Credences are similar to levels of confidence, represented as a value on the [0,1] interval. This chapter sheds light on questions about credence, including its relationship to full belief, with an eye toward the empirical relevance of credence. First, I’ll provide a brief epistemological history of credence and lay out some of the main theories of the nature of credence. Then, I’ll provide an overview of the main views on how credences relate to full beliefs. Finally, I’ll turn to the (...) empirical, and suggest some ways that cognitive science does and could answer questions about credence, such as what credences one has, how credences relate to beliefs, and the extent to which we can control our credences. (shrink)

Bayesian Rationality (Oaksford & Chater 2007) illustrates the strengths of Bayesian models of cognition: the systematicity of rational explanations, transparent assumptions about human learners, and combining structured symbolic representation with statistics. However, the book also highlights some of the challenges this approach faces: of providing psychological mechanisms, explaining the origins of the knowledge that guides human learning, and accounting for how people make genuinely new discoveries.

Three correctives can get researchers out of the trap of constructing unitary theories of “thinking”: (1) Strong inference methods largely avoid problems associated with universal prescriptive normativism; (2) theories must recognize that significant modularity of cognitive processes is antithetical to general accounts of thinking; and (3) consideration of the domain-specificity of rationality render many of the present article's issues moot.

The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology – namely, Behaviorism and evolutionary psychology – that set aside mechanistic explanations or make use of optimality assumptions. Through (...) these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls that have plagued previous theoretical movements. (shrink)

Intelligence can be understood as a form of rationality, in the sense that an intelligent system does its best when its knowledge and resources are insufficient with respect to the problems to be solved. The traditional models of rationality typically assume some form of sufficiency of knowledge and resources, so cannot solve many theoretical and practical problems in Artificial Intelligence (AI). New models based on the Assumption of Insufficient Knowledge and Resources (AIKR) cannot be obtained by minor revisions or extensions (...) of the traditional models, and have to be established fully according to the restrictions and freedoms provided by AIKR. The practice of NARS, an AI project, shows that such new models are feasible and promising in providing a new theoretical foundation for the study of rationality, intelligence, consciousness, and mind. (shrink)

This essay addresses the methodology of philosophy of science and illustrates how formal and empirical methods can be fruitfully combined. Special emphasis is given to the application of experimental methods to confirmation theory and to recent work on the conjunction fallacy, a key topic in the rationality debate arising from research in cognitive psychology. Several other issue can be studied in this way. In the concluding section, a brief outline is provided of three further examples.

Various semantics for studying the square of opposition have been proposed recently. So far, only [14] studied a probabilistic version of the square where the sentences were interpreted by (negated) defaults. We extend this work by interpreting sentences by imprecise (set-valued) probability assessments on a sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square in terms of acceptability and show how to construct probabilistic versions of the square (...) of opposition by forming suitable tripartitions. Finally, as an application, we present a new square involving generalized quantifiers. (shrink)

In this paper we exploit the notions of conjoined and iterated conditionals, which are defined in the setting of coherence by means of suitable conditional random quantities with values in the interval [0,1]. We examine the iterated conditional (B|K)|(A|H), by showing that A|H p-entails B|K if and only if (B|K)|(A|H) = 1. Then, we show that a p-consistent family F={E1|H1, E2|H2} p-entails a conditional event E3|H3 if and only if E3|H3= 1, or (E3|H3)|QC(S) = 1 for some nonempty subset S (...) of F, where QC(S) is the quasi conjunction of the conditional events in S. Then, we examine the inference rules And, Cut, Cautious Monotonicity, and Or of System P and other well known inference rules (Modus Ponens, Modus Tollens, Bayes). We also show that QC(F)|C(F) = 1, where C(F) is the conjunction of the conditional events in F. We characterize p-entailment by showing that F p-entails E3|H3 if and only if (E3|H3)|C(F) = 1. Finally, we examine Denial of the antecedent and Affirmation of the consequent, where the p-entailment of (E3|H3) from F does not hold, by showing that (E3|H3)|C(F) is not equal to 1. (shrink)

This chapter subsumes David Marr’s levels of analysis account of explanation in cognitive science under the framework of mechanistic explanation: Answering the questions that define each one of Marr’s three levels is tantamount to describing the component parts and operations of mechanisms, as well as their organization, behavior, and environmental context. By explicating these questions and showing how they are answered in several different cognitive science research programs, this chapter resolves some of the ambiguities that remain in Marr’s account, and (...) shows that many different areas and traditions of cognitive scientific research can be unified under the mechanistic framework. (shrink)

