Concessive Knowledge Attributions Cannot Be Explained Pragmatically

“I know that p but it is possible that not-p” sounds contradictory. Some philosophers, notably David Lewis, have taken this as evidence that knowledge requires infallibility. Others have attempted to undermine that inference by arguing that there is a plausible pragmatic explanation of why such sentences sound odd, and thus do not undermine fallibilism. I argue that the proffered pragmatic explanations fail and I raise challenges for any possible pragmatic explanation of the character of concessive knowledge attributions. It is reasonable to conclude that concessive knowledge attributions are genuine contradictions.