The negated conditional: A litmus test for the suppositional conditional?

Abstract

Under the suppositional account of conditionals, when people think about a conditional assertion, "if p then q," they engage in a mental simulation in which they imagine p holds and evaluate the probability that q holds under this supposition. One implication of this account is that belief in a conditional equates to conditional probability [P(q/p)]. In this paper, the authors examine a further implication of this analysis with respect to the wide-scope negation of conditional assertions, "it is not the case that if p then q." Under the suppositional account, nothing categorically follows from the negation of a conditional, other than a second conditional, "if p then not-q." In contrast, according to the mental model theory, a negated conditional is consistent only with the determinate state of affairs, p and not-q. In 4 experiments, the authors compare the contrasting predictions that arise from each of these accounts. The findings are consistent with the suppositional theory but are incongruent with the mental model theory of conditionals.

Disjunctive illusory inferences and how to eliminate them

“…Previous studies have demonstrated their occurrence, but they have tended to rely on conditionals of the form if A then B (Johnson-Laird & Savary, 1999). The meanings of conditionals are controversial, and critics have argued that the illusory conclusions are, in fact, valid (Handley, Evans, & Thompson, 2006;Rips, 1997;Stenning & van Lambalgen, 2008). Although we do not accept this argument, in our present study, we used novel instances of illusory inferences that are simpler than those previously studied and that use connectives with uncontroversial meanings, such as disjunctions and conjunctions.…”

Is the basic conditional probabilistic?

“…For this sort of conditional, unlike the specific conditionals used in the present experiments, there is no clear-cut way to determine the conditional probability of the consequent given the antecedent and no directly relevant frequency data that can be brought to bear to determine this conditional probability. Perhaps largely as a result of this, past research that has examined how people judge the probability of conditionals has eschewed examining such conditionals about truly unique events, favoring conditionals that are amenable to the presentation of relevant probabilistic evidence (see, e.g., Handley et al, 2006;Oberauer et al, 2007;Oberauer & Wilhelm, 2003; although see Douven & Verbrugge, 2012;Over et al, 2007, for relevant exceptions).…”

“…Studies that have asked for assessments of degree of belief in conditional assertions or of the probability of conditional assertions appear to have generally favored Evans et al's (2003) conditional probability hypothesis by showing that individuals' judgment of the probability that a conditional statement is true declines roughly linearly as a function of the conditional probability of the consequent given the antecedent (e.g., Evans et al, 2003Evans et al, , 2007Handley et al, 2006;Oberauer et al, 2007;Oberauer & Wilhelm, 2003;; although for countervailing argument and evidence, see also Girotto & Johnson-Laird, 2004;Johnson-Laird, 2011).…”

“…Accordingly, the conditional can be seen as making a deterministic statement about the single event or case in question, such that the conditional is true when both antecedent and consequent are true and is false when the antecedent is true and the consequent false. Nonetheless, information pertaining to the distribution of pertinent cases may still be relied upon to judge the probability of a specific conditional statement being true of the case in question-as has been corroborated empirically (see, e.g., Evans et al, 2003Evans et al, , 2007Handley, Evans, & Thompson, 2006;Oberauer, Geiger, Fischer, & Weidenfeld, 2007;Oberauer & Wilhelm, 2003;Over, Hadjichristidis, Evans, Handley, & Sloman, 2007). Thus, because, in the defective truth table, p also only ever occurs with q and never occurs with not q, the consequent's following from the antecedent is just as invariable according to the defective interpretation as it is on an interpretation that corresponds to material implication (David Over, personal communication, February 13, 2012).…”

Mental Logic and the Denials of Conjunctions and Disjunctions

“…Sometimes they appear to deny it as ¬(p -> q), but other times they seem to deny it as p -> ¬q. This problem has been studied in many works and papers (HANDLEY; EVANS; THOMPSON, 2006;). Even Khemlani, Orenes and Johnson-Laird (2014) analyzes it as well.…”