 Next, given a credence function \(c\) and a world \(w\), the perfectly calibrated counterpart of \(c\) at \(w\) is a credence function also defined on \(\mathcal{F}\) that is defined as follows: for each \(A\) in \(\mathcal{F}\)   \[c^w(A) = \mathrm{Freq}(\mathcal{F}, A, \sim_c, w)\]   That is, the perfectly calibrated counterpart of \(c\) at \(w\) assigns to each proposition \(A\) the frequency of truths at \(w\) amongst all propositions to which \(c\) assigns the same credence that it assigns to \(A\). Note that \(c^w\) is perfectly calibrated at \(w\). And if \(c\) is perfectly calibrated at \(w\), then \(c^w = c\). Now, we define the distance that a credence function \(c\) lies from calibration at a world \(w\) to be the distance, \(\mathfrak{D}(c^w, c)\), from \(c^w\) to \(c\). Now, as we saw in Objection 1 from  section 4.3  above, this measure does not itself give a measure of epistemic disutility. The problem is that an agent can move closer to calibration at a world \(w\) while moving uniformly further from the omniscient credence function at that world: that is, the measure of epistemic disutility provided by the distance of the credence function from its perfectly calibrated counterpart is not truth-directed. Thus, if an agent’s distance from her perfectly calibrated counterpart is to contribute to a measure of her inaccuracy, it must be supplemented by something that ensures that the resulting measure avoids this consequence. The idea that Pettigrew proposes is this: the inaccuracy of \(c\) at \(w\) is given by the distance of \(c\) from the omniscient credence function \(v_w\) at \(w\); and that is given by adding the distance of \(c\) from its perfectly calibrated counterpart \(c^w\) to the distance of \(c^w\) from \(v_w\). Thus, while moving to a credence function that is closer to its perfectly calibrated counterpart may move you further from the omniscient credence function, this can only be because the perfectly calibrated counterpart of your new credence function is further from the omniscient credence function than the perfectly calibrated counterpart of your current credence function. If their perfectly calibrated counterparts are the same, or if they are different but equally close to the omniscient credence function, then moving closer to them will move you closer to the omniscient credence function. Thus, Pettigrew imposes the following constraint: