The 'modus ponens' is, along with 'modus tollens' and the two logically not valid counterparts 'denying the antecedent' and 'affirming the consequent', the argument form that was most often investigated in the psychology of human reasoning. The present contribution reports the results of three experiments on the probabilistic versions of 'modus ponens' and 'denying the antecedent'. In probability logic these arguments lead to conclusions with imprecise probabilities. In the 'modus ponens' tasks the participants inferred probabilities that agreed much better with the coherent normative values than in the 'denying the antecedent' tasks, a result that mirrors results found with the classical argument versions. For 'modus ponens' a surprisingly high number of lower and upper probabilities agreed perfectly with the conjugacy property (upper probabilities equal one complements of the lower probabilities). When the probabilities of the premises are imprecise the participants do not ignore irrelevant ('silent') boundary probabilities. The results show that human mental probability logic is close to predictions derived from probability logic for the most elementary argument form, but has considerable difficulties with the more complex forms involving negations.
Keywords. mental probability logic, modus ponens, coherence, imprecise probabilities
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Authors addresses:
Niki Pfeifer
Department of Psychology
University of Salzburg
Hellbrunnerstrasse 34
A-5020 Salzburg
Gernot Kleiter
Institut für Psychologie Universität Salzburg
Hellbrunnerstr. 34,A-5020,Salzburg,
Austria
E-mail addresses:
| Niki Pfeifer | niki.pfeifer@sbg.ac.at |
| Gernot Kleiter | gernot.kleiter@sbg.ac.at |
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