Faced with extreme demands, hypothetical thinking runs the danger of total failure. Paradoxical propositions such as the Liar ("I am lying") provide an opportunity to test it to its limits, while the Liar's nonparadoxical counterpart, the Truthteller ("I am telling the truth"), provides a useful comparison. Two experiments are reported, one with abstract materials ("If I am a knave then I live in Emerald City") and one with belief-laden materials (a judge says: "If I am a knave then I enjoy pop music"). In both experiments, conditionals with Truthteller-type antecedents were "collapsed" to responses of conditional probability closely resembling estimates of control items. Liar-type antecedents, in contrast, dramatically weakened belief in conditionals in which they were embedded. The results are discussed in the framework of the theory of hypothetical thinking.