For most of its history, the psychology of reasoning was dominated by binary extensional logic. The so-called “new paradigm” instead puts subjective degrees of belief center stage, often represented as probabilities. We argue that the “new paradigm” is too vaguely defined and therefore does not allow a clear decision about what falls within its scope and what does not. We also show that there was not one settled theoretical “old” paradigm, before the new developments emerged, and that the alleged new (...) paradigm is less revolutionary as the term suggests. A more veridical view is that current progress is developing in continuities where rival research programs can thrive or fail in the face of new experimental findings. The article closes with some topics where more connections between competing research programs are likely to promote progress in our understanding of human reasoning. (shrink)

Peter Wason provided his four-card selection task over five decades ago. It keeps causing difficulties from both the linguistic, the psychological, and the cognitive point of view. Many psychology theories have been proposed in order to remove its problems. This paper tries to offer one more possible account. That account is based on the method of extension and intension presented by Rudolf Carnap. Hence, it resorts to the concept of state-description. The basic ideas of the argumentation are two: 1) people (...) might tend to consider state-descriptions when processing information, and 2) if conditionals are not expressed with a clear contextual framework, they might be interpreted as biconditionals. (shrink)

Two notions from philosophical logic and linguistics are brought together and applied to the psychological study of defeasible conditional reasoning. The distinction between disabling conditions and alternative causes is shown to be a special case of Pollock’s (1987) distinction between ‘rebutting’ and ‘undercutting’ defeaters. ‘Inferential’ conditionals are shown to come in two varieties, one that is sensitive to rebutters, the other to undercutters. It is thus predicted and demonstrated in two experiments that the type of inferential conditional used as the (...) major premise of conditional arguments can reverse the heretofore classic, distinctive effects of defeaters. (shrink)

I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...) collapsing filter on the standard model) match with many intuitions underlying Wittgensteins philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any meaningful mathematical question. (shrink)

People can reason about the preferences of other agents, and predict their behavior based on these preferences. Surprisingly, the psychology of reasoning has long neglected this fact, and focused instead on disinterested inferences, of which preferences are neither an input nor an output. This exclusive focus is untenable, though, as there is mounting evidence that reasoners take into account the preferences of others, at the expense of logic when logic and preferences point to different conclusions. This article summarizes the most (...) recent account of how reasoners predict the behavior and attitude of other agents based on conditional rules describing actions and their consequences, and reports new experimental data about which assumptions reasoners retract when their predictions based on preferences turn out to be false. (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)

This is a position paper concerning the role of empirical studies of human default reasoning in the formalization of AI theories of default reasoning. We note that AI motivates its theoretical enterprise by reference to human skill at default reasoning, but that the actual research does not make any use of this sort of information and instead relies on intuitions of individual investigators. We discuss two reasons theorists might not consider human performance relevant to formalizing default reasoning: (a) that intuitions (...) are sufficient to describe a model, and (b) that human performance in this arena is irrelevant to a competence model of the phenomenon. We provide arguments against both these reasons. We then bring forward three further considerations against the use of intuitions in this arena: (a) it leads to an unawareness of predicate ambiguity, (b) it presumes an understanding of ordinary language statements of typicality, and (c) it is similar to discredited views in other fields. We advocate empirical investigation of the range of human phenomena that intuitively embody default reasoning. Gathering such information would provide data with which to generate formal default theories and against which to test the claims of proposed theories. Our position is that such data are the very phenomena that default theories are supposed to explain. (shrink)

When reasoning about deontic rules (what one may, should, or should not do in a given set of circumstances), reasoners adopt a violation‐detection strategy, a strategy they do not adopt when reasoning about indicative rules (descriptions of purported state of affairs). I argue that this indicative‐deontic distinction constitutes a primitive in the cognitive architecture. To support this claim, I show that this distinction emerges early in development, is observed regardless of the cultural background of the reasoner, and can be selectively (...) disrupted at the neurological level. I also argue that this distinction emerged as a result of selective pressure favouring the evolution of reasoning strategies that determine survival within dominance hierarchies. (shrink)

