of human reasoning, discusses the value of adopting a universal logic perspective, answers the questions posed in the call for this special issue, and suggests some specific research challenges. (shrink)

Current theories of reasoning such as mental models or mental logic assume a universal cognitive mechanism that underlies human reasoning performance. However, there is evidence that this is not the case, for example, the work of Ford (1995), who found that some people adopted predominantly spatial and some verbal strategies in a syllogistic reasoning task. Using written and think-aloud protocols, the present study confirmed the existence of these individual differences. However, in sharp contrast to Ford, the present study found few (...) differences in reasoning performance between the two groups, in terms of accuracy or type of conclusion generated. Hence, reasoners present an outward appearance of ubiquity, despite underlying differences in reasoning processes. These findings have implications for theoretical accounts of reasoning, and for attempts to model reasoning data. Any comprehensive account needs to account for strategic differences and how these may develop in logically untrained individuals. (shrink)

This paper reviews the psychological investigation of reasoning with conditionals, putting an emphasis on recent work. In the first part, a few methodological remarks are presented. In the second part, the main theories of deductive reasoning (mental rules, mental models, and the probabilistic approach) are considered in turn; their content is summarised and the semantics they assume for if and the way they explain formal conditional reasoning are discussed, in particular in the light of experimental work on the probability of (...) conditionals. The last part presents the recent shift of interest towards the study of conditional reasoning in context, that is, with large knowledge bases and uncertain premises. (shrink)

Language employs various coordinators to connect propositions, a subset of which are “logical” in nature and thus analogous to the truth operators of formal logic. We here focus on two linguistic connectives and their negations: conjunction _and_ and (inclusive) disjunction _or_. Linguistic connectives exhibit a truth-conditional component as part of their meaning (their semantics), but their use in context can give rise to various implicatures and presuppositions (the domain of pragmatics) as well as to inferences that go beyond semantic/pragmatic properties (...) (the result of reasoning processes). We provide a comprehensive review of the role of the logical connectives in language and argue that three sets of factors—semantic, pragmatic, and those related to reasoning—are separate and separable, though some details may differ cross-linguistically. As a way to showcase the argument, we present two experiments in language comprehension in Spanish wherein pragmatic content was minimised and reasoning processes neutered, thus potentially highlighting what might be the default meanings of the connectives under study. In Experiment 1 we show that the conjunctive reading of inclusive disjunction is available in positive contexts other than in syntactically intricate cases such as downward entailing and free choice contexts, contrary to what has been claimed in the literature. In Experiment 2 we show that negated conjunctions and disjunctions in Spanish can easily receive the same interpretation when contrasted against the same context and, moreover, that these interpretations match those available in English, despite claims from the literature that linguistic connectives and local negation interact differently in English and Romance languages. (shrink)

Psychological research on people’s understanding of natural language connectives has traditionally used truth table tasks, in which participants evaluate the truth or falsity of a compound sentence given the truth or falsity of its components in the framework of propositional logic. One perplexing result concerned the indicative conditional if A then C which was often evaluated as true when A and C are true, false when A is true and C is false but irrelevant“ (devoid of value) when A is (...) false (whatever the value of C). This was called the “psychological defective table of the conditional.” Here we show that far from being anomalous the “defective” table pattern reveals a coherent semantics for the basic connectives of natural language in a trivalent framework. This was done by establishing participants’ truth tables for negation, conjunction, disjunction, conditional, and biconditional, when they were presented with statements that could be certainly true, certainly false, or neither. We review systems of three-valued tables from logic, linguistics, foundations of quantum mechanics, philosophical logic, and artificial intelligence, to see whether one of these systems adequately describes people’s interpretations of natural language connectives. We find that de Finetti’s (1936/1995) three-valued system is the best approximation to participants’ truth tables. (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)

In agreement with some of the ideas expressed by Perruchet & Vinter (P&V), we believe that some phenomena hitherto attributed to processing may in fact reflect a fundamental distinction between direct and reflexive forms of consciousness. This dichotomy, developed by the phenomenological tradition, is substantiated by examples coming from experimental psychology and lesion neuropsychology.

