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Skovgaard-Olsen N, Collins P, Klauer KC. Possible worlds truth table task. Cognition 2023; 238:105507. [PMID: 37331324 DOI: 10.1016/j.cognition.2023.105507] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2022] [Revised: 05/26/2023] [Accepted: 05/30/2023] [Indexed: 06/20/2023]
Abstract
In this paper, a novel experimental task is developed for testing the highly influential, but experimentally underexplored, possible worlds account of conditionals (Lewis, 1973; Stalnaker, 1968). In Experiment 1, this new task is used to test both indicative and subjunctive conditionals. For indicative conditionals, five competing truth tables are compared, including the previously untested, multi-dimensional possible worlds semantics of Bradley (2012). In Experiment 2, these results are replicated and it is shown that they cannot be accounted for by an alternative hypothesis proposed by our reviewers. In Experiment 3, individual variation in truth assignments of indicative conditionals is investigated via Bayesian mixture models that classify participants as following one of several competing truth tables. As a novelty of this study, it is found that a possible worlds semantics of Lewis and Stalnaker is capable of accounting for participants' aggregate truth value assignments in this task. Applied to indicative conditionals, we show across three experiments, that the theory both captures participants' truth values at the aggregate level (Experiments 1 and 2) and that it makes up the largest subgroup in the analysis of individual variation in our experimental paradigm (Experiment 3).
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Affiliation(s)
| | - Peter Collins
- School of Human Sciences, University of Greenwich, UK
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2
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Bourlier M, Jacquet B, Lassiter D, Baratgin J. Coherence, not conditional meaning, accounts for the relevance effect. Front Psychol 2023; 14:1150550. [PMID: 37255509 PMCID: PMC10225734 DOI: 10.3389/fpsyg.2023.1150550] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2023] [Accepted: 04/21/2023] [Indexed: 06/01/2023] Open
Abstract
Missing-link conditionals like "If bats have wings, Paris is in France" are generally felt to be unacceptable even though both clauses are true. According to the Hypothetical Inferential Theory, this is explained by a conventional requirement of an inferential connection between conditional clauses. Bayesian theorists have denied the need for such a requirement, appealing instead to a requirement of discourse coherence that extends to all ways of connecting clauses. Our experiment compared conditionals ("If A, C"), conjunctions ("A and C"), and bare juxtapositions ("A. C."). With one systematic exception that is predicted by prior work in coherence theory, the presence or absence of an inferential link affected conditionals and other statement types in the same way. This is as expected according to the Bayesian approach together with a general theory of discourse coherence.
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Affiliation(s)
- Maxime Bourlier
- Université Paris 8, Laboratoire Cognition Humaine et Artificielle (CHArt, RNSR 200515259U), Saint-Denis, France
| | - Baptiste Jacquet
- Université Paris 8, Laboratoire Cognition Humaine et Artificielle (CHArt, RNSR 200515259U), Saint-Denis, France
- Probability, Assessment, Reasoning and Inferences Studies Association, Paris, France
| | - Daniel Lassiter
- School of Philosophy, Psychology and Language Sciences, University of Edinburgh, Edinburgh, United Kingdom
| | - Jean Baratgin
- Université Paris 8, Laboratoire Cognition Humaine et Artificielle (CHArt, RNSR 200515259U), Saint-Denis, France
- Probability, Assessment, Reasoning and Inferences Studies Association, Paris, France
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3
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Wang M, Over D, Liang L. EXPRESS: What is required for the truth of a general conditional? Q J Exp Psychol (Hove) 2022; 75:2105-2117. [PMID: 35262439 DOI: 10.1177/17470218221089331] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
General conditionals, if p then q, can be used to make assertions about sets of objects. Previous studies have found that people generally judge the probability of one these conditionals to be the conditional probability of q given p, P(q|p). Two experiments investigated the qualitative relation between the exhaustive possibilities, p & q, p & ¬q, ¬p & q, and ¬p & ¬q, and truth and possibility judgments about general conditionals. In Experiment 1, for truth judgments, people evaluated a general conditional as "true" in sets containing p & q cases but no p & ¬q, and "true" judgments depended only on P(q|p). In Experiment 2, for possibility judgments, people's responses implied that only p & q cases have to be possible in a set for a general conditional to be true of the set. Our results add to earlier findings against representing a general conditional as the material conditional of extensional logic, and they provide novel disconfirmation of two recent proposals: the modal semantics of revised mental model theory and certain inferentialist accounts of conditionals. They supply new support for suppositional theories of conditionals.
