 By a different argument, David Lewis (1976) was the first to prove this remarkable result: there is no proposition \(A*B\) such that, in all probability distributions, \(\mathbf{p}(A*B) = \mathbf{p}_A (B)\). Conditional probability does not measure the probability of the truth of any proposition. If a conditional has truth conditions, one should believe it to the extent that one thinks it is probably true. If Supp is correct, that one believes “If \(A, B\)” to the extent that one thinks it probable that \(B\) on the supposition that \(A\), then this is not equivalent to believing some proposition to be probably true. Hence, it appears, if Supp is right, conditionals shouldn’t be construed as having truth conditions at all. A conditional judgement involves two propositions, which play different roles. One is the content of a supposition. The other is the content of a judgement made under that supposition. They do not combine to yield a single proposition which is judged to be likely to be true just when the second is judged likely to be true on the supposition of the first.