Truth table tasks: Irrelevance and cognitive ability

Abstract

Two types of truth table task are used to examine people's mental representation of conditionals. In two within-participants experiments, participants either receive the same task-type twice (Experiment 1) or are presented successively with both a possibilities task and a truth task (Experiment 2). Experiment 3 examines how people interpret the three-option possibilities task and whether they have a clear understanding of it. The present study aims to examine, for both task-types, how participants' cognitive ability relates to the classification of the truth table cases as irrelevant, and their consistency in doing so. Looking at the answer patterns, participants' cognitive ability influences their classification of the truth table cases: A positive correlation exists between cognitive ability and the number of false-antecedent cases classified as “irrelevant”, both in the possibilities task and the truth task. This favours a suppositional representation of conditionals.

Keywords:

• Conditionals
• Cognitive ability
• Mental model accounts
• Suppositional theory
• Truth table task

Acknowledgments

This research was carried out with the financial support of the National Council for Scientific Research – Flanders, Belgium (FWO grant G.0320.05) and the Odysseus Type 1 project granted to Prof. Dr I. Douven. We thank David Over, Pierre Barrouillet, and an anonymous reviewer for their helpful comments on this manuscript. We are also grateful to Jean-François Bonnefon and Klaus Oberauer for their inspiring suggestions.

Notes

¹Note that the participants are asked to judge the cards based on a rule, e.g., “If there is an A on the front, there is a 2 on the back of the card”. They have to assume that the machine produces the cards following this rule; however, it is never explicitly mentioned to the participants that they have to consider this rule to be “true”. The conditional rule is thus presented as “given that if p then q” and not as “given that if p then q is true”. This is an important difference, hinging on the distinction between the pleonastic use of “true” as is the case in the present study, and its use to refer to an objective state of affairs (see also Adams, 1998; Douven & Verbrugge, 2010; Edgington, 2003; Politzer et al., 2010).