Robert Trueman

Contingentists—who hold that it is contingent what there is—are divided on the claim that having a property or standing in a relation requires being something. This claim can be formulated as a natural schematic principle of higher-order modal logic. On this formulation, I argue that contingentists who are also higher-order contingentists—and so hold that it is contingent what propositions, properties and relations there are—should reject the claim. Moreover, I argue that given higher-order contingentism, having a property or standing in a relation does not even require possibly being something.

This book develops an argument for a foundational theory of modality using higher-order logic. The use of higher-order logic in metaphysics is motivated, and a particular higher-order logic is introduced. Fine-grained theories of propositional individuation are shown to be problematic, and a course-grained theory of propositional individuation is defended. On the basis of this theory, it is argued that the metaphysical necessities can be delineated using purely logical terms; by adding an actuality operator, it is shown that the logic of metaphysical necessity is S5. The theoretical role of possible worlds is articulated, and shown to be satisfied by maximal propositions if it satisfied by anything; the existence of such maximal propositions is demonstrated using plural propositional quantification. The resulting theory reduces metaphysical modal terms to higher-order logical terms, and thereby vindicates a widespread modal conception of metaphysics.