The probability of causal conditionals

Over, David E.; Hadjichristidis, Constantinos; Evans, Jonathan St. B. T.; Handley, Simon J.; Sloman, Steven A.

doi:10.1016/j.cogpsych.2006.05.002

Cited by 192 publications

(264 citation statements)

References 32 publications

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“…Evans et al (2003) assumed that this latter pattern of response is given by shallow processors who cut short the Ramsey test and stop at the p q cases, an assumption corroborated by the fact that the participants giving conjunctive responses to the probability task have lower cognitive capacities than the others (Evans, Handley, Neilens, & Over, 2007). Oberauer and Wilhelm (2003) reported approximately the same results that have been extended to causal conditionals (Over, Hadjchristidis, Evans, Handley, & Sloman, 2007). The evaluation of the probability of conditionals as a conditional probability, along with the defective table observed in truth table tasks, was considered by Evans et al (2005) as the main evidence contradicting Johnson-Laird and Byrne's mental model theory.…”

Section: The Probability Of Conditionalssupporting

confidence: 69%

Heuristic and analytic processes in mental models for conditionals: An integrative developmental theory

Gauffroy

Barrouillet

2009

Developmental Review

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a b s t r a c tThis article presents a developmental dual-process theory of the understanding of conditionals that integrates Evans' heuristic-analytic theory within the revised mental model theory of conditional proposed by Barrouillet, Gauffroy, and Lecas (2008). According to this theory, the interpretation of a conditional sentence is driven by unconscious and implicit heuristic processes that provide individuals with an initial representation that captures its meaning by representing the cases that make it true. This initial model can be enriched with additional models (a process named fleshing out within the mental model theory) through the intervention of conscious and demanding analytic processes. Being optional, these processes construct representations of cases that are only compatible with the conditional, leaving its truth-value indeterminate when they occur. Because heuristic processes are relatively immune to developmental changes, while analytic processes strongly develop with age, the initial model remains stable through development whereas the number of additional models that can be constructed increases steadily. Thus, the dual-process mental model theory predicts in which cases conditionals will be deemed true, indeterminate, or false and how these cases evolve with age. These predictions were verified in children, adolescents and adults who were asked to evaluate the truth value and the probability of several types of conditionals. The results reveal a variety of developmental trajectories in the way different conditionals are interpreted, which can all be accounted for by our revised mental model theory.

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Section: The Probability Of Conditionalssupporting

confidence: 69%

Heuristic and analytic processes in mental models for conditionals: An integrative developmental theory

Gauffroy

Barrouillet

2009

Developmental Review

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“…Other theorists have maintained the notion of validity, but postulated a probabilistic semantics for conditionals: "In everyday contexts it seems to be more plausible to interpret conditionals not by material implications, but by much weaker conditional probabilities" (Pfeifer & Kleiter, 2005). Likewise, many theorists have proposed that the probability of a conditional is the corresponding conditional probability of its consequent given its antecedent (e.g., Evans, Handley, Neilens, & Over, 2007;Evans, Handley, & Over, 2003;Hadjichristidis et al, 2001;Over, Hadjichristidis, Evans, Handley, & Sloman, 2007;Oberauer & Wilhelm, 2003). Oberauer and his colleagues have argued that the model theory needs to be revised in order to explain their participants' judgements of the probabilities of conditionals, which usually corroborated the conditional probability hypothesis (Oberauer, Geiger, Fischer, & Weidenfeld, 2007).…”

Section: Modulation Of Conditionalsmentioning

confidence: 99%

The modulation of conditional assertions and its effects on reasoning

Quelhas

Johnson‐Laird

Juhos

2010

Quarterly Journal of Experimental Psychology

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The theory of mental models postulates that conditionals of the sort, if A then C, have a “core” meaning referring to three possibilities: A and C, not-A and C, and not-A and not-C. The meaning of a conditional's clauses and general knowledge can modulate this meaning, blocking certain possibilities or adding relations between the clauses. Four experiments investigated such interpretations in factual and deontic domains. In Experiment 1, the participants constructed instances of what was possible and what was impossible according to various conditionals. The results corroborated the general predictions of the model theory and also the occurrence of modulation. The resulting interpretations governed the conclusions that participants accepted in Experiment 2, which also yielded the predicted effects of a time limit on responding. In Experiment 3, the participants drew the predicted conclusions for themselves. In Experiment 4, modulation led to predicted temporal relations between A and C. We relate these results to current theories of conditionals.

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“…Empirical evidence supporting this proposal is based on a probabilistic truth table task (hereafter, the probability task) in which participants are asked to assess the probability of an If p then q conditional from the probabilities of the four truth-table possibilities p & q, p & not-q, not-p & q, not-p & not-q. Several studies observed that a majority of adults judge the probability of the conditional as the conditional probability P(q|p), that is the probability of p & q divided by the summed probabilities of p & q and p & not-q (Evans, Handley, & Over, 2003;Fugard, Pfeifer, Mayerfofer, & Kleiter, 2011;Oberauer & Wilhelm, 2003;Over, Hadjichristidis, Evans, Handley, & Sloman, 2007).…”

Section: The New Paradigm and The Question Of Developmentmentioning

confidence: 99%

Probability in reasoning: A developmental test on conditionals

Barrouillet

Gauffroy

2015

Cognition

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a b s t r a c tProbabilistic theories have been claimed to constitute a new paradigm for the psychology of reasoning. A key assumption of these theories is captured by what they call the Equation, the hypothesis that the meaning of the conditional is probabilistic in nature and that the probability of If p then q is the conditional probability, in such a way that P(if p then q) = P(q|p). Using the probabilistic truth-table task in which participants are required to evaluate the probability of If p then q sentences, the present study explored the pervasiveness of the Equation through ages (from early adolescence to adulthood), types of conditionals (basic, causal, and inducements) and contents. The results reveal that the Equation is a late developmental achievement only endorsed by a narrow majority of educated adults for certain types of conditionals depending on the content they involve. Agerelated changes in evaluating the probability of all the conditionals studied closely mirror the development of truth-value judgements observed in previous studies with traditional truth-table tasks. We argue that our modified mental model theory can account for this development, and hence for the findings related with the probability task, which do not consequently support the probabilistic approach of human reasoning over alternative theories.

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The probability of causal conditionals

Cited by 192 publications

References 32 publications

Heuristic and analytic processes in mental models for conditionals: An integrative developmental theory

Heuristic and analytic processes in mental models for conditionals: An integrative developmental theory

The modulation of conditional assertions and its effects on reasoning

Probability in reasoning: A developmental test on conditionals

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