This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without (...) providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. (shrink)

Reasons-responsive accounts of praiseworthiness say, roughly, that an agent is praiseworthy for an action just in case the reasons that explain why they acted are also the reasons that explain why the action is right. In this paper, we argue that reasons-responsive accounts imply that some actions of non-human animals are praiseworthy. Trying to exclude non-human animals, we argue, risks neglecting cases of inadvertent virtue in human action and undermining the anti-intellectualist commitments that are typically associated with reasons-responsive accounts. Of (...) course, this could be taken as a reason to reject reasons-responsive accounts, rather than as a reason to attribute praiseworthiness to non-human animal action. We respond to two reasons that one might resist the implication that non-human animal action can be praiseworthy. The first appeals to intuition: it’s too counterintuitive to attribute praiseworthiness to non-human animal action. In response, we argue that once the factors that determine an action’s praiseworthiness are disambiguated from the factors that determine whether an agent should be praised, the intuitive objection loses much of its force. The second appeals to empirical evidence: attributing praiseworthiness to non-human animal action involves a problematic kind of anthropomorphizing. First, we point out that this objection is mostly an _a priori_ objection in _a posteriori_ clothes: whether we give anthropomorphic vs. anthropectic explanations is a methodological choice, not an empirical one. Second, we argue that considerations from the literature on rational analysis and radical interpretation actually support anthropomorphic explanations over anthropectic explanations. (shrink)

Bayesian reverse-engineering is a research strategy for developing three-level explanations of behavior and cognition. Starting from a computational-level analysis of behavior and cognition as optimal probabilistic inference, Bayesian reverse-engineers apply numerous tweaks and heuristics to formulate testable hypotheses at the algorithmic and implementational levels. In so doing, they exploit recent technological advances in Bayesian artificial intelligence, machine learning, and statistics, but also consider established principles from cognitive psychology and neuroscience. Although these tweaks and heuristics are highly pragmatic in character and (...) are often deployed unsystematically, Bayesian reverse-engineering avoids several important worries that have been raised about the explanatory credentials of Bayesian cognitive science: the worry that the lower levels of analysis are being ignored altogether; the challenge that the mathematical models being developed are unfalsifiable; and the charge that the terms ‘optimal’ and ‘rational’ have lost their customary normative force. But while Bayesian reverse-engineering is therefore a viable and productive research strategy, it is also no fool-proof recipe for explanatory success. (shrink)

Mercier and Sperber (2011a, 2011b; Mercier, 2011a, 2011b, 2011c, and 2011d) have presented a stimulating and provocative new theory of reasoning: the argumentative theory of reasoning. They maintain that argumentation is a meta-representational module. In their evolutionary view of argumentation, the function of this module would be to regulate the flow of information between interlocutors through persuasiveness on the side of the communicator and epistemic vigilance on the side of the audience. The aim of this paper is to discuss the (...) perspective of the authors in which they conceive this competence as the natural scenario of reflective reasoning. (shrink)

In moral psychology, “psychological rationalism” is the view that moral judgments are caused by a process of reasoning. Jonathan Haidt argues against this view by showing that people succumb to “moral dumbfounding”—they cannot adequately provide reasoning for their moral judgment. I argue that this evidence undermines psychological rationalism only if the view is committed to two claims about reasoning: (a) reasoning must meet an adequacy condition, and (b) reasoning must be sufficiently conscious. I argue that plausible variants of psychological rationalism (...) are not committed to these requirements. Thus, the efficacy of the dumbfounding objection is more limited than it might initially seem. (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 probabilistic approach to human reasoning is exemplified by the information gain model for the Wason card selection task. Although the model is elegant and original, several key aspects of the model warrant further discussion, particularly those concerning the scope of the task and the choice process of individuals.

InSuppose and Tell, Williamson makes a new and original attempt to defend the material conditional account of indicative conditionals. His overarching argument is that this account offers the best explanation of the data concerning how people evaluate and use such conditionals. We argue that Williamson overlooks several important alternative explanations, some of which appear to explain the relevant data at least as well as, or even better than, the material conditional account does. Along the way, we also show that Williamson (...) errs at important junctures about what exactly the relevant data are. (shrink)

