Peter Fritz

This article explores the connection between two theses: the principle of conditional excluded middle for the counterfactual conditional, and the claim that it is a contingent matter which (coarse grained) propositions there are. Both theses enjoy wide support, and have been defended at length by Robert Stalnaker. We will argue that, given plausible background assumptions, these two principles are incompatible, provided that conditional excluded middle is understood in a certain modalized way. We then show that some (although not all) arguments for conditional excluded middle can in fact be extended to motivate this modalized version of the principle.

Robert Stalnaker has recently advocated propositional contingentism, the claim that it is contingent what propositions there are. He has proposed a philosophical theory of contingency in what propositions there are and sketched a possible worlds model theory for it. In this paper, such models are used to interpret two propositional modal languages: one containing an existential propositional quantifier, and one containing an existential propositional operator. It is shown that the resulting logic containing an existential quantifier is not recursively axiomatizable, as it is recursively isomorphic to second-order logic, and a natural candidate axiomatization for the resulting logic containing an existential operator is shown to be incomplete.

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.

Propositional modal logic over relational frames is naturally extended with propositional quantifiers by letting them range over arbitrary sets of worlds of the relevant frame. This is also known as second-order propositional modal logic. The propositionally quantified modal logic of a class of relational frames is often not axiomatizable, although there are known exceptions, most notably the case of frames validating the strong modal logic$\mathrm {S5}$. Here, we develop new general methods with which many of the open questions in this area can be answered. We illustrate the usefulness of these methods by applying them to a range of examples, which provide a detailed picture of which normal modal logics define classes of relational frames whose propositionally quantified modal logic is axiomatizable. We also apply these methods to establish new results in the multimodal case.

A significant part of Kit Fine’s work in metaphysics assumes a very fine-grained individuation of propositions and facts. This article discusses how such fine distinctions lead to inconsistency in ways which are similar to the inconsistency of naive set comprehension. The case of constraints on individuation arising from a relation of metaphysical ground will be considered in particular. Fine has developed a view of sets in response to the inconsistency of naive set comprehension according to which sets are postulated, and so form a merely potential hierarchy. This article explores what an analogous potentialist response might look like in the case of finely distinguished propositions and facts, and applies the resulting view to the case of metaphysical grounding. A potentially problematic feature of the view is highlighted, which is that it is unclear how it might allow one to formulate in suitable generality the claim that grounding is a well-founded relation among possible propositions.