The Analytic Truth and Falsity of Disjunctions

Abstract

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.

Semantic ambiguity does not imply syntactic ambiguity

“…It has been raised that generative grammar has several problems to remove (HORNSTEIN, 1987) and proposed that the theory of mental models (e.g., QUELHAS, RASGA, & JOHNSON-LAIRD, 2019) can do that (LÓPEZ-ASTORGA, 2019a). However, this paper will be focused on only one of those problems: ambiguity.…”

Logical Forms Depend on Semantic Models: the Illusory Disjunctive Sentences as Pieces of Evidence

“…(1) "Either the food is hot or else it is tepid, but not both" (Quelhas et al, 2019, p. 9). Quelhas et al (2019) experimentally show that people usually evaluate sentences such as (1), which is literally one of their examples, as true. Nevertheless, they can be false.…”

“…Its claims are several, but perhaps, as far as the aims of this paper are concerned, it can be said that it proposes that logic is not a basic element in the human mind, that syntax is a secondary aspect in the intellectual activity, that semantics and pragmatics are more essential in that very activity, and that reasoning and language are led by models describing reality in an iconic way (e.g., Johnson-Laird, 2012;Orenes & Johnson-Laird, 2012;Quelhas, Rasga, & Johnson-Laird, 2019). Thus, it gives accounts of many controversial results reported in the specialized literature, including those referring to the way people apply inference rules such as Modus Tollendo Tollens (e.g., Byrne & Johnson-Laird, 2009), to how individuals often understand certain paradoxical inferences (e.g., Orenes & Johnson-Laird, 2012), to the case of certain illusory disjunctive sentences (e.g., Quelhas et al, 2019), or to the manner the human mind tends to consider probabilities (e.g., Johnson-Laird, Khemlani, & Goodwin, 2015). However, it might also lead one to a very important philosophical and linguistic consequence: it makes logical form superfluous.…”

“…As Quelhas et al (2019) show, there are disjunctions with a special characteristic. Although these disjunctions can be false, people usually ignore that possibility.…”

“…So, the problem with this kind of disjunctions is that, in spite of the fact that they are contingent disjunctions, individuals tend to deem them as analytic disjunctions. 'Contingent disjunctions' is the denomination in Quelhas et al (2019). However, it is obvious that other expressions could also be used to refer to them.…”