Effects of context on the rate of conjunctive responses in the probabilistic truth table task

ABSTRACT

The probabilistic truth table task involves assessing the probability of "If A then C" conditional sentences. Previous studies have shown that a majority of participants assess this probability as the conditional probability P(C│A) while a substantial minority responds with the probability of the conjunction A and C. In an experiment involving 96 participants, we investigated the impact on the rate of conjunctive responses of the context in which the task is framed. We show that a context intended to lead participants to consider all the possible cases (i.e. the throw of a die known to allow six possibilities) elicited more conjunctive responses than a context assumed not to have this effect (an unfamiliar deck of cards). These results suggest that the step of inferring the probability can distort our assessment of participants' interpretation of conditional sentences. This might compromise the validity of the probabilistic task in studying conditional reasoning.

KEYWORDS:

• Conditional reasoning
• probabilistic truth table task
• context effect

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ According to Johnson-Laird and Byrne (2002), basic conditionals are conditionals in which the antecedent and the consequent have no semantic or referential relations, or relations based on knowledge.

² Truth table tasks are tasks in which participants are asked to assess the truth-value of a connective for each logical case.

³ To circumvent this potential difficulty, Pfeifer (2013) suggests prompting participants to evaluate to what degree the conditional “holds” instead of to what degree it is “true”. We did not follow this advice because we found impossible to accurately translate “holds” in French. Moreover, it does not seem that the use of “holds” has a strong impact on the rate of conjunctive responses.

⁴ Biconditional and material implication responses correspond to P(A & C) + P(¬A & ¬C) and P(A & C) + P(¬A & ¬C) + P(¬A & C), respectively.

⁵ Overall, 28% of our participants shifted toward a conditional interpretation. Among them, 78% exhibited a conjunctive modal response before shifting. Besides, 7% of our participants shifted toward a conjunctive interpretation, 29% of them did so from a conditional modal response.

⁶ We thank an anonymous reviewer for making us aware of this possibility.

Additional information

Funding

This research was supported by the Swiss National Science Foundation [grant number 100014_159394] to Pierre Barrouillet.