The monotonicity of essence

Kit Fine’s logic of essence and his reduction of modality crucially rely on a principle called the ‘monotonicity of essence’. This principle says that for all pluralities, xx and yy, if some xx belong to some yy, then if it is essential to xx that p, it is also essential to yy that p. I argue that on the constitutive notion of essence, this principle is false. In particular, I show that this principle is false because it says that some propositions are essential to yy even though those propositions are only about some of its members. I then consider modifications to the principle appealing to consequential essence and argue that such a modification is inconsistent with a central desideratum of Fine’s approach to metaphysics, what I call his neutrality condition.