Conditional learning, where agents learn a conditional sentence ‘If A, then B,’ is difficult to incorporate into existing Bayesian models of learning. This is because conditional learning is not uniform: in some cases, learning a conditional requires decreasing the probability of the antecedent, while in other cases, the antecedent probability stays constant or increases. I argue that how one learns a conditional depends on the causal structure relating the antecedent and the consequent, leading to a causal model of conditional learning. (...) This model extends traditional Bayesian learning by incorporating causal models into agents’ epistemic states. On this theory, conditional learning proceeds in two steps. First, an agent learns a new causal model with the appropriate relationship between the antecedent and the consequent. Then, the agent narrows down the set of possible worlds to include only those which make the conditional proposition true. This model of learning can incorporate both standard cases of Bayesian learning and the non-uniform learning required to learn conditional information. (shrink)

The appropriateness, or acceptability, of a conditional does not just ‘go with’ the corresponding conditional probability. A condition of dependence is required as well. In this paper a particular notion of dependence is proposed. It is shown that under both a forward causal and a backward evidential reading of the conditional, this appropriateness condition reduces to conditional probability under some natural circumstances. Because this is in particular the case for the so-called diagnostic reading of the conditional, this analysis might help (...) to explain some of Douven and Verbrugge’s empirical observations. (shrink)

Bayes’ inference cannot reliably account for uncertainty in mental processes. The reason is that Bayes’ inference is based on the assumption that the order in which the relevant features are evaluated is indifferent, which is not the case in most of mental processes. Instead of Bayes’ rule, a more general, probabilistic rule of inference capable of accounting for these order effects is established. This new rule of inference can be used to improve the current Bayesian models of cognition. Moreover, it (...) should play an essential role in the search for artificial emotional intelligence. (shrink)

In this paper we discuss the new Tweety puzzle. The original Tweety puzzle was addressed by approaches in non-monotonic logic, which aim to adequately represent the Tweety case, namely that Tweety is a penguin and, thus, an exceptional bird, which cannot fly, although in general birds can fly. The new Tweety puzzle is intended as a challenge for probabilistic theories of epistemic states. In the first part of the paper we argue against monistic Bayesians, who assume that epistemic states can (...) at any given time be adequately described by a single subjective probability function. We show that monistic Bayesians cannot provide an adequate solution to the new Tweety puzzle, because this requires one to refer to a frequency-based probability function. We conclude that monistic Bayesianism cannot be a fully adequate theory of epistemic states. In the second part we describe an empirical study, which provides support for the thesis that monistic Bayesianism is also inadequate as a descriptive theory of cognitive states. In the final part of the paper we criticize Bayesian approaches in cognitive science, insofar as their monistic tendency cannot adequately address the new Tweety puzzle. We, further, argue against monistic Bayesianism in cognitive science by means of a case study. In this case study we show that Oaksford and Chater’s (2007, 2008) model of conditional inference—contrary to the authors’ theoretical position—has to refer also to a frequency-based probability function. (shrink)

Inductive reasoning requires exploiting links between evidence and hypotheses. This can be done focusing either on the posterior probability of the hypothesis when updated on the new evidence or on the impact of the new evidence on the credibility of the hypothesis. But are these two cognitive representations equally reliable? This study investigates this question by comparing probability and impact judgments on the same experimental materials. The results indicate that impact judgments are more consistent in time and more accurate than (...) probability judgments. Impact judgments also predict the direction of errors in probability judgments. These findings suggest that human inductive reasoning relies more on estimating evidential impact than on posterior probability. (shrink)

Mercier & Sperber (M&S) claim that the phenomenon of belief bias provides fundamental support for their argumentative theory and its basis in intuitive judgement. We propose that chronometric evidence necessitates a more nuanced account of belief bias that is not readily captured by argumentative theory.

Oaksford & Chater (O&C) focus on patterns of typical adult reasoning from a probabilistic perspective. We discuss implications of extending the probabilistic approach to lifespan development, considering the role of working memory, strategy use, and expertise. Explaining variations in human reasoning poses a challenge to Bayesian rational analysis, as it requires integrating knowledge about cognitive processes.

Several of Beller, Bender, and Medin’s (2012) issues are as relevant within cognitive science as between it and anthropology. Knowledge-rich human mental processes impose hermeneutic tasks, both on subjects and researchers. Psychology's current philosophy of science is ill suited to analyzing these: Its demand for ‘‘stimulus control’’ needs to give way to ‘‘negotiation of mutual interpretation.’’ Cognitive science has ways to address these issues, as does anthropology. An example from my own work is about how defeasible logics are mathematical models (...) of some aspects of simple hermeneutic processes. They explain processing relative to databases of knowledge and belief—that is, content. A specific example is syllogistic reasoning, which raises issues of experimenters’ interpretations of subjects’ reasoning. Science, especially since the advent of understandings of computation, does not have to be reductive. How does this approach transfer onto anthropological topics? Recent cognitive science approaches to anthropological topics have taken a reductive stance in terms of modules. We end with some speculations about a different cognitive approach to, for example, religion. (shrink)

Oaksford & Chater (O&C) advocate Bayesian probability as a way to deal formally with the pervasive nonmonotonicity of common sense reasoning. We show that some forms of nonmonotonicity cannot be treated by Bayesian methods.

