Higher-Order Contingentism, Part 1: Closure and Generation

Abstract

This paper is a study of higher-order contingentism -the view, roughly, that it is contingent what properties and propositions there are. We explore the motivations for this view and various ways in which it might be developed, synthesizing and expanding on work by Kit Fine, Robert Stalnaker, and Timothy Williamson. Special attention is paid to the question of whether the view makes sense by its own lights, or whether articulating the view requires drawing distinctions among possibilities that, according to the view itself, do not exist to be drawn. The paper begins with a nontechnical exposition of the main ideas and technical results, which can be read on its own. This exposition is followed by a formal investigation of higher-order contingentism, in which the tools of variable-domain intensional model theory are used to articulate various versions of the view, understood as theories formulated in a higher-order modal language. Our overall assessment is mixed: higher-order contingentism can be fleshed out into an elegant systematic theory, but perhaps only at the cost of abandoning some of its original motivations.

Counterfactuals and Propositional Contingentism

“…So Stalnaker denies that there actually are any propositions that distinguish between them, such as the proposition that both are flipped and only x lands heads. A similar picture is developed in Fine (1977b), see Fritz and Goodman (2016) for an extended investigation of such views. Stalnaker (1968 has also been a prominent defender of the principle of conditional excluded middle for natural language conditionals, according to which negating a nonvacuous conditional is equivalent to negating its consequent.…”

“…However, it is valid on the subclass of equivalence systems that are coherent in the sense described in §8.1. This coherence constraint is developed in Fritz (2016) on the basis of work in Stalnaker (2012, Appendix A); as shown in Fritz (forthcoming), the resulting class of structures is equivalent to the propositional fragment of the more general model theory of Fine (1977b), as well as several variants discussed in Fritz and Goodman (2016). §2.…”

“…Rather, the interpretation of the counterfactual conditional is left completely unconstrained in order to show that our results require no further model-theoretic assumptions. For explorations of models of higher-order logic with variable domains for all syntactic types, see Fritz and Goodman (2016).…”

An Argument For Necessitism*

“…It is worth noting that the most systematic developments of contingentism have been in a Booleanist setting (e.g., Fine () and Williamson (), although see Fritz and Goodman (, section 3.4) for a way in which non‐Booleanists might reinterpret such theories) and that many contingentists are in fact Booleanists (e.g., Stalnaker (), Rayo (), and Bacon (forthcoming)). So the appeal to Booleanism in the above argument for adjunction does not beg the question against contingentism.…”

Higher-Order Contingentism, Part 2: Patterns of Indistinguishability

“…Part 1 (Fritz and Goodman, 2016) explores models for the view that it is a contingent matter what propositions, properties and relations there are, building on work by Fine (1977) and Stalnaker (2012). Stalnaker (2012, Appendix A) focuses in particular on the view that it is a contingent matter what propositions there are, and develops two kinds of models for it.…”