A Priori True and False Conditionals

2018

Self Cite

What is the relation between factual conditionals: If A happened then B happened, and counterfactual conditionals: If A had happened then B would have happened? Some theorists propose quite different semantics for the two. In contrast, the theory of mental models and its computer implementation interrelates them. It postulates that both can have a priori truth values, and that the semantic bases of both are possibilities: states that are possible for factual conditionals, and that were once possible but that did not happen for counterfactual conditionals. Two experiments supported these relations. Experiment 1 showed that, like factual conditionals, certain counterfactuals are true a priori, and others are false a priori. Experiment 2 replicated this result and showed that participants selected appropriate paraphrases, referring, respectively, to real and to counterfactual possibilities, for the two sorts of conditional. These results are contrary to alternative accounts of conditionals.

Section: The Theory Of Mental Modelsmentioning

confidence: 60%

The Relation Between Factual and Counterfactual Conditionals

Quelhas¹,

Rasga²,

2018

Self Cite

“…Hence, interpretation cannot be truth functional (Johnson-Laird & Byrne, 2002). This claim is corroborated in the finding that people judge the not-A cases as possible not only for conditionals that are true a priori, but also for conditionals that are false a priori (Quelhas, Rasga, & Johnson-Laird, 2017). For example, the case of not-A and C is judged possible both for the true conditional, If Pat is reading the article then Pat is alive, and also for the false conditional, If Pat is reading the article then Pat is dead.…”

Section: Introductionmentioning

confidence: 85%

“…Johnson‐Laird and Byrne () accordingly distinguished between everyday conditionals and material implications (p. 655), and they rejected the notion that conditionals have any sort of truth‐functional meaning (p. 673). Likewise, the fact that cases in which the if ‐clause is false are possible for both true and false conditionals is also contrary to material implication (Quelhas et al., ).…”

Section: Discussionmentioning

confidence: 99%

The Truth of Conditional Assertions

Goodwin

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 which participants judged whether sets of assertions about a specific individual, such as: If A then C, not-A, C, could all be true at the same time; and one in which participants judged the truth of conditional predictions about specific future events. The results consistently matched the three possibilities, thereby corroborating the model theory. They also showed a massive violation of the probability calculus in estimates of the probabilities of the four cases in the partition of conditionals (A and C, A and not-C, not-A and C, and not-A and not-C), which summed to over 200%.

“…Prediction 1: when a disjunction refers to the same possibilities as those in knowledge, participants tended to judge that the disjunction was true; when it refers to possibilities that conflict with those in knowledge, they tended to judge that it was false; and otherwise, they tended to judge that is impossible to determine whether it is true or false, that is, it is contingent. These judgments of truth‐value showed that the existence of assertions that are true (and that are false) on the basis of their meanings or knowledge is no longer an unempirical dogma (contrary to Quine, ), and that it is no longer restricted to the special case of conditionals (Quelhas et al, ), because it occurs with disjunctions too. However, as predicted, true judgments included illusory ones for disjunctions that in fact are contingent.…”

Section: Discussionmentioning

confidence: 99%

“…to be false (Quelhas, Rasga, & Johnson‐Laird, ). But proponents of the probabilistic approach to reasoning argue that conditionals are exceptional: They differ in meaning from their counterparts in classical logic, whereas other compounds such as disjunctions do not (e.g., Evans & Over, ; Oaksford & Chater, ).…”

Section: Introductionmentioning

confidence: 99%

The Analytic Truth and Falsity of Disjunctions

Quelhas¹,

Rasga²,

2019

Self Cite

Disjunctive inferences are difficult. According to the theory of mental models, it is because of the alternative possibilities to which disjunctions refer. Three experiments corroborated further predictions of the mental model theory. Participants judged that disjunctions, such as Either this year is a leap year or it is a common year are true. Given a disjunction such as Either A or B, they tended to evaluate the four cases in its ‘partition’: A and B, A and not‐B, not‐A and B, not‐A and not‐B, as ‘possible’ or ‘impossible’ in ways that bore out the difference between inclusive disjunctions (‘or both’) and exclusive disjunctions (‘but not both’). Knowledge usually concerns what is true, and so when participants judge that a disjunction is false, or contingent, and evaluate the cases in its partition, they depend on inferences that yield predictable errors. They tended to judge that disjunctions, such as follows: Either the food is cold or else it is tepid, but not both, are true, though in fact they could be false. They tended to infer ‘mirror‐image’ evaluations that yield the same possibilities for false disjunctions as those for true disjunctions. The article considers the implications of these results for alternative theories based on classical logic or on the probability calculus.