First, I will review some historical examples that appear to be cases of knowledge obtained via deductive inference from premises (some of) which are false. Then, I will discuss some recent analyses of such cases, with an emphasis on the precise role that the false beliefs play in the acquisition of inferential knowledge. Finally, I will offer some new examples which seem to (a) bolster the role played by the false premises, and (b) call into question some of the recent analyses of such cases. My emphasis in this talk will be on (rather simple) cases involving deductive inference. This is just "Part I" of a larger project, which also includes inductive inferential knowledge from falsehood, and -- more generally -- inferential knowledge from true premises which are not known (and, even more generally, cases in which the knowledge in question may even be non-empirical).