 Here is Gibbard’s example: two henchmen, Zack and Jack, observe a poker game, between Sly Pete and Mr Stone. Zack sees Stone’s hand, and signals its contents to Pete. He knows that Pete won’t call unless he has the winning hand. Jack sees both hands, and sees that Pete does not have the winning hand. The room is cleared. Outside, Zack hands a note to the boss which says “If Pete called, he won”. Jack hands a note to the boss which says “If Pete called, he lost”. Boss trusts them both, and concludes that Pete did not call. But Boss cannot simply take over both conditionals as suppositional judgements on the supposition that Pete called: if one gets a high value, the other gets a low value. (Nor can Boss think that in the nearest world in which Pete called, he lost and he won.) Williamson has several variants of examples of this structure. (As some have pointed out, Gibbard’s example is perhaps not perfectly symmetric, as Jack’s judgement might seem the most securely based; but plenty of perfectly symmetric examples have since been given.) 