Believing Probabilistic Contents: On the Expressive Power and Coherence of Sets of Sets of Probabilities

Moss (2018) argues that rational agents are best thought of not as having degrees of belief in various propositions but as having beliefs in probabilistic contents, or probabilistic beliefs. Probabilistic contents are sets of probability functions. Probabilistic belief states, in turn, are modeled by sets of probabilistic contents, or sets of sets of probability functions. We argue that this Mossean framework is of considerable interest quite independently of its role in Moss’ account of probabilistic knowledge or her semantics for epistemic modals and probability operators. It is an extremely general model of uncertainty. Indeed, it is at least as general and expressively powerful as every other current imprecise probability framework, including lower probabilities, lower previsions, sets of probabilities, sets of desirable gambles, and choice functions. In addition, we partially answer an important question that Moss leaves open, viz., why should rational agents have consistent probabilistic beliefs? We show that an important subclass of Mossean believers avoid Dutch bookability iff they have consistent probabilistic beliefs

Probabilistic Knowledge and Cognitive Ability

Moss (2013) argues that degrees of belief or credences can amount to knowledge in much the way that full beliefs can. This paper explores a new kind of objective Bayesianism designed to take us some way toward securing such knowledge-constituting credences, or 'probabilistic knowledge'. Whatever else it takes for an agent’s credences to amount to knowledge, their success, or accuracy must be the product of cognitive ability or skill. The brand of Bayesianism developed here helps ensure this ability condition is satisfied. Cognitive ability, in turn, helps make credences valuable in other ways: it helps mitigate their dependence on epistemic luck, for example. What we end up with, at the end of the day, are credences that are particularly good candidates for constituting probabilistic knowledge. What’s more, examining the character of these credences teaches us something important about what the pursuit of probabilistic knowledge demands from us. It does not demand that we give hypotheses equal treatment, by affording them equal credence. Rather, it demands that we give them equal consideration, by affording them an equal chance of being discovered

Degrees of Incoherence, Dutch Bookability & Guidance Value

Why is it good to be less, rather than more incoherent? Julia Staffel, in her excellent book "Unsettled Thoughts," answers this question by showing that if your credences are incoherent, then there is some way of nudging them toward coherence that is guaranteed to make them more accurate and reduce the extent to which they are Dutch-bookable. This seems to show that such a nudge toward coherence makes them better fit to play their key epistemic and practical roles: representing the world and guiding action. In this paper, I argue that Staffel's strategy needs a small tweak. While she identifies appropriate measures of epistemic value, she does not identify appropriate measures of practical value. Staffel measures practical value using Dutch-bookability scores. But credences have practical value in virtue of recommending actions that produce as much utility as possible. And while susceptibility to a Dutch book is a surefire sign that one's credences are needlessly bad at this task, one's degree of Dutch-bookability is not itself a good measure of how well they recommend practically valuable actions. Strictly proper scoring rules, I argue, are the right tools for measuring both epistemic and practical value. I show that we can rerun Staffel's strategy swapping in strictly proper scoring rules for Dutch-bookability measures. So long as one's epistemic scoring rule and practical scoring rule are ``sufficiently similar,'' there is some way of nudging incoherent credences toward coherence that is guaranteed to yield more of both types of value

New Foundations for Imprecise Bayesianism.

