It is widely accepted that knowledge is factive, but two different understandings of “factivity” should be distinguished, namely, the implication version and the presupposition version. While the former only takes the truth of P as a necessary requirement for “S knows that P,” the latter considers it also necessary for “S does not know that P.” In this paper, I argue against presupposition and defend implication. More specifically, I argue against Wang and Tai’s defense of the presupposition version as presented in a recent paper and propose a pragmatic response to the “persistence problem” of implication. In other words, my positive proposal is an account of implication plus pragmatic implicature. To conclude, I use my version to analyze Wang and Tai’s distinction between inner skepticism and outer skepticism. My conclusion is that, after abandoning presupposition, we can identify two types of intermediate skepticism between Wang and Tai’s inner and outer skepticism.