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Affiliation(s)
- Moyun Wang
- School of Psychology, Shaanxi Normal University, Xi'an 710062, China 12401
| | - David Over
- Psychology Department, Durham University, Durham, United Kingdom 3057
| | - Lixia Liang
- School of Psychology, Shaanxi Normal University, Xi'an 710062, China 543811
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4
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Berto F. Williamson on indicatives and suppositional heuristics. SYNTHESE 2022; 200:1-12. [PMID: 35194257 PMCID: PMC8853152 DOI: 10.1007/s11229-022-03518-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2021] [Accepted: 11/23/2021] [Indexed: 06/02/2023]
Abstract
Timothy Williamson has defended the claim that the semantics of the indicative 'if' is given by the material conditional. Putative counterexamples can be handled by better understanding the role played in our assessment of indicatives by a fallible cognitive heuristic, called the Suppositional Procedure. Williamson's Suppositional Conjecture has it that the Suppositional Procedure is humans' primary way of prospectively assessing conditionals. This paper raises some doubts on the Suppositional Procedure and Conjecture.
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Affiliation(s)
- Francesco Berto
- Arché, University of St Andrews, St Andrews, UK
- Institute for Logic,Language and Computation (ILLC), University of Amsterdam, Amsterdam, The Netherlands
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5
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Douven I, Elqayam S, Gärdenfors P, Mirabile P. Conceptual spaces and the strength of similarity-based arguments. Cognition 2021; 218:104951. [PMID: 34801861 DOI: 10.1016/j.cognition.2021.104951] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Revised: 10/26/2021] [Accepted: 11/01/2021] [Indexed: 11/17/2022]
Abstract
Central to the conceptual spaces framework is the thought that concepts can be studied mathematically, by geometrical and topological means. Various applications of the framework have already been subjected to empirical testing, mostly with excellent results, demonstrating the framework's usefulness. So far untested is the suggestion that conceptual spaces may help explain certain inferences people are willing to make. The experiment reported in this paper focused on similarity-based arguments, testing the hypothesis that the strength of such arguments can be predicted from the structure of the conceptual space in which the items being reasoned about are represented. A secondary aim of the experiment concerned a recent inferentialist semantics for indicative conditionals, according to which the truth of a conditional requires the presence of a sufficiently strong inferential connection between its antecedent and consequent. To the extent that the strength of similarity-based inferences can be predicted from the geometry and topology of the relevant conceptual space, such spaces should help predict truth ratings of conditionals embodying a similarity-based inferential link. The results supported both hypotheses.
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Affiliation(s)
- Igor Douven
- IHPST/CNRS/Panthéon-Sorbonne University, France.
| | - Shira Elqayam
- School of Applied Social Sciences, De Montfort University, United Kingdom
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Sebben S, Ullrich J. Can conditionals explain explanations? A modus ponens model of B because A. Cognition 2021; 215:104812. [PMID: 34246085 DOI: 10.1016/j.cognition.2021.104812] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2019] [Revised: 06/02/2021] [Accepted: 06/11/2021] [Indexed: 11/19/2022]
Abstract
We suggest a normative model for the evaluation of explanations B because A based on probabilistic conditional reasoning and compare it with empirical data. According to the modus ponens model of explanations, the probability of B because A should equal the joint probability of the conditional if A then B and the explanans A. We argue that B because A expresses the conjunction of A and B as well as positive relevance of A for B. In Study 1, participants (N = 80) judged the subjective probabilities of 20 sets of statements with a focus on belief-based reasoning under uncertainty. In Study 2, participants (N = 376) were assigned to one of six item sets for which we varied the inferential relevance of A for B to explore boundary conditions of our model. We assessed the performance of our model across a range of analyses and report results on the Equation, a fundamental model in research on probabilistic reasoning concerning the evaluation of conditionals. In both studies, results indicate that participants' belief in statements B because A followed model predictions systematically. However, a sizeable proportion of sets of beliefs contained at least one incoherence, indicating deviations from the norms of rationality suggested by our model. In addition, results of Study 2 lend support to the idea that inferential relevance may be relevant for the evaluation of both conditionals and explanations.
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Affiliation(s)
- Simone Sebben
- Department of Psychology, University of Zurich, Switzerland.
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7
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Abstract
A major hypothesis about conditionals is the Equation in which the probability of a conditional equals the corresponding conditional probability: p(if A then C) = p(C|A). Probabilistic theories often treat it as axiomatic, whereas it follows from the meanings of conditionals in the theory of mental models. In this theory, intuitive models (system 1) do not represent what is false, and so produce errors in estimates of p(if A then C), yielding instead p(A & C). Deliberative models (system 2) are normative, and yield the proportion of cases of A in which C holds, i.e., the Equation. Intuitive estimates of the probability of a conditional about unique events: If covid-19 disappears in the USA, then Biden will run for a second term, together with those of each of its clauses, are liable to yield joint probability distributions that sum to over 100%. The error, which is inconsistent with the probability calculus, is massive when participants estimate the joint probabilities of conditionals with each of the different possibilities to which they refer. This result and others under review corroborate the model theory.
