Robert Brandom holds that what we mean is best understood in terms of what inferences we are prepared to defend, and that such a defence is best understood in terms of rule-governed social interactions. This manages to explain quite a lot. However, for those who think that there is more to making correct/incorrect inferences than obeying/breaking accepted rules, Brandom’s account fails to adequately capture what it means to reason properly. Thus, in an effort to sketch an alternative that does not (...) rely primarily on peer pressure, I draw on the work of C. S. Peirce. Peirce argued that, when we reason, we manipulate abstract diagrams in order to observe what results. Since some manipulations are barred by the self-same nature of the diagrams, I try to show that this qualitative incompatibility, which I dub “contrapiction,” is a good reason to regard some reasoning as bad. (shrink)