A Probabilistic Interpretation of “If-Then”

Abstract

This study proposes that subjects interpret thematic conditionals (“if p then q”) probabilistically in solving conditional reasoning problems. Experiment 1 found that subjects’ correct responses increased with the perceived probability of q, given p for each of the four forms of conditional arguments: modus ponens (MP), modus tollens (MT), denial of the antecedent (DA), and affirmation of the consequent (AC). Experiment 2 ruled out two alternative explanations based on the comprehensibility of conditionals and on subjects interpreting conditionals as biconditionals. In Experiment 3, subjects solved two types of problems: (a) complete probabilistic problems, such as “If p then q; knowing p; how probable is q?”, and (b) reduced probabilistic problems, such as “Knowing p; how probable is q?” Two sources of information that determine the observable reasoning responses are identified. One source of information is based on one's general knowledge, and another is based on taking all premises into account.