In this paper I am concerned with the question of whether degrees of belief can figure in reasoning processes that are executed by humans. It is generally accepted that outright beliefs and intentions can be part of reasoning processes, but the role of degrees of belief remains unclear. The literature on subjective Bayesianism, which seems to be the natural place to look for discussions of the role of degrees of belief in reasoning, does not address the question of whether degrees (...) of belief play a role in real agents’ reasoning processes. On the other hand, the philosophical literature on reasoning, which relies much less heavily on idealizing assumptions about reasoners than Bayesianism, is almost exclusively concerned with outright belief. One possible explanation for why no philosopher has yet developed an account of reasoning with degrees of belief is that reasoning with degrees of belief is not possible for humans. In this paper, I will consider three arguments for this claim. I will show why these arguments are flawed, and conclude that, at least as far as these arguments are concerned, it seems like there is no good reason why the topic of reasoning with degrees of belief has received so little attention. (shrink)

Conditionals somehow express conditional beliefs. However, conditional belief is a bi-propositional attitude that is generally not truth-evaluable, in contrast to unconditional belief. Therefore, this article opts for an expressivistic semantics for conditionals, grounds this semantics in the arguably most adequate account of conditional belief, that is, ranking theory, and dismisses probability theory for that purpose, because probabilities cannot represent belief. Various expressive options are then explained in terms of ranking theory, with the intention to set out a general interpretive scheme (...) that is able to account for the most variegated usage of conditionals. The Ramsey test is only the first option. Relevance is another, familiar, but little understood item, which comes in several versions. This article adds a further family of expressive options, which is able to subsume also counterfactuals and causal conditionals, and indicates at the end how this family allows for partial recovery of truth conditions for conditionals. (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)

Judea Pearl won the 2010 Rumelhart Prize in computational cognitive science due to his seminal contributions to the development of Bayes nets and causal Bayes nets, frameworks that are central to multiple domains of the computational study of mind. At the heart of the causal Bayes nets formalism is the notion of a counterfactual, a representation of something false or nonexistent. Pearl refers to Bayes nets as oracles for intervention, and interventions can tell us what the effect of action will (...) be or what the effect of counterfactual possibilities would be. Counterfactuals turn out to be necessary to understand thought, perception, and language. This selection of papers tells us why, sometimes in ways that support the Bayes net framework and sometimes in ways that challenge it. (shrink)

The main goal of this paper is to investigate what explanatory resources Robert Brandom’s distinction between acknowledged and consequential commitments affords in relation to the problem of logical omniscience. With this distinction the importance of the doxastic perspective under consideration for the relationship between logic and norms of reasoning is emphasized, and it becomes possible to handle a number of problematic cases discussed in the literature without thereby incurring a commitment to revisionism about logic. One such case in particular is (...) the preface paradox, which will receive an extensive treatment. As we shall see, the problem of logical omniscience not only arises within theories based on deductive logic; but also within the recent paradigm shift in psychology of reasoning. So dealing with this problem is important not only for philosophical purposes but also from a psychological perspective. (shrink)

Ranking theory is a formal epistemology that has been developed in over 600 pages in Spohn's recent book The Laws of Belief, which aims to provide a normative account of the dynamics of beliefs that presents an alternative to current probabilistic approaches. It has long been received in the AI community, but it has not yet found application in experimental psychology. The purpose of this paper is to derive clear, quantitative predictions by exploiting a parallel between ranking theory and a (...) statistical model called logistic regression. This approach is illustrated by the development of a model for the conditional inference task using Spohn's ranking theoretic approach to conditionals. (shrink)

This paper examines precursors and consequents of perceived relevance of a proposition A for a proposition C. In Experiment 1, we test Spohn's assumption that ∆P = P − P is a good predictor of ratings of perceived relevance and reason relations, and we examine whether it is a better predictor than the difference measure − P). In Experiment 2, we examine the effects of relevance on probabilistic coherence in Cruz, Baratgin, Oaksford, and Over's uncertain “and-to-if” inferences. The results suggest (...) that ∆P predicts perceived relevance and reason relations better than the difference measure and that participants are either less probabilistically coherent in “and-to-if” inferences than initially assumed or that they do not follow P = P. Results are discussed in light of recent results suggesting that the Equation may not hold under conditions of irrelevance or negative relevance. (shrink)

