Reasoning from or reasoning about beliefs: Truth-based or possibility-based compatibility judgments and Handley et al.’s (2006) litmus test of the suppositional conditional

How do people go about in evaluating the consistency of their beliefs? Do people reason from or do they reason about their beliefs in judging whether they are compatible, or both? The paper investigates how people evaluate belief in contrary conditionals and .  Experiment 1 (N=141) indicates people do not use a notion of possibility-based compatibility according to which claims are compatible when they share a common possibility: After being given this definition, there was no improvement of compatibility judgments even though more than 60% confirmed a shared possibility. Experiment 2 (N = 95) and Experiment 3 (N=93) test the alternative truth-based notion of compatibility, according to which contrary conditionals are incompatible because they cannot be true at the same time. The sets people construct for a true conditional invariably include “A and C” cases (Experiment 2) and “if A then C” is judged “un-assertable” about sets that do no include such cases (Experiment 3). Such “A and C” cases are at the same time impossible when  "if A then not-C" is true. Findings thus suggest contrary conditionals are judged incompatible because they cannot be true at the same time.