Conditional inferences can be phrased with unspecific terms (“If a person is on a diet, then the person loses weight. A person is on a diet. The person loses weight”) or specific terms (“If Anna is on a diet, then Anna loses weight. Anna is on a diet. Anna loses weight”). We investigate whether the specificity of terms affects people's acceptance of inferences. In Experiment 1, inferences with specific terms received higher acceptance ratings than inferences with unspecific terms. In Experiments (...) 2 and 3, we used the same problems as in Experiment 1 but also problems with unspecific terms in the conditional and specific terms in the categorical and vice versa. When the conditional and the categorical had the same specificity, results were as in Experiment 1. When the specificity of the conditional and the categorical mismatched, acceptance ratings were lower. Our results illustrate the importance of phrasing on reasoning. (shrink)

People accept conclusions of valid conditional inferences (e.g., if p then q, p therefore q) less, the more disablers (circumstances that prevent q to happen although p is true) exist. We investigated whether rules that through their phrasing exclude disablers evoke higher acceptance ratings than rules that do not exclude disablers. In three experiments we re-phrased content-rich conditionals from the literature as either universal or existential rules and embedded these rules in Modus Ponens and Modus Tollens inferences. In Experiments 2 (...) and 3, we also used abstract rules. The acceptance of conclusions increased when the rule was phrased with “all” instead of “some” and the number of disablers had a higher impact on existential rules than on universal rules. Further, the effect of quantifier was more pronounced for abstract rules and when tested within subjects. We discuss the relevance of phrasing, quantifiers and knowledge on reasoning. (shrink)

In defeasible reasoning, initially drawn conclusions can be withdrawn in light of new information. In this paper, we examine how the conclusions drawn from conditionals describing positive or negative situations can be defeated by subsequent negative or positive information, respectively. Participants were confronted with conditionals of the form “If [situation], then I am happy/sad” which were either followed by no additional information or by additional information describing situations of the same or the opposite valence. The participant's task was to decide (...) on a question asking for a possible conclusion (“Am I happy?” vs. “Am I sad?”). We found a negativity bias in defeasible reasoning: negative information defeated positively charged conclusions more strongly than positive information defeated negatively charged conclusions. We discuss our results in relation to the new psychology of reasoning. (shrink)

Probabilistic theories of reasoning assume that people use their prior knowledge to estimate the conditional probability of q given p and that this probability predicts the acceptance of modus ponens inferences. But how do people reason with unfamiliar conditionals for which they do not have prior knowledge? Reasoning without prior knowledge has been extensively investigated in experiments in which participants were instructed to reason deductively. But it is still not clear how people reason with unfamiliar conditionals when they are instructed (...) to reason as in daily life. Can probabilities also predict reasoning with unfamiliar content? In two experiments we instructed participants to reason as in everyday life and to evaluate conclusions from familiar and unfamiliar conditionals. Results showed that reasoning with familiar conditionals can be predicted by the conditional probability. For unfamiliar conditionals, however, this was not the case. Conclusions from unfamiliar conditionals were accepted more strongly than what could be expected according to their conditional probability. Our findings challenge probabilistic theories of reasoning and suggest that other approaches, such as a dual-strategy model, describe our results more adequately. (shrink)

Argumentation as the public exchange of reasons is widely thought to enhance deliberative interactions that generate and justify reasonable public policies. Adopting an argumentation-theoretic perspective, we survey the norms that should govern public argumentation and address some of the complexities that scholarly treatments have identified. Our focus is on norms associated with the ideals of correctness and participation as sources of a politically legitimate deliberative outcome. In principle, both ideals are mutually coherent. If the information needed for a correct deliberative (...) outcome is distributed among agents, then maximising participation increases information diversity. But both ideals can also be in tension. If participants lack competence or are prone to biases, a correct deliberative outcome requires limiting participation. The central question for public argumentation, therefore, is how to strike a balance between both ideals. Rather than advocating a preferred normative framework, our main purpose is to illustrate the complexity of this theme. (shrink)

The aim of the article is to develop precise epistemic rules for good public political arguments, by which political measures in the broad sense are justified. By means of a theory of deliberative democracy, it is substantiated that the justification of a political measure consists in showing argumentatively that this measure most promotes the common good or is morally optimal. It is then discussed which argumentation-theoretical approaches are suitable for providing epistemically sound rules for arguments for such theses and for (...) the associated premises, rules whose compliance implies the truth or acceptability of the thesis. Finally, on the basis of the most suitable approach, namely the epistemological one, such systems of rules for the required types of arguments are presented that fulfil the conditions mentioned. (shrink)