Suppose that two competing norms, N1 and N2, can be identified such that a given person’s response can be interpreted as correct according to N1 but incorrect according to N2. Which of these two norms, if any, should one use to interpret such a response? In this paper we seek to address this fundamental problem by studying individual variation in the interpretation of conditionals by establishing individual profiles of the participants based on their case judgments and reflective attitudes. To investigate (...) the participants’ reflective attitudes we introduce a new experimental paradigm called the Scorekeeping Task. As a case study, we identify the participants who follow the Suppositional Theory of conditionals (N1) versus Inferentialism (N2) and investigate to what extent internally consistent competence models can be reconstructed for the participants on this basis. After extensive empirical investigations, an apparent reasoning error with and-to-if inferences was found in one of these two groups. The implications of this case study for debates on the proper role of normative considerations in psychology are discussed. (shrink)

Recent studies indicate that indicative conditionals like "If people wear masks, the spread of Covid-19 will be diminished" require a probabilistic dependency between their antecedents and consequents to be acceptable (Skovgaard-Olsen et al., 2016). But it is easy to make the slip from this claim to the thesis that indicative conditionals are acceptable only if this probabilistic dependency results from a causal relation between antecedent and consequent. According to Pearl (2009), understanding a causal relation involves multiple, hierarchically organized conceptual dimensions: (...) prediction, intervention, and counterfactual dependence. In a series of experiments, we test the hypothesis that these conceptual dimensions are differentially encoded in indicative and counterfactual conditionals. If this hypothesis holds, then there are limits as to how much of a causal relation is captured by indicative conditionals alone. Our results show that the acceptance of indicative and counterfactual conditionals can become dissociated. Furthermore, it is found that the acceptance of both is needed for accepting a causal relation between two co-occurring events. The implications that these findings have for the hypothesis above, and for recent debates at the intersection of the psychology of reasoning and causal judgment, are critically discussed. Our findings are consistent with viewing indicative conditionals as answering predictive queries requiring evidential relevance (even in the absence of direct causal relations). Counterfactual conditionals in contrast target causal relevance, specifically. Finally, we discuss the implications our results have for the yet unsolved question of how reasoners succeed in constructing causal models from verbal descriptions. (shrink)

The extent to which human learning should be thought of in terms of elementary, automatic versus controlled, cognitive processes is unresolved after nearly a century of often fierce debate. Mitchell et al. provide a persuasive review of evidence against automatic, unconscious links. Indeed, unconscious processes seem to play a negligible role in any form of learning, not just in Pavlovian conditioning. But a modern connectionist framework, in which phenomena are emergent properties, is likely to offer a fuller account of human (...) learning than the propositional framework Mitchell et al. propose. (shrink)

According to the weak version of linguistic relativity, also called the Sapir-Whorf hypothesis, the features of an individual’s native language influence his worldview and perception. We decided to test this hypothesis on the sufficient conditional and the necessary conditional, expressed differently in Chinese and French. In Chinese, connectors for both conditionals exist and are used in everyday life, while there is only a connector for the sufficient conditional in French. A first hypothesis follows from linguistic relativity: for the necessary conditional, (...) better logic performance is expected in Chinese participants rather than French participants. As a second hypothesis, for all participants, we expect performance on the sufficient conditional to be better than on the necessary conditional. Indeed, despite the isomorphism of the two conditionals, they differ in how information is processed for reasoning. We decided to study reasoning under uncertainty as it reflects reality more accurately. To do so, we analyzed the coherence of participants using de Finetti’s theory for deduction under uncertainty. The results of our study show no significant difference in performance between Chinese and French participants, neither on the sufficient conditional nor on the necessary conditional. Thus, our first hypothesis derived from the weak version of linguistic relativity is not confirmed. In contrast, our results confirm the second hypothesis in two out of three inference schemas. (shrink)

Although I agree with Elqayam & Evans' (E&E's) criticisms of is-ought and ought-is fallacies, I criticize their rejection of normativism on two grounds: (1) Contrary to E&E's assumption, not every normative system of reasoning consists of formal rules. (2) E&E assume that norms of reasoning are grounded on intuition or authority, whereas in contemporary epistemology they have to be justified, primarily by their truth-conduciveness.

