 I turn to various objections to Carnap’s program that have been offered in the literature, noting that this remains an area of lively debate. (See Maher (2010) for rebuttals of some of these objections and for defenses of the program.) Firstly, is there a correct setting of \(\lambda\), or said another way, how ‘inductive’ should the confirmation function be? The concern here is that any particular setting of \(\lambda\) is arbitrary in a way that compromises Carnap’s claim to be offering a logical notion of probability. Also, it turns out that for any such setting, a universal statement in an infinite universe always receives zero confirmation, no matter what the (finite) evidence. Many find this counterintuitive, since laws of nature with infinitely many instances can apparently be confirmed. Earman (1992) discusses the prospects for avoiding the unwelcome result.