This chapter applies probabilistic techniques to reconsider the acceptability of different kinds of appealing, but supposedly logically fallacious arguments, arguing, for example, that circular arguments need not always be ‘vicious'. It reviews recent work on the classic fallacy of the ‘argument from ignorance’. This fallacy can be given a formal, Bayesian treatment, which suggests that there is nothing structurally amiss with arguments from ignorance, rather they are differentially strong or weak as a function of their specific content, that is, the specific probabilistic quantities involved. It re-examines the relative strength of such inferences and seeks to clarify the role of two widely cited mechanisms in language acquisition, pre-emp...