Two programs in epistemology were born in the early sixties but raised separately.  The epistemic utility program was ushered into the world in 1960 by Carl Hempel (in “Inductive inconsistencies”), and the truthlikeness program in 1963 by Karl Popper (in Conjectures and Refutations).  Methodologically these two philosophers were at odds—one a probabilist and the other a falsificationist—but they shared a number of important assumptions.  Both assumed that truth, or the truth, is the goal of inquiry, and that some stages in an inquiry, though falling short of perfectly fulfilling this goal, may be do a better job of fulfilling it than others. That is, some propositons are closer to the truth than others, and some credal states that take propositions as objects have greater epistemic utility.  Those working in the truthlikeness program (TL) were after a measure of the distance of propositions from the whole truth of some matter, while those working in  the epistemic utility program (EU) were seeking a measure of the epistemic utility of different credal states.  On the face of it these two programs are attempting to solve roughly the same problem—that of characterizing the value of cognitive states with respect to the aim of truth. But are the two programs compatible?  In this paper I outline an intuitively compelling constraint on the notion of closeness to the truth—the proximity constraint. This arose very naturally within the TL program, and it has been endorsed by every minimally adequate proposal within that program. No matter how much they might bicker and disagree about other matters TL theorists seem unanimously to endorse the proximity constraint.  It is a constraint on the closeness to truth of propositions, but it generalizes simply and elegantly to an equally intuitive constraint on the value of credal states.  Even though EU theorists have not articulated the proximity constraint precisely,  some have intimated that something in the ball-park needs to be respected by a measure of cognitive value.  What I show is that the most celebrated measures of epistemic utility  — namely, the Brier measures  — cannot capture this very simple and intuitively obvious proximity constraint.  Many take the Brier measure to be the clearest example of an adequate measure of epistemic utility, and some even argue that they are singled out by desiderata that any measure of epistemic value should satisfy (cosntraints such as propriety, additivity, and convexity).  So at a minimum the proximity constraint shows that those desiderata cannot be jointly satisfied. Thus some of those desiderata have to be jettisoned. I finish with what seem to me to be the most promising responses to the incompatiblity proof.