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)

One of the most debated questions in psychology and cognitive science is the nature and the functioning of the mental processes involved in deductive reasoning. However, all existing theories refer to a specific deductive domain, like syllogistic, propositional or relational reasoning.Our goal is to unify the main types of deductive reasoning into a single set of basic procedures. In particular, we bring together the microtheories developed from a mental models perspective in a single theory, for which we provide a formal (...) foundation. We validate the theory through a computational model (UNICORE) which allows fine‐grained predictions of subjects' performance in different reasoning domains.The performance of the model is tested against the performance of experimental subjects—as reported in the relevant literature—in the three areas of syllogistic, relational and propositional reasoning. The computational model proves to be a satisfactory artificial subject, reproducing both correct and erroneous performance of the human subjects. Moreover, we introduce a developmental trend in the program, in order to simulate the performance of subjects of different ages, ranging from children (3–6) to adolescents (8–12) to adults (>21). The simulation model performs similarly to the subjects of different ages.Our conclusion is that the validity of the mental model approach is confirmed for the deductive reasoning domain, and that it is possible to devise a unique mechanism able to deal with the specific subareas. The proposed computational model (UNICORE) represents such a unifying structure. (shrink)

We report the results of two experiments that show that participants rely on both emotion and reason in moral judgments. Experiment 1 showed that when participants were primed to communicate feelings, they provided emotive justifications not only for personal dilemmas, e.g., pushing a man from a bridge that will result in his death but save the lives of five others, but also for impersonal dilemmas, e.g., hitting a switch on a runaway train that will result in the death of one (...) man but save the lives of five others; when they were primed to communicate thoughts, they provided non-emotive justifications for both personal and impersonal dilemmas. Experiment 2 showed that participants read about a protagonist's emotions more quickly when the protagonist was faced with a personal dilemma than an impersonal one, but they read about the protagonist's decision to act or not act equally quickly for personal and impersonal dilemmas. (shrink)

The social contracts theory claims that, in social exchange circumstances, human reasoning is not necessarily led by logic, but by certain evolved mental mechanisms that are useful for catching offenders. An emblematic experiment carried out with the intention to prove this thesis is the first experiment described by Fiddick, Cosmides, and Tooby in their paper of 2000. Lopez Astorga has questioned that experiment claiming that its results depend on an underlying conditional logical form not taken into account by Fiddick, Cosmides, (...) and Tooby. In this paper, I propose an explanation alternative to that of Lopez Astorga, which does not depend on logical forms and is based on the mental models theory. Thus, I conclude that this other alternative explanation is one more proof that the experiment in question does not demonstrate the fundamental thesis of the social contracts theory. (shrink)

Logical theory codifies rules of correct inferences. On the other hand, logical reasoning is typically considered as one of the most fundamental cognitive activities. Thus, cognitive science is a natural meeting-point for investigations about the place of logic in human cognition. Investigations in this perspective strongly depend on a possible understanding of logic. This paper focuses on logic in the strict sense; that is, the theory of deductive inferences. Two problems are taken into account, namely: do humans apply logical rules (...) in ordinary reasoning?; the genesis of logic. The second issue is analyzed from the naturalistic point of view. (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.

The human imagination remains one of the last uncharted terrains of the mind. People often imagine how events might have turned out something had been different. The of reality, those aspects more readily changed, indicate that counterfactual thoughts are guided by the same principles as rational thoughts. In the past, rationality and imagination have been viewed as opposites. But research has shown that rational thought is more imaginative than cognitive scientists had supposed. In The Rational Imagination, I argue that imaginative (...) thought is more rational than scientists have imagined. People exhibit remarkable similarities in the sorts of things they change in their mental representation of reality when they imagine how the facts could have turned out differently. For example, they tend to imagine alternatives to actions rather than inactions, events within their control rather than those beyond their control, and socially unacceptable events rather than acceptable ones. Their thoughts about how an event might have turned out differently lead them to judge that a strong causal relation exists between an antecedent event and the outcome, and their thoughts about how an event might have turned out the same lead them to judge that a weaker causal relation exists. In a simple temporal sequence, people tend to imagine alternatives to the most recent event. The central claim in the book is that counterfactual thoughts are organised along the same principles as rational thought. The idea that the counterfactual imagination is rational depends on three steps: (1) humans are capable of rational thought; (2) they make inferences by thinking about possibilities; and (3) their counterfactual thoughts rely on thinking about possibilities, just as rational thoughts do. The sorts of possibilities that people envisage explain the mutability of certain aspects of mental representations and the immutability of other aspects. (shrink)

Reasoning research has focussed mainly on the type of cognitive processes involved when representing premises and when producing conclusions. But less is known about the factors that guide these representational and inferential processes. What premises are actually taken as input in reasoning? And what conclusions are intended? In this paper it is argued that considerations of relevance (Sperber and Wilson, Relevance: communication and cognition. Blackwell, Oxford, 1995) are helpful for addressing these issues as a pragmatic analysis of two sorts of (...) tasks is carried out, Wason’s 2-4-6 problem (Study 1) and a conditional reasoning problem (Study 2). Study 1 indicates that the way this task is communicated may encourage participants to consider misleading information as highly relevant for solving it. Two experiments go on to show that when the relevance of misleading information is contextually diminished, participants are more efficient at providing the correct solution. Study 2 compares the production rate of two sorts of conclusions: logically valid but weakly relevant conclusions and invalid but relevant and pragmatically justified conclusions. This study shows that the relevance of conclusions determines to a large extent whether or not they will be produced. (shrink)