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Nickerson RS, Butler SF, Barch DH. Looking behind: Turning cards in the selection task. Q J Exp Psychol (Hove) 2021; 74:1451-1464. [PMID: 33629644 DOI: 10.1177/17470218211001293] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Wason's selection task requires that one imagine which of four cards, each of which has a letter on one side and a number on the other, one would have to turn over to determine whether a statement about the cards is true or false. For example, one might see four cards showing T, H, 6, and 4 and be asked to say which card or cards one would have to turn over to determine whether a statement in the form of If a card has T on one side, it has 4 on the other is true. In the great majority of experiments with this task no cards are actually turned. This limits the conclusions that can be drawn from experimental results. In two experiments participants actually turned (had a computer turn) virtual cards so as to show what they contained on their originally hidden sides. Participants were given a monetary incentive to do well on the task, and they performed it, with trial-by-trial feedback, many times. Performance was much better than is typically obtained with the more common way of performing the task. Results also demonstrate the importance of the precise wording of the statement to be evaluated and how a misinterpretation could help account for a tendency for people to turn only a single card even when the turning of two is required. Results prompt several questions of a theoretical nature and are discussed as they relate to recent theoretical treatments of the selection task.
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Stewart AJ, Singmann H, Haigh M, Wood JS, Douven I. Tracking the eye of the beholder: is explanation subjective? JOURNAL OF COGNITIVE PSYCHOLOGY 2021. [DOI: 10.1080/20445911.2020.1870986] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Andrew J. Stewart
- School of Psychological Sciences, University of Manchester, Manchester, UK
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Collins PJ, Krzyżanowska K, Hartmann S, Wheeler G, Hahn U. Conditionals and testimony. Cogn Psychol 2020; 122:101329. [PMID: 32805584 DOI: 10.1016/j.cogpsych.2020.101329] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2018] [Revised: 06/02/2020] [Accepted: 06/21/2020] [Indexed: 11/16/2022]
Abstract
Conditionals and conditional reasoning have been a long-standing focus of research across a number of disciplines, ranging from psychology through linguistics to philosophy. But almost no work has concerned itself with the question of how hearing or reading a conditional changes our beliefs. Given that we acquire much-perhaps most-of what we believe through the testimony of others, the simple matter of acquiring conditionals via others' assertion of a conditional seems integral to any full understanding of the conditional and conditional reasoning. In this paper we detail a number of basic intuitions about how beliefs might change in response to a conditional being uttered, and show how these are backed by behavioral data. In the remainder of the paper, we then show how these deceptively simple phenomena pose a fundamental challenge to present theoretical accounts of the conditional and conditional reasoning - a challenge which no account presently fully meets.
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Affiliation(s)
- Peter J Collins
- Dept. of Psychological Sciences, Birkbeck, Univ. of London, United Kingdom; Munich Center for Mathematical Philosophy, LMU Munich, Germany.
| | - Karolina Krzyżanowska
- Munich Center for Mathematical Philosophy, LMU Munich, Germany; Institute for Logic, Language and Computation, University of Amsterdam, Netherlands; Arché Research Centre, University of St Andrew's, United Kingdom.
| | | | | | - Ulrike Hahn
- Dept. of Psychological Sciences, Birkbeck, Univ. of London, United Kingdom; Munich Center for Mathematical Philosophy, LMU Munich, Germany
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Mirabile P, Douven I. Abductive conditionals as a test case for inferentialism. Cognition 2020; 200:104232. [DOI: 10.1016/j.cognition.2020.104232] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2019] [Revised: 02/05/2020] [Accepted: 02/07/2020] [Indexed: 11/29/2022]
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12
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Douven I. The ecological rationality of explanatory reasoning. STUDIES IN HISTORY AND PHILOSOPHY OF SCIENCE 2020; 79:1-14. [PMID: 32072922 DOI: 10.1016/j.shpsa.2019.06.004] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2018] [Revised: 05/16/2019] [Accepted: 06/28/2019] [Indexed: 06/10/2023]
Abstract
There is growing evidence that explanatory considerations influence how people change their degrees of belief in light of new information. Recent studies indicate that this influence is systematic and may result from people's following a probabilistic update rule. While formally very similar to Bayes' rule, the rule or rules people appear to follow are different from, and inconsistent with, that better-known update rule. This raises the question of the normative status of those updating procedures. Is the role explanation plays in people's updating their degrees of belief a bias? Or are people right to update on the basis of explanatory considerations, in that this offers benefits that could not be had otherwise? Various philosophers have argued that any reasoning at deviance with Bayesian principles is to be rejected, and so explanatory reasoning, insofar as it deviates from Bayes' rule, can only be fallacious. We challenge this claim by showing how the kind of explanation-based update rules to which people seem to adhere make it easier to strike the best balance between being fast learners and being accurate learners. Borrowing from the literature on ecological rationality, we argue that what counts as the best balance is intrinsically context-sensitive, and that a main advantage of explanatory update rules is that, unlike Bayes' rule, they have an adjustable parameter which can be fine-tuned per context. The main methodology to be used is agent-based optimization, which also allows us to take an evolutionary perspective on explanatory reasoning.
