 We could use the word “valid” in such a way that an argument is valid provided it preserves certainty. If our interest in logic is confined to its application to mathematics or other a priori matters, that is fine. Further, when our arguments do not contain conditionals, if we have certainty-preservation, probability-preservation comes free. But if we use conditionals when arguing about contingent matters, then great caution will be required. Unless we are 100% certain of the premises, the arguments above which are invalid on Adams’s criterion guarantee nothing about what you are entitled to think about the conclusion. The line between 100% certainty and something very close is hard to make out: it’s not clear how you tell which side of it you are on. The epistemically cautious might admit that they are never, or only very rarely, 100% certain of contingent conditionals. So it would be useful to have another category of argument, the “super-valid”, which preserves high probability as well as certainty. Adams has shown us which arguments (on Supp’s reading of “if”) are super-valid.