Iterated conditionals of the form If p, then if q, r are an important topic in philosophical logic. In recent years, psychologists have gained much knowledge about how people understand simple conditionals, but there are virtually no published psychological studies of iterated conditionals. This paper presents experimental evidence from a study comparing the iterated form, If p, then if q, r with the “imported,” noniterated form, If p and q, then r, using a probability evaluation task and a truth-table task, (...) and taking into account qualitative individual differences. This allows us to critically contrast philosophical and psychological approaches that make diverging predictions regarding the interpretation of these forms. The results strongly support the probabilistic Adams conditional and the “new paradigm” that takes this conditional as a starting point. (shrink)

Iterated conditionals of the form If p, then if q, r are an important topic in philosophical logic. In recent years, psychologists have gained much knowledge about how people understand simple conditionals, but there are virtually no published psychological studies of iterated conditionals. This paper presents experimental evidence from a study comparing the iterated form, If p, then if q, r with the “imported,” noniterated form, If p and q, then r, using a probability evaluation task and a truth‐table task, (...) and taking into account qualitative individual differences. This allows us to critically contrast philosophical and psychological approaches that make diverging predictions regarding the interpretation of these forms. The results strongly support the probabilistic Adams conditional and the “new paradigm” that takes this conditional as a starting point. (shrink)

In two experiments we tested the hypothesis that the mechanisms that produce belief bias generalise across reasoning tasks. In formal reasoning (i.e., syllogisms) judgements of validity are influenced by actual validity, believability of the conclusions, and an interaction between the two. Although apparently analogous effects of belief and argument strength have been observed in informal reasoning, the design of those studies does not permit an analysis of the interaction effect. In the present studies we redesigned two informal reasoning tasks: the (...) Argument Evaluation Task (AET) and a Law of Large Numbers (LLN) task in order to test the similarity of the phenomena concerned. Our findings provide little support for the idea that belief bias on formal and informal reasoning is a unitary phenomenon. First, there was no correlation across individuals in the extent of belief bias shown on the three tasks. Second, evidence for belief by strength interaction was observed only on AET and under conditions not required for the comparable finding on syllogistic reasoning. Finally, we found that while conclusion believability strongly influenced assessments of arguments strength, it had a relatively weak influence on the verbal justifications offered on the two informal reasoning tasks. (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)

The aim is to motivate theoretically a relevance approach to conditionals in a comparative discussion of the main alternatives. In particular, it will be argued that a relevance approach to conditionals is better motivated than the suppositional theory currently enjoying wide endorsement. In the course of this discussion, an argument will be presented for why failures of the epistemic relevance of the antecedent for the consequent should be counted as genuine semantic defects. Furthermore, strategies for dealing with compositionality and the (...) perceived objective purport of indicative conditionals will be put forward. (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)

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)

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

ABSTRACTThe new paradigm in the psychology of reasoning redirects the investigation of deduction conceptually and methodologically because the premises and the conclusion of the inferences are assumed to be uncertain. A probabilistic counterpart of the concept of logical validity and a method to assess whether individuals comply with it must be defined. Conceptually, we used de Finetti's coherence as a normative framework to assess individuals' performance. Methodologically, we presented inference schemas whose premises had various levels of probability that contained non-numerical (...) expressions and, as a control, sure levels. Depending on the inference schemas, from 60% to 80% of the participants produced coherent conclusions when the premises were uncertain. The data also show that except for schemas involving conjunction, performance was consistently lower with certain than uncertain premises, the rate of conjunction fallacy was consistently low (not exceeding 20%,.. (shrink)

This position paper advocates combining formal epistemology and the new paradigm psychology of reasoning in the studies of conditionals and reasoning with uncertainty. The new paradigm psychology of reasoning is characterized by the use of probability theory as a rationality framework instead of classical logic, used by more traditional approaches to the psychology of reasoning. This paper presents a new interdisciplinary research program which involves both formal and experimental work. To illustrate the program, the paper discusses recent work on the (...) paradoxes of the material conditional, nonmonotonic reasoning, and Adams’ Thesis. It also identifies the issue of updating on conditionals as an area which seems to call for a combined formal and empirical approach. (shrink)

We present a unified approach for investigating rational reasoning about basic argument forms involving indicative conditionals, counterfactuals, and basic quantified statements within coherence-based probability logic. After introducing the rationality framework, we present an interactive view on the relation between normative and empirical work. Then, we report a new experiment which shows that people interpret indicative conditionals and counterfactuals by coherent conditional probability assertions and negate conditionals by negating their consequents. The data support the conditional probability interpretation of conditionals and the (...) narrow-scope reading of the negation of conditionals. Finally, we argue that coherent conditional probabilities are important for probabilistic analyses of conditionals, nonmonotonic reasoning, quantified statements, and paradoxes. (shrink)

