On the standard interpretation of Lewis's criticism of Russell, Lewis takes his own account of strict implication to be more intuitive than the paradoxes to which Russell's material implication leads. This chapter argues against the standard interpretation by showing that Russell's views are not counterintuitive, but that appeals to "intuition" are not the substance of Lewis's criticism of Russell. Lewis's debate with Russell undergoes two main phases. In the first phase, Lewis argues both that the logic of material implication fails to represent correctly the distinction between correct and incorrect inferences and that the logic of material implication is not useful. In the second phase, Lewis argues that Russell's explication of implication neither coheres fully with Russell's deductive practices nor can Russell avoid appealing to strict implications. A better understanding of the Russell-Lewis dispute points to a conception of the nature of logic: it must be possible for logical principles to play a practical role in reasoning, else logic becomes disconnected from rational thought and discourse.