We examine two competing effects of beliefs on conditional inferences. The suppression effect occurs for conditionals, for example, “if she watered the plants they bloomed,” when beliefs about additional background conditions, for example, “if the sun shone they bloomed” decrease the frequency of inferences such as modus tollens (from “the plants did not bloom” to “therefore she did not water them”). In contrast, the counterfactual elevation effect occurs for counterfactual conditionals, for example, “if she had watered the plants they would (...) have bloomed,” when beliefs about the known or presupposed facts, “she did not water the plants and they did not bloom” increase the frequency of inferences such as modus tollens. We report six experiments that show that beliefs about additional conditions take precedence over beliefs about presupposed facts for counterfactuals. The modus tollens inference is suppressed for counterfactuals that contain additional conditions (Experiments 1a and 1b). The denial of the antecedent inference (from “she did not water the plants” to “therefore they did not bloom”) is suppressed for counterfactuals that contain alternatives (Experiments 2a and 2b). We report a new “switched‐suppression” effect for conditionals with negated components, for example, “if she had not watered the plants they would not have bloomed”: modus tollens is suppressed by alternatives and denial of the antecedent by additional conditions, rather than vice versa (Experiments 3a and 3b). We discuss the implications of the results for alternative theories of conditional reasoning. (shrink)

This reply to Oaksford and Chater’s ’s critical discussion of our use of logic programming to model and predict patterns of conditional reasoning will frame the dispute in terms of the semantics of the conditional. We begin by outlining some common features of LP and probabilistic conditionals in knowledge-rich reasoning over long-term memory knowledge bases. For both, context determines causal strength; there are inferences from the absence of certain evidence; and both have analogues of the Ramsey test. Some current work (...) shows how a combination of counting defeaters and statistics from network monitoring can provide the information for graded responses from LP reasoning. With this much introduction, we then respond to O&C’s specific criticisms and misunderstandings. (shrink)

Cognitive relativists‐pragmatists (Stich, Churchland) claim that human cognitive strategies, lacking a common goal, are in addition divergent to the point of incommensurability. They appeal to the study of reasoning heuristics for evidence on cognitive diversity and incorrigibility. It is here argued that no such evidence is offered by the research, which, on the contrary (1) presents heuristics as uniform across great variations; (2) offers advice for correcting and improving human reasoning; and (3) very often postulates a uniformity of core logical (...) strategies, built into reasoning competence. Cognitive research thus supports a moderate rationalism rather than relativism‐pragmatism. (shrink)

The suppression of the Modus Ponens inference is described as a loss of confidence in the conclusion C of an argument ''If A1 then C; If A2 then C; A1'' where A2 is a requirement for C to happen. It is hypothesised that this loss of confidence is due to the derivation of the conversational implicature ''there is a chance that A2 might not be satisfied'', and that different syntactic introductions of the requirement A2 (e.g., ''If C then A2'') will (...) lead to various frequencies in the derivation of this implicature, according to previous studies in the field of causal explanation. An experiment is conducted, whose results support those claims. Results are discussed in the light of the Mental Logic and Mental Model theories, as well as in the light of the pragmatic approach to uncertain reasoning. (shrink)

Reasoning about social groups and their associated markers was investigated as a particular case of human reasoning about cue-category relationships. Assertions that reasoning involving cues and associated categories elicits specific probabilistic assumptions are supported by the results of three experiments. This phenomenon remains intact across the use of categorical syllogisms, conditional syllogisms, and the use of social groups that vary in their perceived cohesiveness, or entitativity. Implications are discussed for various theories of reasoning, and additional aspects of social group/coalitional reasoning (...) are also discussed. (shrink)

The term "non-monotonic logic" covers a family of formal frameworks devised to capture and represent defeasible inference , i.e., that kind of inference of everyday life in which reasoners draw conclusions tentatively, reserving the right to retract them in the light of further information. Such inferences are called "non-monotonic" because the set of conclusions warranted on the basis of a given knowledge base does not increase (in fact, it can shrink) with the size of the knowledge base itself. This is (...) in contrast to classical (first-order) logic, whose inferences, being deductively valid, can never be "undone" by new information. (shrink)

Rational analysis (Anderson 1990, 1991a) is an empiricalprogram of attempting to explain why the cognitive system isadaptive, with respect to its goals and the structure of itsenvironment. We argue that rational analysis has two importantimplications for philosophical debate concerning rationality. First,rational analysis provides a model for the relationship betweenformal principles of rationality (such as probability or decisiontheory) and everyday rationality, in the sense of successfulthought and action in daily life. Second, applying the program ofrational analysis to research on human reasoning (...) leads to a radicalreinterpretation of empirical results which are typically viewed asdemonstrating human irrationality. (shrink)