ABSTRACTTreating conditionals as probabilistic statements has been referred to as a defining feature of the “new paradigm” in cognitive psychology. Doing so is attractive for several reasons, but it complicates the problem of assessing the merits of conditional arguments. We consider several variables that relate to judging the persuasiveness of conditional arguments with uncertain premises. We also explore ways of judging the consistency of people's beliefs as represented by components of conditional arguments. Experimental results provide evidence that inconsistencies in beliefs (...) are more prevalent if the arguments’ components are spatially and temporally dispersed than if they are contiguous in space and time. This supports the idea that assuring the consistency among even a small number of beliefs is difficult to do, especially if the beliefs in question are not brought into consciousness at the same time; but consistency can be enhanced when beliefs are considered simultaneously or nea... (shrink)

An experiment was conducted to test the effectiveness of brief instruction in information structuring (i.e., representing and integrating information) for improving the coherence of probability judgments and binary choices among intelligence analysts. Forty-three analysts were presented with comparable sets of Bayesian judgment problems before and immediately after instruction. After instruction, analysts’ probability judgments were more coherent (i.e., more additive and compliant with Bayes theorem). Instruction also improved the coherence of binary choices regarding category membership: after instruction, subjects were more likely (...) to invariably choose the category to which they assigned the higher probability of a target’s membership. The research provides a rare example of evidence-based validation of effectiveness in instruction to improve the statistical assessment skills of intelligence analysts. Such instruction could also be used to improve the assessment quality of other types of experts who are required to integrate statistical information or make probabilistic assessments. (shrink)

This article presents a fundamental advance in the theory of mental models as an explanation of reasoning about facts, possibilities, and probabilities. It postulates that the meanings of compound assertions, such as conditionals (if) and disjunctions (or), unlike those in logic, refer to conjunctions of epistemic possibilities that hold in default of information to the contrary. Various factors such as general knowledge can modulate these interpretations. New information can always override sentential inferences; that is, reasoning in daily life is defeasible (...) (or nonmonotonic). The theory is a dual process one: It distinguishes between intuitive inferences (based on system 1) and deliberative inferences (based on system 2). The article describes a computer implementation of the theory, including its two systems of reasoning, and it shows how the program simulates crucial predictions that evidence corroborates. It concludes with a discussion of how the theory contrasts with those based on logic or on probabilities. (shrink)

We describe a dual-process theory of how individuals estimate the probabilities of unique events, such as Hillary Clinton becoming U.S. President. It postulates that uncertainty is a guide to improbability. In its computer implementation, an intuitive system 1 simulates evidence in mental models and forms analog non-numerical representations of the magnitude of degrees of belief. This system has minimal computational power and combines evidence using a small repertoire of primitive operations. It resolves the uncertainty of divergent evidence for single events, (...) for conjunctions of events, and for inclusive disjunctions of events, by taking a primitive average of non-numerical probabilities. It computes conditional probabilities in a tractable way, treating the given event as evidence that may be relevant to the probability of the dependent event. A deliberative system 2 maps the resulting representations into numerical probabilities. With access to working memory, it carries out arithmetical operations in combining numerical estimates. Experiments corroborated the theory's predictions. Participants concurred in estimates of real possibilities. They violated the complete joint probability distribution in the predicted ways, when they made estimates about conjunctions: P, P, P, disjunctions: P, P, P, and conditional probabilities P, P, P. They were faster to estimate the probabilities of compound propositions when they had already estimated the probabilities of each of their components. We discuss the implications of these results for theories of probabilistic reasoning. (shrink)

ABSTRACTThe probabilistic truth table task involves assessing the probability of "If A then C" conditional sentences. Previous studies have shown that a majority of participants assess this probability as the conditional probability P while a substantial minority responds with the probability of the conjunction A and C. In an experiment involving 96 participants, we investigated the impact on the rate of conjunctive responses of the context in which the task is framed. We show that a context intended to lead participants (...) to consider all the possible cases elicited more conjunctive responses than a context assumed not to have this effect. These results suggest that the step of inferring the probability can distort our assessment of participants' interpretation of conditional sentences. This might compromise the validity of the probabilistic task in studying conditional reasoning. (shrink)

The new paradigm in the psychology of reasoning draws on Bayesian formal frameworks, and some advocates of the new paradigm think of these formal frameworks as providing a computational-level theory of rational human inference. I argue that Bayesian theories should not be seen as providing a computational-level theory of rational human inference, where by “Bayesian theories” I mean theories that claim that all rational credal states are probabilistically coherent and that rational adjustments of degrees of belief in the light of (...) new evidence must be in accordance with some sort of conditionalization. The problems with the view I am criticizing can best be seen when we look at chains of inferences, rather than single-step inferences. Chains of inferences have been neglected almost entirely within the new paradigm. (shrink)

