A number of inference patterns involving epistemic modalities, including Modus Ponens, display a split behavior. They seem valid by the lights of all-or-nothing judgments: whenever the premises are accepted as true, the conclusion must be accepted as true as well. But they seem invalid by the lights of probabilistic judgments: we can specify intuitive credal assignments where the drop in probability between premises and conclusions is incompatible with validity. I suggest that we explain this asymmetry by endorsing two bridge principles between logical notions and rational constraints on attitudes. The first links a notion of classical consequence to rational constraints on probabilistic states. The second links a broadly dynamic notion of consequence (so-called informational consequence) to rational constraints on acceptance. In existing literature, classical and informational consequence are seen as alternatives; I argue instead that we can and should have both.