 The truth-functional, material conditional turns out to be useful here. The suppositional conditional entails the truth-functional conditional. Zack is committed to “Pete called \(\supset\) Pete won”, i.e., either Pete didn’t call, or he won. Jack is committed to “Pete called \(\supset\) Pete lost”, i.e., either Pete didn’t call, or he lost. From both, it straightforwardly follows that Pete didn’t call. The truth-functional conditional is the strongest proposition which gets transmitted by conditional testimony. Testimony, at its best, concerns the transmission of facts; and we can always resort to the truth-functional conditional as a fact that gets transmitted by a reliable conditional statement, when problems arise from the differing background knowledge of our informants (as suppositionalists can agree). 