Grades of Essentialism in Quantified Modal Logic

W. V. Quine distinguishes three grades of modal involvement.2 The first grade occurs when predicates like analytic are appended to names of sentences. The second occurs when a word like necessarily is used within sentences as an operator. And the third occurs as soon as this necessity operator is allowed to precede open sentences containing variables which are bound by quantifiers which precede the operator. This third grade of modal involvement, Quine says, commits one to Aristotelian essentialism3-a philosophically suspect doctrine. From this ground, Quine launches an attack on the meaningfulness of a quantified modal logic which permits modal operators to intermingle with quantifiers. The structure of his attack is this: (i) quantified modal logic permits quantifiers outside of a modal operator to bind variables within the scope of that operator (i.e., we have the third grade of modal involvement); (ii) therefore quantified modal logic is committed to Aristotelian essentialism; (iii) but there are insuperable difficulties in making sense of Aristotelian essentialism; so (iv) there are insuperable difficulties in making sense of quantified modal logic.4