Essence and explanation: a logical mismatch

Let Essentialism be the view that at least some object has at least some property essentially. And let Relative Essentialism be the view that Essentialism is true, but that for any object that has any property essentially, it has it essentially only relative to the value of some parameter. Meghan Sullivan has recently put forward a promising new version of Relative Essentialism, according to which the relevant parameter is an explanatory framework. We argue that despite its promise, Sullivan's version unfortunately fails, due to the mismatch between the logic of essentiality and the logic of explanation.