How knowledge makes disjunctions “analytically” true or false
Cristina Quelhas, Célia Rasga, and Phil Johnson-Laird published a paper in Cognitive Science on what makes disjunctions, such as A or B or both, analytically true or false. For instance, this disjunction is true:
“Either the food is cold or else it is tepid, but not both.”
The authors present new studies that show how knowledge modulates the interpretation of disjunctions. The paper can be downloaded here, and the abstract is here:
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 predic- tions 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 ‘pos- sible’ 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 fol- lows: 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 dis- junctions 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.