Is the truth table task mistaken?

Abstract

There is ample evidence that in classical truth table task experiments false antecedents are judged as “irrelevant”. Instead of interpreting this in support of a suppositional representation of conditionals, Schroyens (2010a, 2010b) attributes it to the induction problem: the impossibility of establishing the truth of a universal claim on the basis of a single case. In the first experiment a truth table task with four options is administered and the correlation with intelligence is inspected. It is observed that “undetermined” is chosen in one third of the judgements and “irrelevant” in another third. A positive correlation is revealed between intelligence and the number of “irrelevant” and “undetermined” judgements. The data do not exclude that a part of the “irrelevant” judgements in classical truth table task experiments might be caused by the induction problem. In the second experiment participants are presented with a simplified four-option truth table task and asked for a justification of their judgements. These justifications show the induction problem is not the reason for choosing the “irrelevant” or “undetermined” option, which is supportive for a suppositional representation of conditionals.

Keywords:

• Conditionals
• Cognitive ability
• Induction problem
• Mental models theory
• Suppositional theory
• Truth table task.

Notes

¹ In the negations paradigm, both the antecedent and the consequent of the conditional rule can contain negated constituents. Within participants, four types of conditional rules are used: “if A then C” (AA), “if A then not-C” (AN), “if not-A then C” (NA) and finally “if not-a then not-C” (NN). For each type of rule, participants have to judge all four situations TT, TF, FT, and FF.

² The fact that the rather subtle manipulation of the wording factor did not yield mean differences does not necessarily imply that correlations are unaffected. Therefore correlations were also computed for each wording group separately. However, the correlational pattern was identical so for the sake of simplicity only the global correlation analysis, conjoining both wording groups, is reported.

³All reported correlations are significant at the .001 level, except for the correlation between APM and “undetermined”, which is significant at the .05 level.

Additional information

Notes on contributors

Aline Sevenants

  This research was carried out with financial support of the OT research project (3H110244) granted to Prof. Dr Walter Schaeken.