 The oddities are harder to tolerate when we consider conditional judgements about empirical matters. The difference is this: in thinking about the empirical world, we often accept and reject propositions with degrees of confidence less than certainty. “I think, but am not sure, that \(A\)” plays no central role in mathematical thinking. We can, perhaps, ignore as unimportant the use of indicative conditionals in circumstances in which we are certain that the antecedent is false. But we cannot ignore our use of conditionals whose antecedent we think is likely to be false. We use them often, accepting some, rejecting others. “I think I won’t need to get in touch, but if I do, I shall need a phone number”, you say as your partner is about to go away; not “If I do I’ll manage by telepathy”. “I think John spoke to Mary; if he didn’t he wrote to her”; not “If he didn’t he shot her”. Hook’s theory has the unhappy consequence that all conditionals with unlikely antecedents are likely to be true. To think it likely that \({\sim}A\) is to think it likely that a sufficient condition for the truth of “\(A \supset B\)” obtains. Take someone who thinks that the Republicans won’t win the election \(({\sim}R)\), and who rejects the thought that if they do win, they will double income tax \((D)\). According to Hook, this person has grossly inconsistent opinions. For if she thinks it’s likely that \({\sim}R\), she must think it likely that at least one of the propositions, \(\{{\sim}R, D\}\) is true. But that is just to think it likely that \(R \supset D\). (Put the other way round, to reject \(R \supset D\) is to accept \(R \amp{\sim}D\); for this is the only case in which \(R \supset D\) is false. How can someone accept \(R \amp{\sim}D\) yet reject \(R\)?) Not only does Hook’s theory fit badly the patterns of thought of competent, intelligent people. It cannot be claimed that we would be better off with \(\supset\). On the contrary, we would be intellectually disabled: we would not have the power to discriminate between believable and unbelievable conditionals whose antecedent we think is likely to be false.