What should one believe about the unobserved? My thesis is a collection of four papers, each of which addresses this question. In the first paper, “Why Subjectivism?”, I consider the standing of a position called radical subjective Bayesianism, or subjectivism. The view is composed of two claims—that agents ought to be logically omniscient, and that there is no further norm of rationality—both of which are subject to seemingly conclusive objections. In this paper, I seek, if not to rehabilitate subjectivism, at (...) least to show its critic what is attractive about the position. I show that the critics of subjectivism assume a particular view about justification, which I call the telic view, and that there exist an alternative view, the poric view, on which subjectivism is appealing. I conclude by noting that the tension between telic and poric conceptions of justification might not be an easy one to resolve. In the second paper, “Bayesianism and the Problem of Induction”, I examine and reject the two existing Bayesian takes on Hume’s problem of induction, and propose my own in their stead. In the third paper, “The Nature of Awareness Growth”, I consider the question of how to model an agent who comes to entertain a new proposition about the unobserved. I argue that, contrary to what is typically thought, awareness growth occurs by refinement of the algebra, both on the poric and the telic pictures of Bayesianism. Finally, in the fourth paper, “Objectivity and the Method of Arbitrary Functions”, I consider whether, as is widely believed, a mathematical theorem known as the method of arbitrary functions can establish that it is in virtue of systems’ dynamics that scientific probabilities are objective. I differentiate between three ways in which authors have claimed that dynamics objectivise probabilities ; and I argue that the method of arbitrary functions can establish no such claims, thus dampening the hope that constraints in what to believe about the unobserved can emerge from dynamical facts in the world. (shrink)

People with the kind of preferences that give rise to the St. Petersburg paradox are problematic---but not because there is anything wrong with infinite utilities. Rather, such people cannot assign the St. Petersburg gamble any value that any kind of outcome could possibly have. Their preferences also violate an infinitary generalization of Savage's Sure Thing Principle, which we call the *Countable Sure Thing Principle*, as well as an infinitary generalization of von Neumann and Morgenstern's Independence axiom, which we call *Countable (...) Independence*. In violating these principles, they display foibles like those of people who deviate from standard expected utility theory in more mundane cases: they choose dominated strategies, pay to avoid information, and reject expert advice. We precisely characterize the preference relations that satisfy Countable Independence in several equivalent ways: a structural constraint on preferences, a representation theorem, and the principle we began with, that every prospect has a value that some outcome could have. (shrink)

You have higher-order uncertainty iff you are uncertain of what opinions you should have. I defend three claims about it. First, the higher-order evidence debate can be helpfully reframed in terms of higher-order uncertainty. The central question becomes how your first- and higher-order opinions should relate—a precise question that can be embedded within a general, tractable framework. Second, this question is nontrivial. Rational higher-order uncertainty is pervasive, and lies at the foundations of the epistemology of disagreement. Third, the answer is (...) not obvious. The Enkratic Intuition---that your first-order opinions must “line up” with your higher-order opinions---is incorrect; epistemic akrasia can be rational. If all this is right, then it leaves us without answers---but with a clear picture of the question, and a fruitful strategy for pursuing it. (shrink)

In this essay, I cast doubt on an apparent truism: namely, that if evidence is available for gathering and use at a negligible cost, then it's always instrumentally rational for us to gather that evidence and use it for making decisions. Call this thesis Value of Information. I show that Value of Information conflicts with two other plausible theses. The first is the view that an agent's evidence can entail non-trivial propositions about the external world. The second is the view (...) that epistemic rationality requires us to update our credences by conditionalization. These two theses, given some plausible assumptions, make room for rationally biased inquiries where Value of Information fails. I go on to argue that this is bad news for defenders of Value of Information. (shrink)

A familiar complaint about conciliatory approaches to disagreement is that they are self-defeating or incoherent because they ‘call for their own rejection’. This complaint seems to be influential but it isn’t clear whether conciliatory views call for their own rejection or what, if anything, this tells us about the coherence of such views. We shall look at two ways of developing this self-defeat objection and we shall see that conciliatory views emerge unscathed. A simple version of the self-defeat objection leaves (...) conciliatory views untouched. A subtle version of the objection contains a subtle but overlooked flaw. If the conciliatory view is right, it might be right to be dogmatically conciliatory (i.e., to continue to be conciliatory however objectionable this might seem to ourselves and to others). (shrink)

Good’s theorem is the apparent platitude that it is always rational to ‘look before you leap’: to gather information before making a decision when doing so is free. We argue that Good’s theorem is not platitudinous and may be false. And we argue that the correct advice is rather to ‘make your act depend on the answer to a question’. Looking before you leap is rational when, but only when, it is a way to do this.