Imprecise probabilities are often modelled with representors, or sets of probability functions. In the recent literature, two ways of interpreting representors have emerged as especially prominent: vagueness interpretations, according to which each probability function in the set represents how the agent's beliefs would be if any vagueness were precisified away; and comparativist interpretations, according to which the set represents those comparative confidence relations that are common to all probability functions therein. I argue that these interpretations have some important limitations. I (...) also propose an alternative—the functional interpretation—according to which representors are best interpreted by reference to the roles they play in the theories that make use of them. (shrink)

One very popular framework in contemporary epistemology is Bayesian. The central epistemic state is subjective confidence, or credence. Traditional epistemic states like belief and knowledge tend to be sidelined, or even dispensed with entirely. Credences are often introduced as familiar mental states, merely in need of a special label for the purposes of epistemology. But whether they are implicitly recognized by the folk or posits of a sophisticated scientific psychology, they do not appear to fit well with perception, as is (...) often noted. -/- This paper investigates the tension between probabilistic cognition and non-probabilistic perception. The tension is real, and the solution—to adapt a phrase from Quine and Goodman—is to renounce credences altogether. (shrink)

ABSTRACT According to comparativism, comparative confidence is more fundamental than absolute confidence. In two recent AJP papers, Stefánsson has argued that comparativism is capable of explaining interpersonal confidence comparisons. In this paper, I will argue that Stefansson’s proposed explanation is inadequate; that we have good reasons to think that comparativism cannot handle interpersonal comparisons; and that the best explanation of interpersonal comparisons requires thinking about confidence in a fundamentally different way than that which comparativists propose: specifically, we should think of (...) confidence as a dimensionless quantity. (shrink)

This guide accompanies the following article(s): Jackson, E., Philosophy Compass 15/6 (2020) pp. 1-13 10.1111/phc3.12668.x.

Standard accuracy-based approaches to imprecise credences have the consequence that it is rational to move between precise and imprecise credences arbitrarily, without gaining any new evidence. Building on the Educated Guessing Framework of Horowitz (2019), we develop an alternative accuracy-based approach to imprecise credences that does not have this shortcoming. We argue that it is always irrational to move from a precise state to an imprecise state arbitrarily, however it can be rational to move from an imprecise state to a (...) precise state arbitrarily. (shrink)

Sometimes epistemologists theorize about belief, a tripartite attitude on which one can believe, withhold belief, or disbelieve a proposition. In other cases, epistemologists theorize about credence, a fine-grained attitude that represents one’s subjective probability or confidence level toward a proposition. How do these two attitudes relate to each other? This article explores the relationship between belief and credence in two categories: descriptive and normative. It then explains the broader significance of the belief-credence connection and concludes with general lessons from the (...) debate thus far. (shrink)

Comparativism is the view that comparative confidences (e.g., being more confident that P than that Q) are more fundamental than degrees of belief (e.g., believing that P with some strength x). In this paper, I outline the basis for a new, non-probabilistic version of comparativism inspired by a suggestion made by Frank Ramsey in `Probability and Partial Belief'. I show how, and to what extent, `Ramseyan comparativism' might be used to weaken the (unrealistically strong) probabilistic coherence conditions that comparativism traditionally (...) relies on. (shrink)

According to the preference-centric approach to understanding partial belief, the connection between partial beliefs and preferences is key to understanding what partial beliefs are and how they’re measured. As Ramsey put it, the ‘degree of a belief is a causal property of it, which we can express vaguely as the extent to which we are prepared to act on it’ The Foundations of Mathematics and Other Logical Essays, Routledge, Oxon, pp 156–198, 1931). But this idea is not as popular as (...) it once was. Nowadays, the preference-centric approach is frequently dismissed out-of-hand as behaviouristic, unpalatably anti-realist, and/or prone to devastating counterexamples. Cases like Eriksson and Hájek’s :183–213, 2007) preferenceless Zen monk and Christensen’s :356–376, 2001) other roles argument have suggested to many that any account of partial belief that ties them too closely to preferences is irretrievably flawed. In this paper I provide a defence of preference-centric accounts of partial belief. (shrink)

The Precautionary Principle (PP) is an influential principle of risk management. It has been widely introduced into environmental legislation, and it plays an important role in most international environmental agreements. Yet, there is little consensus on precisely how to understand and formulate the principle. In this paper I prove some impossibility results for two plausible formulations of the PP as a decision-rule. These results illustrate the difficulty in making the PP consistent with the acceptance of any trade-offs between catastrophic risks (...) and more ordinary goods. (shrink)

I explore how rational belief and rational credence relate to evidence. I begin by looking at three cases where rational belief and credence seem to respond differently to evidence: cases of naked statistical evidence, lotteries, and hedged assertions. I consider an explanation for these cases, namely, that one ought not form beliefs on the basis of statistical evidence alone, and raise worries for this view. Then, I suggest another view that explains how belief and credence relate to evidence. My view (...) focuses on the possibilities that the evidence makes salient. I argue that this makes better sense of the difference between rational credence and rational belief than other accounts. (shrink)

According to comparativism, degrees of belief are reducible to a system of purely ordinal comparisons of relative confidence. (For example, being more confident that P than that Q, or being equally confident that P and that Q.) In this paper, I raise several general challenges for comparativism, relating to (i) its capacity to illuminate apparently meaningful claims regarding intervals and ratios of strengths of belief, (ii) its capacity to draw enough intuitively meaningful and theoretically relevant distinctions between doxastic states, and (...) (iii) its capacity to handle common instances of irrationality. (shrink)

‘Bayesian epistemology’ became an epistemological movement in the 20th century, though its two main features can be traced back to the eponymous Reverend Thomas Bayes (c. 1701-61). Those two features are: (1) the introduction of a formal apparatus for inductive logic; (2) the introduction of a pragmatic self-defeat test (as illustrated by Dutch Book Arguments) for epistemic rationality as a way of extending the justification of the laws of deductive logic to include a justification for the laws of inductive logic. (...) The formal apparatus itself has two main elements: the use of the laws of probability as coherence constraints on rational degrees of belief (or degrees of confidence) and the introduction of a rule of probabilistic inference, a rule or principle of conditionalization. (shrink)

This paper discusses a challenge for Comparativists about belief, who hold that numerical degree of belief (in particular, subjective probability) is a useful fiction, unlike comparative belief, which they regard as real. The challenge is to make sense of claims like ‘I am twice as confident in A as in B’ in terms of comparative belief only. After showing that at least some Comparativists can meet this challenge, I discuss implications for Zynda’s [2000] and Stefánsson’s [2017] defences of Comparativism.

Philosophy and Phenomenological Research, Volume 104, Issue 2, Page 343-363, March 2022.

A probability function is non-conglomerable just in case there is some proposition E and partition \ of the space of possible outcomes such that the probability of E conditional on any member of \ is bounded by two values yet the unconditional probability of E is not bounded by those values. The paradox of non-conglomerability is the counterintuitive—and controversial—claim that a rational agent’s subjective probability function can be non-conglomerable. In this paper, I present a qualitative analogue of the paradox. I (...) show that, under antecedently plausible assumptions, an analogue of the paradox arises for rational comparative confidence. As I show, the qualitative paradox raises its own distinctive set of philosophical issues. (shrink)