 How does measuring coherence this way vindicate Shogenji’s reply to Klein &amp; Warfield, that the increase in the detective’s coherence is outweighed by an increase in the strength of her beliefs? The denominator in the formula for \(\textit{coh}\) tracks strength: the more propositions there are, and the more specific they are, the smaller this denominator will be. So if we compare two belief-sets with the same strength, their denominators will be the same. Thus, if one is more coherent than the other, it must be because its numerator is greater. Thus coherence increases with overall probability, provided strength is held constant. Since in the detective’s case overall probability does not increase despite the increase in coherence, it must be because the strength of her commitments had an even stronger influence.