What does it mean to deny the conditional statement, "if you steal an apple, you go to jail"? One theory argues that, because conditionals are probabilistic, their denials are too. And so the conditional probability, P(not-jail | steal-apple), best describes a conditional denial. Another theory argues that conditional denials concern possibilities, i.e., they activate imagined situations in which you cheat on your taxes but don’t go to jail. The two accounts make diverging predictions: only the latter predicts that people should assess conditionals and their denials as mutually inconsistent. Two experiments corroborate the possibility-based account: the studies show that both in implicit and explicit evaluations of consistency, conditional denials conflict with the conditionals they deny.

This paper explores the dual meaning of counterfactual conditionals, such as ‘if there had been gloves, then therewould have been scarves’, by tracking the temporal course to envisage the possibility corresponding to the conjecture ‘therewere gloves and there were scarves’ and the presupposed facts, ‘there were no gloves and there were no scarves’. To testthis, we used the visual world paradigm, in which counterfactual and indicative conditionals were heard while four imagescorresponding to the conjecture, such as an image of gloves and scarves, and the presupposed facts, such as an image of nogloves and no scarves, and two distractors were shown on the screen and eye movements were monitored. We found thatpeople looked at the affirmative image in the indicative conditional, and both types of images (affirmative and negative) in thecounterfactual conditional. Results support the dual meaning of counterfactuals.