Studies of categorical induction typically examine how belief in a premise (e.g., Falcons have an ulnar artery) projects on to a conclusion (e.g., Robins have an ulnar artery). We study induction in cases in which the premise is uncertain (e.g., There is an 80% chance that falcons have an ulnar artery). Jeffrey's rule is a normative model for updating beliefs in the face of uncertain evidence. In three studies we tested the descriptive validity of Jeffrey's rule and a related probability (...) theorem, the rule of total probability. Although these rules provided good approximations to mean judgments in some cases, the results from regression and correlation analyses suggest that participants focus on the parts of these rules that are associated with the highest overall probability. We relate our findings to rational models of judgment. (shrink)

Given a basic conditional of the form, If A then C, individuals usually list three cases as possible: A and C, not‐A and not‐C, not‐A and C. This result corroborates the theory of mental models. By contrast, individuals often judge that the conditional is true only in the case of A and C, and that cases of not‐A are irrelevant to its truth or falsity. This result corroborates other theories of conditionals. To resolve the discrepancy, we devised two new tasks: (...) the “collective” truth task, in which participants judged whether sets of assertions about a specific individual, such as: If A then C, not‐A, C, could all be true at the same time; and one in which participants judged the truth of conditional predictions about specific future events. The results consistently matched the three possibilities, thereby corroborating the model theory. They also showed a massive violation of the probability calculus in estimates of the probabilities of the four cases in the partition of conditionals (A and C, A and not‐C, not‐A and C, and not‐A and not‐C), which summed to over 200%. (shrink)

Dual-process theories of higher cognition, distinguishing between intuitive (Type 1) and reflective (Type 2) thinking, have become increasingly popular, although also subject to recent criticism. A key question, to which a number of contributions in this special issue relate, is how to define the difference between the two kinds of processing. One issue discussed is whether they differ at Marr’s computational level of analysis. I believe they do but that ultimately the debate will decided at the implementational level where distinct (...) cognitive and neural systems need to be demonstrated. Other distinctions raised in the issue are the unique ability for metarepresentation, cognitive decoupling and hypothetical thinking at the Type 2 level, and the association of emotion and metacognitive feelings with the Type 1 level. The relation of the latter to cognitive control is also discussed. (shrink)

In recent years, the psychology of reasoning has been undergoing a paradigm shift, with general Bayesian, probabilistic approaches replacing the older, much more restricted binary logic paradigm. At the same time, dual processing theories have been gaining influence. We argue that these developments should be integrated and moreover that such integration is already underway. The new reasoning paradigm should be grounded in dual processing for its algorithmic level of analysis just as it uses Bayesian theory for its computational level of (...) analysis. Moreover, we propose that, within the new paradigm, these levels of analysis reflect on each other. Bayesianism suggests a specific theoretical understanding of dual processing. Just as importantly, the duality in processing carries over to duality in function; although both types of processes compute degrees of belief, they generate different functions. (shrink)

We conducted a thorough investigation of the impact of representativeness on reasoning and metacognitive processes by employing the Linda problem. In congruent versions, the more representative res...

Common-sense (or folk) psychology holds that (generally) we do what we do for the reasons we have. This common-sense approach is embodied in claims like ‘I went to the kitchen because I wanted a drink’ and ‘She took a coat because she thought it might rain and hoped to stay dry’. However, the veracity of these common-sense psychological explanations has been challenged by experimental evidence (primarily from behavioural economics and social psychology) which appears to show that individuals are systematically irrational—that (...) often we do not do what we do because of the reasons we have. Recently, some of the same experimental evidence has also been used to level a somewhat different challenge at the common-sense view, arguing that the overarching aim of reasoning is not to deliver better or more reason-governed decisions for individual reasoners, but to improve group decision making or to protect an individual’s sense of self. This paper explores the range of challenges that experimental work has been taken to raise for the common-sense approach and suggests some potential responses. Overall, I argue that the experimental evidence surveyed should not lead us to a rejection of individual rationality. (shrink)

(2013). Formal Models of Reasoning in Cognitive Psychology. Argument & Computation: Vol. 4, Formal Models of Reasoning in Cognitive Psychology, pp. 1-3. doi: 10.1080/19462166.2013.767559.

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)

The new Bayesian paradigm in the psychology of reasoning aims to integrate the study of human reasoning, decision making, and rationality. It is supported by two findings. One, most people judge the probability of the indicative conditional, P(if A then B), to be the conditional probability, P(B|A), as implied by the Ramsey test. Two, they judge if A then B to be void when A is false. Their three-valued response table used to be called ‘defective’, but should be termed the (...) de Finetti table. We show how to study general de Finetti truth tables for negations, conjunctions, disjunctions, and conditionals. (shrink)

Habilitation thesis in psychology. The book consists of a collection of reasoning studies. The experimental investigations will take us from people’s reasoning about probabilities, entailments, pragmatic factors, argumentation, and causality to morality. An overarching theme of the book is norm pluralism and individual differences in rationality research.