This study on conditional relations examines two kinds of background knowledge that influence interpretations of `if-then' conditionals asserting a causal relation between an antecedent and a consequent: the presence of contextual assertions affirming or denying the existence of alternative plausible causes, and the extremity or rarity of the consequent event. Both major hypotheses got substantial support in a conditional reasoning task. An innovative analytic method is also used to reveal subjects' systematic tendencies to apparent logical self-contradiction, which may be associated with pragmatic factors.