The epistemology of modality has focused on metaphysical modality and, more recently, counterfactual conditionals. Knowledge of kinds of modality that are not metaphysical has so far gone largely unexplored. Yet other theoretically interesting kinds of modality, such as nomic, practical, and ‘easy’ possibility, are no less puzzling epistemologically. Could Clinton easily have won the 2016 presidential election—was it an easy possibility? Given that she didn’t in fact win the election, how, if at all, can we know whether she easily could (...) have? This paper investigates the epistemology of the broad category of ‘objective’ modality, of which metaphysical modality is a special, limiting case. It argues that the same cognitive mechanisms that are capable of producing knowledge of metaphysical modality are also capable of producing knowledge of all other objective modalities. This conclusion can be used to explain the roles of counterfactual reasoning and the imagination in the epistemology of objective modality. (shrink)

Kripke models, interpreted realistically, have difficulty making sense of the thesis that there might have existed things that do not in fact exist, since a Kripke model in which this thesis is true requires a model structure in which there are possible worlds with domains that contain things that do not exist. This paper argues that we can use Kripke models as representational devices that allow us to give a realistic interpretation of a modal language. The method of doing this (...) is sketched, with the help of an analogy with a Galilean relativist theory of spatial properties and relations. (shrink)

This article concerns the treatment of propositional quantification in a framework of labelled natural deduction for modal logic developed by Basin, Matthews and Viganò. We provide a detailed analysis of a basic calculus that can be used for a proof-theoretic rendering of minimal normal multimodal systems with quantification over stable domains of propositions. Furthermore, we consider variations of the basic calculus obtained via relational theories and domain theories allowing for quantification over possibly unstable domains of propositions. The main result of (...) the article is that fragments of the labelled calculi not exploiting reductio ad absurdum enjoy the Church–Rosser property and the strong normalization property; such result is obtained by combining Girard’s method of reducibility candidates and labelled languages of lambda calculus codifying the structure of modal proofs. (shrink)

Propositional contingentism is the view that what propositions there are is a contingent matter—certain propositions ontologically depend on objects which themselves only contingently exist. Possible worlds are, loosely, complete ways the world could have been. That is to say, the ways in which everything in its totality could have been. Propositional contingentists make use of possible worlds frequently. However, a neglected, but important, question concerns whether there are any notions of worlds which are both theoretically adequate and consistent with propositional (...) contingentism. Some notion of a possible world is adequate if the systematic connection between, at least, possibility and truth at some possible world holds. Here, I argue that no adequate notion of a possible world is available to at least those who subscribe to one natural formulation of propositional contingentism. I also show that this result contrasts with a simple and adequate definition of a possible world available to the necessitist—those who hold that necessarily everything necessarily exists. (shrink)

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. (shrink)

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 non-technical 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. (shrink)

The models of contingency in what propositions, properties and relations there are developed in Part 1 are related to models of contingency in what propositions there are due to Robert Stalnaker. It is shown that some but not all of the classes of models of Part 1 agree with Stalnaker’s models concerning the patterns of contingency in what propositions there are they admit. Further structural connections between the two kinds of models are explored.

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. (shrink)

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. (shrink)

We consider extending the modal logic KD45, commonly taken as the baseline system for belief, with propositional quantifiers that can be used to formalize natural language sentences such as “everything I believe is true” or “there is something that I neither believe nor disbelieve.” Our main results are axiomatizations of the logics with propositional quantifiers of natural classes of complete Boolean algebras with an operator validating KD45. Among them is the class of complete, atomic, and completely multiplicative BAOs validating KD45. (...) Hence, by duality, we also cover the usual method of adding propositional quantifiers to normal modal logics by considering their classes of Kripke frames. In addition, we obtain decidability for all the concrete logics we discuss. (shrink)

The impossibility theorem of Dekel, Lipman and Rustichini has been thought to demonstrate that standard state-space models cannot be used to represent unawareness. We first show that Dekel, Lipman and Rustichini do not establish this claim. We then distinguish three notions of awareness, and argue that although one of them may not be adequately modeled using standard state spaces, there is no reason to think that standard state spaces cannot provide models of the other two notions. In fact, standard space (...) models of these forms of awareness are attractively simple. They allow us to prove completeness and decidability results with ease, to carry over standard techniques from decision theory, and to add propositional quantifiers straightforwardly. (shrink)