Algorithmic-level specifications carry part of the explanatory burden in most psychological theories. It is, thus, inappropriate to limit a comparison and evaluation of theories to the computational level. A rational analysis considers people's goal-directed and environmentally adaptive rationality; it is not normative. Adaptive rationality is by definition non-absolute; hence, neither deductive logic nor Bayesian probability theory has absolute normative status.

We provide a new link between deductive and probabilistic reasoning fallacies. Illusory inferences from disjunction are a broad class of deductive fallacies traditionally explained by recourse to a matching procedure that looks for content overlap between premises. In two behavioral experiments, we show that this phenomenon is instead sensitive to real-world causal dependencies and not to exact content overlap. A group of participants rated the strength of the causal dependence between pairs of sentences. This measure is a near perfect predictor (...) of fallacious reasoning by an independent group of participants in illusory inference tasks with the same materials. In light of these results, we argue that all extant accounts of these deductive fallacies require non-trivial adjustments. Crucially, these novel _indirect_ illusory inferences from disjunction bear a structural similarity to seemingly unrelated _probabilistic reasoning_ problems, in particular the conjunction fallacy from the heuristics and biases literature. This structural connection was entirely obscure in previous work on these deductive problems, due to the theoretical and empirical focus on content overlap. We argue that this structural parallelism provides arguments against the need for rich descriptions and individuating information in the conjunction fallacy, and we outline a unified theory of deductive illusory inferences from disjunction and the conjunction fallacy, in terms of Bayesian confirmation theory. (shrink)

During the last decades, the psychology of reasoning has identified experimentally many fallacies committed by spontaneous reasoners. Given these experimental results, some theories have been developed about this phenomenon, mainly algorithmic theories. This paper develops instead a computational modelling of these current fallacies which appear as simplifications in the treatment of information that do not respect the formal rules of classical propositional logic. These fallacies are explained as crushes in the Klein group structure and so, in squares of opposition. These (...) crushes are an effect of not to take into account the dual of the binary operator at work in the major premise of the inference. This analysis allows predictions on fallacies not identified before, which are fallacies produced when reasoning with incompatibilities. The paper concludes with consequences of the analysis on pedagogical strategies for the teaching of logic. (shrink)

According to Stalnaker’s Thesis, the probability of a conditional is the conditional probability. Under some mild conditions, the thesis trivialises probabilities and conditionals, as initially shown by David Lewis. This article asks the following question: does still lead to triviality, if the probability function in is replaced by a probability-like function? The article considers plausibility functions, in the sense of Friedman and Halpern, which additionally mimic probabilistic additivity and conditionalisation. These quasi probabilities comprise Friedman–Halpern’s conditional plausibility spaces, as well as (...) other known representations of conditional doxastic states. The paper proves Lewis’ triviality for quasi probabilities and discusses how this has implications for three other prominent strategies to avoid Lewis’ triviality: Adams’ thesis, where the probability function on the left in is replaced by a probability-like function, abandoning conditionalisation, where probability conditionalisation on the right in is replaced by another propositional update procedure and the approximation thesis, where equality in is replaced by approximation. The paper also shows that Lewis’ triviality result is really about ‘additiveness’ and ‘conditionality’. (shrink)

The knowledge representation and reasoning of both humans and artificial systems often involves conditionals. A conditional connects a consequence which holds given a precondition. It can be easily recognized in natural languages with certain key words, like “if” in English. A vast amount of literature in both fields, both artificial intelligence and psychology, deals with the questions of how such conditionals can be best represented and how these conditionals can model human reasoning. On the other hand, findings in the psychology (...) of reasoning, such as those in the Suppression Task, have led to a paradigm shift from the monotonicity assumptions in human inferences towards nonmonotonic reasoning. Nonmonotonic reasoning is sensitive for information change, that is, inferences are drawn cautiously such that retraction of previous information is not required with the addition of new information. While many formalisms of nonmonotonic reasoning have been proposed in the field of Artificial Intelligence, their capability to model properties of human reasoning has not yet been extensively investigated. In this paper, we analyzed systematically from both a formal and an empirical perspective the power of formal nonmonotonic systems to model possible explicit defeaters, as in the Suppression Task, and more implicit conditional rules that trigger nonmonotonic reasoning by the keywords in such rules. The results indicated that the classical evaluation for the correctness of inferences has to be extended in the three major aspects regarding the inference system, the knowledge base, and possible assumed exceptions for the rule. (shrink)