Four experiments examined the strategies that individuals develop in sentential reasoning. They led to the discovery of five different strategies. According to the theory proposed in the paper, each of the strategies depends on component tactics, which all normal adults possess, and which are based on mental models. Reasoners vary their use of tactics in ways that have no deterministic account. This variation leads different individuals to assemble different strategies, which include the construction of incremental diagrams corresponding to mental models, (...) and the pursuit of the consequences of a single model step by step. Moreover, the difficulty of a problem (i.e., the number of mental models required by the premises) predisposes reasoners towards certain strategies. Likewise, the sentential connectives in the premises also bias reasoners towards certain strategies, e.g., conditional premises tend to elicit reasoning step by step whereas disjunctive premises tend to elicit incremental diagrams. (shrink)

Four experiments examined the strategies that individuals develop in sentential reasoning. They led to the discovery of five different strategies. According to the theory proposed in the paper, each of the strategies depends on component tactics, which all normal adults possess, and which are based on mental models. Reasoners vary their use of tactics in ways that are not deterministic. This variation leads different individuals to assemble different strategies, which include the construction of incremental diagram corresponding to mental models, and (...) the pursuit of the consequences of a single model step by step. Moreover, the difficulty of a problem (i.e. the number of mental models required by the premises) predisposes reasoners towards certain strategies. Likewise, the sentential connectives in the premises also bias reasoners towards certain strategies, e.g., conditional premises tend to elicit reasoning step by step whereas disjunctive premises tend to elicit incremental diagrams. (shrink)

Researchers currently working on relational reasoning typically argue that mental model theory (MMT) is a better account than the inference rule approach (IRA). They predict and observe that determinate (or one-model) problems are easier than indeterminate (or two-model) problems, whereas according to them, IRA should lead to the opposite prediction. However, the predictions attributed to IRA are based on a mistaken argument. The IRA is generally presented in such a way that inference rules only deal with determinate relations and not (...) with indeterminate ones. However, (a) there is no reason to presuppose that a rule-based procedure could not deal with indeterminate relations, and (b) applying a rule-based procedure to indeterminate relations should result in greater difficulty. Hence, none of the recent articles devoted to relational reasoning currently presents a conclusive case for discarding IRA by using the well-known determinate vs indeterminate problems comparison. (shrink)

We conducted a computer-based psychological experiment in which a random mix of 40 tautologies and 40 non-tautologies were presented to the participants, who were asked to determine which ones of the formulas were tautologies. The participants were eight university students in computer science who had received tuition in propositional logic. The formulas appeared one by one, a time-limit of 45 s applied to each formula and no aids were allowed. For each formula we recorded the proportion of the participants who (...) classified the formula correctly before timeout and the mean response time among those participants. We propose a new proof formalism for modeling propositional reasoning with bounded cognitive resources. It models declarative memory, visual memory, working memory, and procedural memory according to the memory model of Atkinson and Shiffrin and reasoning processes according to the model of Newell and Simon. We also define two particular proof systems, T and NT, for showing propositional formulas to be tautologies and non-tautologies, respectively. The accuracy was found to be higher for non-tautologies than for tautologies ( p T was.89 and for non-tautologies the correlation between latency and minimum proof length in NT was.87. (shrink)

First, we describe a psychological experiment in which the participants were asked to determine whether sentences of first-order logic were true or false in finite graphs. Second, we define two proof systems for reasoning about truth and falsity in first-order logic. These proof systems feature explicit models of cognitive resources such as declarative memory, procedural memory, working memory, and sensory memory. Third, we describe a computer program that is used to find the smallest proofs in the aforementioned proof systems when (...) capacity limits are put on the cognitive resources. Finally, we investigate the correlation between a number of mathematical complexity measures defined on graphs and sentences and some psychological complexity measures that were recorded in the experiment. (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)

