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156On imagining what is true (and what is false)Thinking and Reasoning 9 (1). 2003.How do people imagine the possibilities in which an assertion would be true and the possibilities in which it would be false? We argue that the mental representation of the meanings of connectives, such as "and", "or", and "if", specify how to construct the true possibilities for simple assertions containing just a single connective. It follows that the false possibilities are constructed by inference from the true possibilities. We report converging evidence supporting this account from four ex…Read more
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131Peirce, logic diagrams, and the elementary operations of reasoningThinking and Reasoning 8 (1). 2002.This paper describes Peirce's systems of logic diagrams, focusing on the so-called ''existential'' graphs, which are equivalent to the first-order predicate calculus. It analyses their implications for the nature of mental representations, particularly mental models with which they have many characteristics in common. The graphs are intended to be iconic, i.e., to have a structure analogous to the structure of what they represent. They have emergent logical consequences and a single graph can ca…Read more
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129The psychological puzzle of SudokuThinking and Reasoning 14 (4): 342-364. 2008.Sudoku puzzles, which are popular worldwide, require individuals to infer the missing digits in a 9 9 array according to the general rule that every digit from 1 to 9 must occur once in each row, in each column, and in each of the 3-by-3 boxes in the array. We present a theory of how individuals solve these puzzles. It postulates that they rely solely on pure deductions, and that they spontaneously acquire various deductive tactics, which differ in their difficulty depending on their “relational…Read more
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118Logic, Models, and Paradoxical InferencesMind and Language 27 (4): 357-377. 2012.People reject ‘paradoxical’ inferences, such as: Luisa didn't play music; therefore, if Luisa played soccer, then she didn't play music. For some theorists, they are invalid for everyday conditionals, but valid in logic. The theory of mental models implies that they are valid, but unacceptable because the conclusion refers to a possibility inconsistent with the premise. Hence, individuals should accept them if the conclusions refer only to possibilities consistent with the premises: Luisa didn't…Read more
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113The processes of inferenceArgument and Computation 4 (1). 2013.(2013). The processes of inference. Argument & Computation: Vol. 4, Formal Models of Reasoning in Cognitive Psychology, pp. 4-20. doi: 10.1080/19462166.2012.674060.
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112An antidote to illusory inferencesThinking and Reasoning 6 (4). 2000.The mental model theory predicts that reasoners normally represent what is true, but not what is false. One consequence is that reasoners should make "illusory" inferences, which are compelling but invalid. Three experiments confirmed the existence of such illusions based on disjunctions of disjunctions. They also established a successful antidote to them: Reasoners are much less likely to succumb to illusions if the inferences concern disjunctions of physical objects (alternative newspaper adve…Read more
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108Descriptions and discourse modelsLinguistics and Philosophy 3 (3). 1979.This paper argues that mental models of discourse are key in any theory of the interpretation of definite descriptions. It considers both referential and attributive uses of such descriptions, in the sense introduced by Donnellan
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69How falsity dispels fallaciesThinking and Reasoning 12 (2). 2006.From certain sorts of premise, individuals reliably infer invalid conclusions. Two Experiments investigated a possible cause for these illusory inference: Reasoners fail to think about what is false. In Experiment 1, 24 undergraduates drew illusory and control inferences from premises based on exclusive disjunctions (“or else”). In one block, participants were instructed to falsify the premises of each illusory and control inference before making the inference. In the other block, participants d…Read more
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62Syllogistic inferenceCognition 16 (1): 1-61. 1984.This paper reviews current psychological theories of syllogistic inference and establishes that despite their various merits they all contain deficiencies as theories of performance. It presents the results of two experiments, one using syllogisms and the other using three-term series problems, designed to elucidate how the arrangement of terms within the premises affects performance. These data are used in the construction of a theory based on the hypothesis that reasoners construct mental mode…Read more