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Affiliation(s)
- Igor Douven
- SND, CNRS, Sorbonne University, 1, rue Victor Cousin, 75005, Paris, France.
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13
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Abstract
The psychology of verbal reasoning initially compared performance with classical logic. In the last 25 years, a new paradigm has arisen, which focuses on knowledge-rich reasoning for communication and persuasion and is typically modeled using Bayesian probability theory rather than logic. This paradigm provides a new perspective on argumentation, explaining the rational persuasiveness of arguments that are logical fallacies. It also helps explain how and why people stray from logic when given deductive reasoning tasks. What appear to be erroneous responses, when compared against logic, often turn out to be rationally justified when seen in the richer rational framework of the new paradigm. Moreover, the same approach extends naturally to inductive reasoning tasks, in which people extrapolate beyond the data they are given and logic does not readily apply. We outline links between social and individual reasoning and set recent developments in the psychology of reasoning in the wider context of Bayesian cognitive science.
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Affiliation(s)
- Mike Oaksford
- Department of Psychological Sciences, Birkbeck, University of London, London WC1E 7HX, United Kingdom
| | - Nick Chater
- Nick Chater, Warwick Business School, University of Warwick, Coventry CV4 7AL, United Kingdom
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14
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Douven I, Elqayam S, Singmann H, Wijnbergen-Huitink JV. Conditionals and inferential connections: toward a new semantics. THINKING & REASONING 2019. [DOI: 10.1080/13546783.2019.1619623] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Igor Douven
- SND/CNRS, Sorbonne University, Paris, France
| | - Shira Elqayam
- School of Applied Social Sciences, De Montfort University, Leicester, UK
| | - Henrik Singmann
- Department of Psychology, University of Warwick, Coventry, UK
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15
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Abstract
Conditionals statements are a common and necessary component in natural languages. The research reported in this paper is on a fundamental question about singular conditionals. Is there an adequate account of people's truth, falsity, and credibility (probability) judgments about these conditionals when their antecedents are false? Two experiments examined people's quantitative credibility ratings and qualitative truth and falsity judgments for singular conditionals, if p then q, given false antecedent, not-p, cases. The results demonstrate that, when relevant knowledge about the conditional probability of q given p, P(q|p), is available to participants in not-p cases, they tend to make credibility ratings based on P(q|p), and to make "true" (or "false") judgments at a high (or low) level of these credibility ratings. These findings favor the Jeffrey table account of these conditionals over the other existing accounts, including that of the de Finetti table.
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Affiliation(s)
- Moyun Wang
- 1 School of Psychology, Shaanxi Key Laboratory of Behavior and Cognitive Neuroscience, Shaanxi Normal University, Xi'an, PR China
| | - Mingyi Zhu
- 1 School of Psychology, Shaanxi Key Laboratory of Behavior and Cognitive Neuroscience, Shaanxi Normal University, Xi'an, PR China
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16
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Assessing the accuracy of diagnostic probability estimation: Evidence for defeasible modus ponens. Int J Approx Reason 2019. [DOI: 10.1016/j.ijar.2018.11.015] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Baratgin J, Politzer G, Over DE, Takahashi T. The Psychology of Uncertainty and Three-Valued Truth Tables. Front Psychol 2018; 9:1479. [PMID: 30233441 PMCID: PMC6131665 DOI: 10.3389/fpsyg.2018.01479] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2018] [Accepted: 07/26/2018] [Indexed: 11/13/2022] Open
Abstract
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.
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Affiliation(s)
- Jean Baratgin
- CHArt (P-A-R-I-S), Université Paris 8 & EPHE, Paris, France.,Institut Jean Nicod, École Normale Supérieure, Paris, France
| | - Guy Politzer
- Institut Jean Nicod, École Normale Supérieure, Paris, France
| | - David E Over
- Psychology Department, Durham University, Durham, United Kingdom
| | - Tatsuji Takahashi
- School of Science and Engineering, Tokyo Denki University, Tokyo, Japan
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Markovits H, de Chantal PL, Brisson J. Abstract reasoning and the interpretation of basic conditionals. THINKING & REASONING 2018. [DOI: 10.1080/13546783.2018.1452795] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Affiliation(s)
- Henry Markovits
- Department of Psychology, Université du Québec à Montréal, Montreal, Canada
| | | | - Janie Brisson
- Department of Psychology, Université du Québec à Montréal, Montreal, Canada
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