We report two studies on the effect of implicitly versus explicitly conveying affirmation and denial problems about conditionals. Recently Evans and Handley (1999) and Schroyens et al. (1999b, 2000b) showed that implicit referencing elicits matching bias: Fewer determinate inferences are made, when the categorical premise (e.g., B) mismatches the conditional's referred clause (e.g., A). Also, the effect of implicit affirmation (B affirms not-A) is larger than the effect of implicit denial (B denies A). Schroyens et al. hypothesised that this interaction (...) is due to uncertainty in the case-wise affirmation of the contrast class of negated elements involved in implicit affirmations. In Experiment 1 we tested this hypothesis by manipulating the set size of the conditional clauses. The results confirm that binary sets, where the contrast class is a singleton, eliminate the differential effect of implicit affirmation and denial. With non-binary sets the interaction is not modulated by the scope of the contrast class (3, 5, 9 elements). Experiment 2 further investigated the role of contrast classes by using class inclusion to construct implicit affirmations (Mammal vs Mammal or Monkey) and implicit denial (No-Mammal vs Mammal or Monkey), in addition to the standard implicit problems mediated by contrast-class inclusion [(No-)Mammal/No-Mammal; Reptile; Snake). Findings indicate that class inclusion (Mammal/Monkey; Reptile/ Snake) only marginally affects performance, and is independent of the type of problem. This would suggest that the implicitness problem-type interaction is dependent on constructing contrast classes. However, the experiment failed to replicate the interaction, even on the subset of problems repeating the abstract letter/number format of Experiment 1. Moreover, with the natural binary set-sizes (vowels/consonants) the implicitness effect was eliminated entirely. (shrink)

We discuss O&C's probabilistic approach from a probability logical point of view. Specifically, we comment on subjective probability, the indispensability of logic, the Ramsey test, the consequence relation, human nonmonotonic reasoning, intervals, generalized quantifiers, and rational analysis.

Traditional theories of how children learn the positive integers start from infants' abilities in detecting the quantity of physical objects. Our target article examined this view and found no plausible accounts of such development. Most of our commentators appear to agree that no adequate developmental theory is presently available, but they attempt to hold onto a role for early enumeration. Although some defend the traditional theories, others introduce new basic quantitative abilities, new methods of transformation, or new types of end (...) states. A survey of these proposals, however, shows that they do not succeed in bridging the gap to knowledge of the integers. We suggest that a better theory depends on starting with primitives that are inherently structural and mathematical. (shrink)

The mental model theory predicts that reasoners normally represent what is true, but not what is false. One consequence is that reasoners should make "illusory" inferences, which are compelling but invalid. Three experiments confirmed the existence of such illusions based on disjunctions of disjunctions. They also established a successful antidote to them: Reasoners are much less likely to succumb to illusions if the inferences concern disjunctions of physical objects (alternative newspaper advertisements) rather disjunctions of the truth values of assertions. The (...) results shed light both on the cause of the illusions and on the current controversy among different theories of reasoning. (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)

An important debate in the reasoning literature concerns the extent to which inference processes are domain-free or domain-specific. Typically, evidence in support of the domain-specific position comprises the facilitation observed when abstract reasoning tasks are set in realistic context. Three experiments are reported here in which the sources of facilitation were investigated for contextualised versions of Raven's Progressive Matrices (Richardson, 1991) and non-verbal analogies from the AH4 test (Richardson & Webster, 1996). Experiment 1 confirmed that the facilitation observed for the (...) contextualised matrices was in part due to extraneous aspects of commentaries originally intended to activate domainspecific processes. Experiments 2 and 3 indicated that the remainder of the facilitation for the matrices, and all of the facilitation for the analogies, could be explained by visual salience: Converting the item elements into realistic objects had enabled them and their transitions to be identified more easily. Hence, performance at simplified abstract items was as good as, or better than, at contextualised items. It is concluded that facilitation effects cannot be interpreted as showing that domain-specific processes constitute a self-contained system separate from domain-free processes. In turn, this means that domain-free processes cannot be dismissed as being unimportant for reasoning. (shrink)

Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept (...) from these beginnings. Proposals for arriving at natural number by (empirical) induction presuppose the mathematical concepts they seek to explain. Moreover, standard experimental tests for children's understanding of number terms do not necessarily tap these concepts. (2) True concepts of number do appear, however, when children are able to understand generalizations over all numbers; for example, the principle of additive commutativity (a+b=b+a). Theories of how children learn such principles usually rely on a process of mapping from physical object groupings. But both experimental results and theoretical considerations imply that direct mapping is insufficient for acquiring these principles. We suggest instead that children may arrive at natural numbers and arithmetic in a more top-down way, by constructing mathematical schemas. (shrink)

The question of whether perception is encapsulated from cognition has been a major topic in the study of perception in the past decade. One locus of debate concerns the role of attention. Some theorists argue that attention is a vehicle for widespread violations of encapsulation; others argue that certain forms of cognitively driven attention are compatible with encapsulation, especially if attention only modulates inputs. This paper argues for an extreme thesis: no effect of attention, whether on the inputs to perception (...) or on perceptual processing itself, constitutes a violation of the encapsulation of perception. (shrink)

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.