Conditional reasoning processes in a logical deduction game

Abstract

Two experiments examined the role of conditional reasoning in the logical deduction game, Mastermind. An analysis suggested that Modus Tollens (MT) reasoning could be used to determine the code structure, for example, in determining if any of the colours in the code are repeated. Consistent with this analysis, Experiment 1 showed that only MT errors are correlated with the number of hypotheses advanced in Mastermind. A subsequent analysis showed that conditional reasoning such as Affirming the Consequent (AC) and Denying the Antecedent (DA) could lead to particularly damaging inferences only when the code was four different colours. When that was known before play, Experiment 2 showed that AC errors, but not MT errors, were significantly correlated with Mastermind hypotheses advanced. A stepwise multiple regression analysis supported these findings: When the solvers knew they were playing a four-colour code, there was a slight diminution in the variance explained by MT errors, and a significant increase in the variance explained by AC errors. An analysis of the number of different possible codes that could be consistent with hypotheses actually played showed that the number of such codes is far fewer when the code consists of four different colours than when its structure is not known. This analysis suggests that reasoners are therefore unlikely to discover many alternative causes for the feedback given when the code consists of four different colours, and it is under these conditions that humans are most likely to engage in AC reasoning.