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62The nature and limits of human understanding (edited book)T & T Clark. 2003.This book is an exploration of human understanding, from the perspectives of psychology, philosophy, biology and theology. The six contributors are among the most internationally eminent in their fields. Though scholarly, the writing is non-technical. No background in psychology, philosophy or theology is presumed. No other interdisciplinary work has undertaken to explore the nature of human understanding. This book is unique, and highly significant for anyone interested in or concerned about th…Read more
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61Does everyone love everyone? The psychology of iterative reasoningThinking and Reasoning 10 (1). 2004.When a quantified premise such as: Everyone loves anyone who loves someone, occurs with a premise such as: Anne loves Beth, it follows immediately that everyone loves Anne. It also follows that Carol loves Diane, where these two individuals are in the domain of discourse. According to the theory of mental models, this inference requires the quantified premise to be used again to update a model of specific individuals. The paper reports four experiments examining such iterative inferences. Experi…Read more
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60Believability and syllogistic reasoningCognition 31 (2): 117-140. 1989.In this paper we investigate the locus of believability effects in syllogistic reasoning. We identify three points in the reasoning process at which such effects could occur: the initial interpretation of premises, the examination of alternative representations of them (in all of which any valid conclusion must be true), and the “filtering” of putative conclusions. The effect of beliefs at the first of these loci is well established. In this paper we report three experiments that examine whether…Read more
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56Referential continuity and the coherence of discourseCognition 11 (1): 29-46. 1982.Two experiments were carried out to investigate the role of referential continuity in understanding discourse. In experiment 1, a group of university students listened to stories and descriptive passages presented in three different versions: the original passages, versions in which the sentences occured in a random order, and randomised versions in which referential continuity had been restored primarily by replacing pronouns and other terms with fuller and more appropriate noun phrases. The or…Read more
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52Illusions of consistency in quantified assertionsIn S. Ohlsson & R. Catrambone (eds.), Proceedings of the 32nd Annual Conference of the Cognitive Science Society, Cognitive Science Society. 2010.
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48The Truth of Conditional AssertionsCognitive Science 42 (8): 2502-2533. 2018.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 whi…Read more
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47The Relation Between Factual and Counterfactual ConditionalsCognitive Science 42 (7): 2205-2228. 2018.
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39Models of Possibilities Instead of Logic as the Basis of Human ReasoningMinds and Machines 34 (3): 1-22. 2024.The theory of mental models and its computer implementations have led to crucial experiments showing that no standard logic—the sentential calculus and all logics that include it—can underlie human reasoning. The theory replaces the logical concept of validity (the conclusion is true in all cases in which the premises are true) with necessity (conclusions describe no more than possibilities to which the premises refer). Many inferences are both necessary and valid. But experiments show that indi…Read more
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38Illusions in ReasoningMinds and Machines 27 (1): 11-35. 2017.Some philosophers argue that the principles of human reasoning are impeccable, and that mistakes are no more than momentary lapses in “information processing”. This article makes a case to the contrary. It shows that human reasoners commit systematic fallacies. The theory of mental models predicts these errors. It postulates that individuals construct mental models of the possibilities to which the premises of an inference refer. But, their models usually represent what is true in a possibility,…Read more
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37Explanations make inconsistencies harder to detectIn S. Ohlsson & R. Catrambone (eds.), Proceedings of the 32nd Annual Conference of the Cognitive Science Society, Cognitive Science Society. 2010.
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33Strategies in sentential reasoningCognitive Science 26 (4): 425-468. 2002.Four experiments examined the strategies that individuals develop in sentential reasoning. They led to the discovery of five different strategies. According to the theory proposed in the paper, each of the strategies depends on component tactics, which all normal adults possess, and which are based on mental models. Reasoners vary their use of tactics in ways that have no deterministic account. This variation leads different individuals to assemble different strategies, which include the constru…Read more
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Lincoln UniversityUndergraduate
Areas of Interest
Philosophy of Cognitive Science |
Philosophy of Probability |