My dissertation examines two kinds of statistical tools for taking prior information into account, and investigates what reasons we have for using one or the other in different sorts of inference and decision problems. Chapter 1 describes a new objective Bayesian method for constructing `precise priors'. Precise prior probability distributions are statistical tools for taking account of your `prior evidence' in an inference or decision problem. `Prior evidence' is the wooly hodgepodge of information that you come to the table with. `Experimental evidence' is the new data that you gather to facilitate inference and decision-making. I leverage this method to provide the seeds of a solution to `the problem of the priors', the problem of providing a compelling epistemic rationale for using some `objective' method or other for constructing priors. You ought to use the proposed method, at least in certain contexts, I argue, because it minimizes your need for epistemic luck in securing accurate `posterior' (post-experiment) beliefs. Chapter 2 addresses a pressing concern about precise priors. Precise priors, some Bayesians say, fail to adequately summarize certain kinds of evidence. As a class, precise priors capture improper responses to unspecific and equivocal evidence. This motivates the introduction of imprecise priors. We need imprecise priors, or sets of distributions to summarize such evidence. I argue that, despite appearances to the contrary, precise priors are, in fact, flexible enough to capture proper responses to unspecific and equivocal evidence. The proper motivation for introducing imprecise priors, then, is not that they are required to summarize such evidence. We ought to search for new epistemic reasons to introduce imprecise priors. Chapter 3 explores two new kinds of reasons for employing imprecise priors. We ought to adopt imprecise priors in certain contexts because they put us in an unequivocally better position to secure epistemically valuable posterior beliefs than precise priors do. We ought to adopt imprecise priors in various other contexts because they minimize our need for epistemic luck in securing such posteriors. This points the way toward a new, potentially promising epistemic foundation for imprecise Bayesianism.PHDPhilosophyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/99960/1/jpkonek_1.pd

The Foundations of Epistemic Decision Theory

According to accuracy-first epistemology, accuracy is the fundamental epistemic good. Epistemic norms — Probabilism, Conditionalization, the Principal Principle, etc. — have their binding force in virtue of helping to secure this good. To make this idea precise, accuracy-firsters invoke Epistemic Decision Theory (EpDT) to determine which epistemic policies are the best means toward the end of accuracy. Hilary Greaves and others have recently challenged the tenability of this programme. Their arguments purport to show that EpDT encourages obviously epistemically irrational behavior. We develop firmer conceptual foundations for EpDT. First, we detail a theory of praxic and epistemic good. Then we show that, in light of their very different good-making features, EpDT will evaluate epistemic states and epistemic acts according to different criteria. So, in general, rational preference over states and acts won’t agree. Finally, we argue that based on direction-of-fit considerations, it’s preferences over the former that matter for normative epistemology, and that EpDT, properly spelt out, arrives at the correct verdicts in a range of putative problem cases

The Foundations of Epistemic Decision Theory

According to accuracy-first epistemology, accuracy is the fundamental epistemic good. Epistemic norms — Probabilism, Conditionalization, the Principal Principle, etc. — have their binding force in virtue of helping to secure this good. To make this idea precise, accuracy-firsters invoke Epistemic Decision Theory (EpDT) to determine which epistemic policies are the best means toward the end of accuracy. Hilary Greaves and others have recently challenged the tenability of this programme. Their arguments purport to show that EpDT encourages obviously epistemically irrational behavior. We develop firmer conceptual foundations for EpDT. First, we detail a theory of praxic and epistemic good. Then we show that, in light of their very different good-making features, EpDT will evaluate epistemic states and epistemic acts according to different criteria. So, in general, rational preference over states and acts won’t agree. Finally, we argue that based on direction-of-fit considerations, it’s preferences over the former that matter for normative epistemology, and that EpDT, properly spelt out, arrives at the correct verdicts in a range of putative problem cases

Independent natural extension for choice functions

We introduce an independence notion for choice functions, which we call ‘epistemic independence’ following the work by De Cooman et al. [17] for lower previsions, and study it in a multivariate setting. This work is a continuation of earlier work of one of the authors [29], and our results build on the characterization of choice functions in terms of sets of binary preferences recently established by De Bock and De Cooman [11]. We obtain the many-to-one independent natural extension in this framework. Given the generality of choice functions, our expression for the independent natural extension is the most general one we are aware of, and we show how it implies the independent natural extension for sets of desirable gambles, and therefore also for less expressive imprecise-probabilistic models. Once this is in place, we compare this concept of epistemic independence to another independence concept for choice functions proposed by Seidenfeld [28], which De Bock and De Cooman [2] have called S-independence. We show that neither is more general than the other