On the Mental Representation of Conditional Sentences

Abstract

Four experiments are reported which attempt to externalize subjects' mental representation of conditional sentences, using novel research methods. In Experiment 1, subjects were shown arrays of coloured shapes and asked to rate the degree to which they appeared to be true of conditional statements such as "If the figure is green then it is a triangle". The arrays contained different distributions of the four logically possible cases in which the antecedent or consequent is true or false: TT, TF, FT, and FF. For example, a blue triangle would be FT for the conditional quoted above. In Experiments 2 to 4, subjects were able to construct their own arrays to make conditional either true or false with any distribution of the four cases they wished to choose. The presence and absence of negative components was varied, as was the form of the conditional, being either "if then" as above or "only if": "The figure is green only if it is a triangle". The first findings was that subjects represent conditional in fuzzy way: conditional that include some counter-example TF cases (Experiment 1) may be rated as true, and such cases are often included when subjects construct an array to make the rule true (Experiments 2 to 4). Other findings included a strong tendency to include psychologically irrelevant FT and FF cases in constructed arrays, presumably to show that conditional statements only apply some of the time. A tendency to construct cases in line with the "matching bias" reported on analogous tasks in the literature was found, but only in Experiment 4, where the number of symbols available to construct each case was controlled. The findings are discussed in relation to the major contemporary theories of conditional reasoning based upon inference rules and mental models, neither of which can account for all the results.

Is the basic conditional probabilistic?

“…9 Evans et al's (1996) later experiments also furnish further support for this view. When participants were asked to construct truth table cases that would make conditionals either true or false, they sometimes included seemingly falsifying p, not q cases, which the authors took to provide evidence for a fuzzy (i.e., probabilistic) interpretation of the conditional.…”

“…Moreover, other evidence, from tasks in which participants have been asked to judge the truth of conditionals, has been interpreted as indicating a probabilistic, exception-tolerating reading of conditionals (see, e.g., Evans, Ellis, & Newstead, 1996;Liu et al, 1996;Oberauer & Wilhelm, 2003). I defer further discussion of this evidence, including some problems with the standard interpretation of these findings, until the General Discussion.…”

“…As mentioned in the introduction, some prior research has been interpreted as providing support for a probabilistic interpretation of conditionals. The tasks used in these prior investigations involved either a conditional inference task (Liu et al, 1996) or a truth judgment task (Evans et al, 1996;Oberauer & Wilhelm, 2003) similar to the tasks used in Experiments 7-9 of the present article. In each case, however, the conclusion that participants made a probabilistic reading of the conditional seems unjustified given the data.…”

“…Thus, contrary to the authors' interpretation, the main finding of this research seems to be that people drew such modus ponens inferences at rates that were much higher than would be predicted by probabilistic inference accounts and that are better accounted for by deterministic accounts (though, of course, the small amount of probabilistic modulation is consistent with probabilistic accounts). Evans et al (1996) presented participants with frequency information about the four truth table rows that are relevant to a conditional assertion, if p then q, manipulating in particular the frequency of the p, q (true antecedent, true consequent) and p, not q (true antecedent, false consequent) cases. The frequency of these cases ranged over five levels, which they presented as follows (see Evans et al, 1996Evans et al, , p. 1093 Participants were asked to indicate on a Ϫ10 (absolutely false) to 10 (absolutely true) scale whether they thought the conditional was true in each case (this task is very similar to the tasks used in Experiments 7 and 8 of the present investigation).…”

“…Evans et al (1996) presented participants with frequency information about the four truth table rows that are relevant to a conditional assertion, if p then q, manipulating in particular the frequency of the p, q (true antecedent, true consequent) and p, not q (true antecedent, false consequent) cases. The frequency of these cases ranged over five levels, which they presented as follows (see Evans et al, 1996Evans et al, , p. 1093 Participants were asked to indicate on a Ϫ10 (absolutely false) to 10 (absolutely true) scale whether they thought the conditional was true in each case (this task is very similar to the tasks used in Experiments 7 and 8 of the present investigation). The proportion of counterexamples did moderate judgments, and participants did not judge conditionals with only a few counterexamples to be absolutely false, which the authors took to support a probabilistic reading of the conditional.…”