Suppose you’re certain that a claim—say, ‘Frida is tall’—does not have a determinate truth value. What attitude should you take towards it? This is the question of the cognitive role of indeterminacy. This paper presents a puzzle for theories of cognitive role. Many of these theories vindicate a seemingly plausible principle: if you are fully certain that A, you are rationally required to be fully certain that A is determinate. Call this principle ‘Certainty’. We show that Certainty, in combination with (...) some minimal side premises, entails a very implausible claim: whenever you’re certain that it’s indeterminate whether A, it is rationally required that you reject A. This is a surprising result, which requires abandoning at least some intuitive views about indeterminacy and cognitive role. (shrink)

On an influential line of thinking tracing back to Ramsey, conditionals are closely linked to the attitude of supposition. When applied to counterfactuals, this view suggests a subjunctive version of the so-called Ramsey test: the probability of a counterfactual If A, would B ought to be equivalent to the probability of B, under the subjunctive supposition that A. I present a collapse result for any view that endorses the subjunctive version of the Ramsey test. Starting from plausible assumptions, the result (...) shows that one’s rational credence in a would-counterfactual and in the corresponding might-counterfactual have to be identical. (shrink)

I generalize the notion of a conditional attitude by bringing together two topics of inquiry. One is the ordinary inquiry into conditional attitudes. The other topic is the inquiry into the attitude of thinking that a proposition is likely, or having a high credence in a proposition. For instance, what is it to intend to go to the game if it is likely that Kershaw pitches? Being likely that Kershaw pitches is the condition of the attitude. Given a natural position (...) about statements like “It is likely that Kershaw pitches,” the target attitude looks different from ordinary conditional attitudes. (shrink)

Counterfactual scepticism holds that most ordinary counterfactuals are false. The main argument for this view appeals to a ‘chance undermines would’ principle: if ψ would have some chance of not obtaining had ϕ obtained, then ϕ □→ ψ is false. This principle seems to follow from two fairly weak principles, namely, that ‘chance ensures could’ and that ϕ □→ ψ and ϕ ⋄→ ¬ ψ clash. Despite their initial plausibility, I show that these principles are independently problematic: given some modest (...) closure principles, they entail absurdities. Moreover, on the most promising strategy for saving these principles, they do not, in the relevant sense, entail the chance-undermines-would principle. Instead, they entail a principle that only supports counterfactual indeterminism, the view that most ordinary counterfactuals are chancy, that is, not settled true. I demonstrate this by developing an indeterminist semantics that vindicates the clash and chance-ensures-could principles but not the chance-undermines-would principle. This view, I argue, offers a better account of our credal and linguistic judgements than counterfactual scepticism. (shrink)

The problem of probabilities of conditionals is one of the long-standing puzzles in philosophy of language. We defend and update Adams' solution to the puzzle: the probability of an epistemic conditional is not the probability of a proposition, but a probability under a supposition. -/- Close inspection of how a triviality result unfolds in a concrete scenario does not provide counterexamples to the view that probabilities of conditionals are conditional probabilities: instead, it supports the conclusion that probabilities of conditionals violate (...) standard probability theory. -/- This does not call into question probability theory per se; rather, it calls for a more careful understanding of its role: probability theory is a theory of probabilities of propositions; but as conditionals do not express propositions, their probabilities are not subject to the standard laws. -/- We argue that both conditional probabilities and probabilities of conditionals are best understood in terms of the dynamics of supposing, modeled as a restriction operation on a probability space. This version of the suppositionalist view allows us to connect Adams' Thesis to the widely held restrictor view of the semantics of conditionals. -/- We address two common objections to Adams' view: that the relevant probabilities are ‘probabilities only in name’, and that giving up conditional propositions puts us at a disadvantage when it comes to interpreting compounds. -/- Finally, we argue that some putative counterexamples to Adams' Thesis can be diagnosed as fallacies of probabilistic reasoning: they arise from applying to conditionals laws of standard probability theory which are invalid for them. (shrink)

Credences are beliefs about evidential probabilities. We give the view an assessment-sensitive formulation, show how it evades the standard objections, and give several arguments in support.

Many recent theories of epistemic discourse exploit an informational notion of consequence, i.e. a notion that defines entailment as preservation of support by an information state. This paper investigates how informational consequence fits with probabilistic reasoning. I raise two problems. First, all informational inferences that are not also classical inferences are, intuitively, probabilistically invalid. Second, all these inferences can be exploited, in a systematic way, to generate triviality results. The informational theorist is left with two options, both of them radical: (...) they can either deny that epistemic modal claims have probability at all, or they can move to a nonstandard probability theory. (shrink)