Often we have coarsely grained knowledge: for example, we know about how many people are present. In possessing such knowledge, we also have finer grained knowledge of what is not: there certainly is nothing like that number of people here. The combination of such knowledge types, through sorites, generates contradiction and bafflement. This paper seeks to resolve the bafflement: it rejects a Timothy Williamson proposal, introduces muddle numbers and inference gaps, and shows how the different grains of knowledge do not (...) always meet. In so doing, the paper identifies a distinctive first‐person inferring. (shrink)