An organizing theme of the dissertation is the issue of how to make philosophical theories useful for scientific purposes. An argument for the contention is presented that it doesn’t suffice merely to theoretically motivate one’s theories, and make them compatible with existing data, but that philosophers having this aim should ideally contribute to identifying unique and hard to vary predictions of their theories. This methodological recommendation is applied to the ranking-theoretic approach to conditionals, which emphasizes the epistemic relevance and the (...) expression of reason relations as part of the semantics of the natural language conditional. As a first step, this approach is theoretically motivated in a comparative discussion of other alternatives in psychology of reasoning, like the suppositional theory of conditionals, and novel approaches to the problems of compositionality and accounting for the objective purport of indicative conditionals are presented. In a second step, a formal model is formulated, which allows us to derive quantitative predictions from the ranking-theoretic approach, and it is investigated which novel avenues of empirical research that this model opens up for. Finally, a treatment is given of the problem of logical omniscience as it concerns the issue of whether ranking theory (and other similar approaches) makes too idealized assumptions about rationality to allow for interesting applications in psychology of reasoning. Building on the work of Robert Brandom, a novel solution to this problem is presented, which both opens up for new perspectives in psychology of reasoning and appears to be capable of satisfying a range of constraints on bridge principles between logic and norms of reasoning, which would otherwise stand in a tension. (shrink)

Previous studies have shown that 1 participants are reluctant to accept a conclusion as certainly true when it is derived from a valid conditional argument that includes a doubtful premise, and 2 participants typically link the degree of uncertainty found in a given premise set to its conclusion. Two experiments were designed to further investigate these phenomena. Ninety adult participants in Experiment 1 were first asked to judge the validity of three conditional arguments Modus Ponens, Denial of the Antecedent, and (...) Affirmation of the Consequent . They were then required to evaluate conclusion uncertainty as a function of two degrees of asserted uncertainty in the major conditional premise If p then it is very probable that q and if p then it is not very probable that q of the arguments from the first task that were otherwise unchanged. Results revealed an effect for asserted-uncertainty in two of the three argument forms. Marginal support was found for the hypothesis that perceived argument validity would be a predictor of performance. Experiment 2 investigated the way 40 adult participants combined two sources of asserted uncertainty, one in the major premise and another in the minor premise, when they had to score the uncertainty of the conclusion. The two most prominent kinds of responses were to choose the same likelihood as the weaker of the two expressed in the premises, or a lower one. However, the within-subject consistency was poor. Theoretical implications are discussed. (shrink)

The explanation of the suppression of Modus Ponens inferences within the framework of linguistic pragmatics and of plausible reasoning (i.e., deduction from uncertain premises) is defended. First, this approach is expounded, and then it is shown that the results of the first experiment of Byrne, Espino, and Santamar a (1999) support the uncertainty explanation but fail to support their counterexample explanation. Second, two experiments are presented. In the first one, aimed to refute one objection regarding the conclusions observed, the additional (...) conditional premise ( if N, C ) was replaced with a statement of uncertainty ( it is not certain that N ); the answers produced by the participants remained qualitatively and quantitatively similar in both conditions. In the second experiment, a fine-grained analysis of the responses to and justifications for an evaluation task was performed. The results of both experiments strongly supported the uncertainty explanation. (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)

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)

Two notions from philosophical logic and linguistics are brought together and applied to the psychological study of defeasible conditional reasoning. The distinction between disabling conditions and alternative causes is shown to be a special case of Pollock’s (1987) distinction between ‘rebutting’ and ‘undercutting’ defeaters. ‘Inferential’ conditionals are shown to come in two varieties, one that is sensitive to rebutters, the other to undercutters. It is thus predicted and demonstrated in two experiments that the type of inferential conditional used as the (...) major premise of conditional arguments can reverse the heretofore classic, distinctive effects of defeaters. (shrink)

Byrne has demonstrated that although subjects can make deductively valid inferences of the modus ponens and modus tollens forms, these valid inferences can be suppressed by presenting an appropriate additional premise “If R then Q” with the original conditional “If P then Q”. This suppression effect challenges the assumption of all syntactic theories of conditional reasoning that formal rules of inference such as modus ponens is part of mental logic. This paper argues that both the syntactic and the mental model (...) accounts of the suppression effect are inadequate because they fail to give a principled account of the critical interpretive component involved in reasoning. In contrast, the relative salience model proposed in this study emphasized the centrality of the interpretative processes with the critical component being the relative salience of premises as judged by subjects on the basis of their prior knowledge activated in particular problem situations. Using 120 undergraduates and 120 policemen as subjects, predictions from the model were tested and confirmed in a suppression paradigm and evidence of convergent validity for the construct of salience were obtained. The results cannot be reconciled with either the syntactic view or the mental model view that have dominated theories of conditional reasoning. (shrink)

(2013). Statistical models as cognitive models of individual differences in reasoning. Argument & Computation: Vol. 4, Formal Models of Reasoning in Cognitive Psychology, pp. 89-102. doi: 10.1080/19462166.2012.674061.