The Truth of Conditional Assertions

Goodwin, Geoffrey P.; Johnson‐Laird, P. N.

doi:10.1111/cogs.12666

Cited by 19 publications

(25 citation statements)

References 59 publications

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“…The process of estimating p( C ) and then nudging it one way or the other to estimate a unique p( C|A ) can lead with estimates of p( A ) and p( C ) to a predictable subadditivity of the JPD (Khemlani et al, 2015 ). When such estimates occur four times in a row to assess the joint probabilities of a conditional with each case in its partition, the result is a massive subadditivity (Byrne & Johnson-Laird, 2019 ; Goodwin & Johnson-Laird, 2018 ). A tell-tale sign of the model theory is accordingly the occurrence of subadditive judgments of probability in the absence of either heuristic cues (Tversky & Kahneman, 1983 ) or the unpacking of categories (Tversky & Koehler, 1994 ).…”

Section: Discussionmentioning

confidence: 99%

“…Likewise, the model theory of intensional probabilities (Khemlani et al, 2015 ) was developed to explain estimates of conditional probabilities, not the probabilities of conditionals, and we did not adjust it to hark back to earlier experimental results. Instead, it inspired intensional studies of the Equation, including two that yield results contrary to p-theories (Byrne & Johnson-Laird, 2019 ; Goodwin & Johnson-Laird, 2018 ).…”

Section: Conditionals In Logic and Probability Logicmentioning

confidence: 99%

“…They judged their joint truth with each case in their partitions, and they also estimated their joint probabilities with each case in their partitions (Goodwin & Johnson-Laird, 2018 ). They were not instructed that these probabilities should sum to 100%.…”

Section: Conditionals In Logic and Probability Logicmentioning

confidence: 99%

See 2 more Smart Citations

The probability of conditionals: A review

2021

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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. Supplementary Information The online version contains supplementary material available at 10.3758/s13423-021-01938-5.

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Section: Discussionmentioning

confidence: 99%

Section: Conditionals In Logic and Probability Logicmentioning

confidence: 99%

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The probability of conditionals: A review

2021

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“…In the mental models theory, not-p cases are relevant to the truth or falsity of conditionals. In particular, in MMT1, a true conditional implies that pq or ¬pq or ¬p¬q is possible, and a conditional is true when any one of the three cases is true and p¬q is impossible (Goodwin & Johnson-Laird, 2018;Johnson-Laird & Byrne, 2002). In MMT2, a true conditional implies that pq, ¬pq, and ¬p¬q are all possible, and a conditional is true only if the three cases are all possible and p¬q is impossible (Johnson-Laird, Khemlani, & Goodwin, 2015;Khemlani, Byrne, & Johnson-Laird, 2018).…”

Section: Resultsmentioning

confidence: 99%

Consistency and inconsistency between instance and categorical modal inferences from conditionals

Wang¹

2021

Preprint

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For the modal meanings of conditionals with the form if p then q, there are three existing psychological accounts: the original suppositional theory, the original and revised mental models theory. They imply different modal meanings of if p then q. Alternatively, we propose a revised suppositional theory with the unique prediction that the set from which the instance referred to by a true conditional was randomly drawn, necessarily includes pq cases, and possibly includes ¬pq / ¬p¬q cases, but impossibly includes p¬q cases. One experiment investigated whether category modal inferences from a conditional would be consistent with preceding instance modal inferences from it. The results revealed that (1) previous instance inferences did not affect subsequent category inferences; (2) relevant cases pq and p¬q tended to elicit consistent response patterns, but irrelevant cases ¬pq and ¬p¬q tended to elicit inconsistent response patterns; (3) the overall response pattern of category inferences is consistent with only the prediction of the revised suppositional theory. The latter implies that only the pq possibility is required by a true conditional, but the ¬pq / ¬p¬q possibility is unrequired. On the whole, these findings favor the revised suppositional theory over the other accounts.

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“…When individuals have to list what is possible given a factual conditional, nearly everyone, children and adults alike, list the first of the three possibilities, and as the capacity of children's working memory increases they tend to list the other two possibilities in the order shown above (e.g., Barrouillet, Grosset, & Lecas, 2000). Individuals also judge that the corresponding assertions, such as A and C, could be jointly true with the conditional (Goodwin & Johnson-Laird, 2018). These default possibilities imply the predicted paraphrases of the conditionals in our experiments.…”

Section: Certain Then Clausesmentioning

confidence: 99%

Possibilities and the parallel meanings of factual and counterfactual conditionals

2020

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The mental model theory postulates that the meanings of conditionals are based on possibilities. Indicative conditionals-such as "If he is injured tomorrow, then he will take some leave"-have a factual interpretation that can be paraphrased as It is possible, and remains so, that he is injured tomorrow, and in that case certain that he takes some leave. Subjunctive conditionals, such as, "If he were injured tomorrow, then he would take some leave," have a prefactual interpretation that has the same paraphrase. But when context makes clear that his injury will not occur, the subjunctive has a counterfactual paraphrase, with the first clause: It was once possible, but does not remain so, that he will be injured tomorrow. Three experiments corroborated these predictions for participants' selections of paraphrases in their native Spanish, for epistemic and deontic conditionals, for those referring to past and to future events, and for those with then clauses referring to what may or must happen. These results are contrary to normal modal logics. They are also contrary to theories based on probabilities, which are inapplicable to deontic conditionals, such as, "If you have a ticket, then you must enter the show."

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The Truth of Conditional Assertions

Cited by 19 publications

References 59 publications

The probability of conditionals: A review

The probability of conditionals: A review

Consistency and inconsistency between instance and categorical modal inferences from conditionals

Possibilities and the parallel meanings of factual and counterfactual conditionals

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