Triviality Results for Probabilistic Modals
In recent years, a number of theorists have claimed that beliefs about probability are transparent. To believe probably p is simply to have a high credence that p. These same theorists have also defended non-factualist theories of probabilistic modals. On this view, probabilistic sentences do not express propositions; rather, they are semantically associated with sets of probability functions. But what exactly is the connection between transparency and nonfactualism? In this paper, I prove a triviality result for probabilistic modals. If these modals satisfy transparency, then they cannot express propositions: they must be nonfactual. However, there is a problem for nonfactualism. I formulate another version of transparency as a principle governing the logic of the probabilistic modal n% likely. I then prove some impossibility results, showing that this second transparency thesis is incompatible with n% likely obeying the probability calculus.
forthcoming in Philosophy and Phenomenological Research | draft
Believing Epistemic Contradictions
What is it to believe something might be the case? We raise a challenge for standard answers to this question. We begin by developing a new puzzle involving belief, epistemic modals, and certainty. After showing that standard treatments of beliefs involving epistemic modals fail to resolve our puzzle, we propose our own solution, which integrates a Bayesian approach to belief with a dynamic semantics for epistemic modals. We go on to investigate a surprising consequence of our solution to the puzzle: virtually all of our beliefs about what might be the case provide counterexamples to the view that rational belief is closed under logical implication.
forthcoming in The Review of Symbolic Logic
coauthored with Bob Beddor | draft
A Preface Paradox for Intention
In this paper I argue that there is a preface paradox for intention. The preface paradox for intention shows that intentions do not obey an agglomeration norm. But what norms do intentions obey? I argue that intentions come in degrees. These `partial' intentions are governed by the norms of the probability calculus. First, I give a dispositional theory of partial intention. Dispositions come in degrees. Intentions are dispositions. So the degree to which you intend to A is simply the degree to which you possess the dispositions characteristic of intending to A. Second, I use this theory to defend probabilism about intentions. Intentions involve some degreed dispositions. Degrees can be ordered from 0 to 1. So an agent's degree of dispositions involved in Aing can satisfy the probability calculus. I show that if they do not, the agent is irrational. But this argument assumes my particular theory of partial intention. One might look for a more general approach. In the rest of the paper, I offer a decision theoretic argument for probabilism about intentions. I show that if an agent's partial intentions do not satisfy the probability calculus, then she violates a variety of plausible decision theoretic norms. These arguments extend `epistemic utility' theory from beliefs to intentions.
Philosophers' Imprint 2016 | final version
work in progress
The Counterfactual Direct Argument
In this paper, I present a new principle in the logic of conditionals. I argue that if A, then B or C entails if A, then if not B then C. In particular, I argue that this principle holds for subjunctive conditionals. I then prove several collapse theorems, demonstrating that if either disjunction introduction or modus ponens hold in addition to sda, then the subjunctive and material conditionals are equivalent. To solve these problems, I propose a new semantics for disjunction and the conditional. This semantics has two main ideas. The first idea is that disjunctions presuppose that their disjuncts are unsettled, where a claim is unsettled iff both it and its negation are possible. The second main idea is that subjunctive conditionals are dynamic, strict conditionals. They operate on a body of information and require that no world in that body of information is one where the antecedent is true and the consequent is false. Crucially, however, subjunctive conditionals place requirements on a different body of information than non-modal claims do.draft