Imprecise evidence without imprecise credences

Philosophical Studies - Does rationality require imprecise credences? Many hold that it does: imprecise evidence requires correspondingly imprecise credences. I argue that this is false. The...     

Intentionality and partial belief

Suppose we wish to provide a naturalistic account of intentionality. Like several other philosophers, we focus on the intentionality of belief, hoping that we may later supplement our account to accommodate other intentional states like desires and fears. Now suppose that we also take partial beliefs or credences seriously. In cashing out our favoured theory of intentionality, we may for the sake of simplicity talk as if belief is merely binary or all-or-nothing. But we should be able to supplement or modify our account to accommodate credences. I shall argue, however, that it is difficult to do so with respect to certain causal or teleological theories of intentionality-in particular, those advanced by the likes of Stalnaker (Inquiry, 1984) and Millikan (J Philos 86:281–297, 1989). I shall first show that such theories are tailor-made to account for the intentionality of binary beliefs. Then I shall argue that it is hard to extend or supplement such theories to accommodate credences. Finally, I shall offer some natural ways of modifying the theories that involve an appeal to objective probabilities. But unfortunately, such modifications face problems.     

The Population Ethics of Belief: In Search of an Epistemic Theory X

Consider Phoebe and Daphne. Phoebe has credences in 1 million propositions. Daphne, on the other hand, has credences in all of these propositions, but she's also got credences in 999 million other propositions. Phoebe's credences are all very accurate. Each of Daphne's credences, in contrast, are not very accurate at all; each is a little more accurate than it is inaccurate, but not by much. Whose doxastic state is better, Phoebe's or Daphne's? It is clear that this question is analogous to a question that has exercised ethicists over the past thirty years. How do we weigh a population consisting of some number of exceptionally happy and satisfied individuals against another population consisting of a much greater number of people whose lives are only just worth living? This is the question that occasions population ethics. In this paper, I go in search of the correct population ethics for credal states.     

Global Constraints on Imprecise Credences: Solving Reflection Violations,Belief Inertia,and Other Puzzles

The move to imprecise credence models leaves many formal norms of rationality surprisingly intact, as rational constraints on precise credences are often reinterpreted as constraints on individual elements of a rational agent’s representor. However, constraints on imprecise credences needn’t take this form. Whether an imprecise agent is rational might just as easily depend on global features of her representor. This paper is an extended investigation of global rules of rationality. I begin by distinguishing and defining multiple notions of globalness. Then I use these notions to solve several problems faced by fans of imprecise credences. On behalf of fans of imprecise credences, I respond to the problem of belief inertia, according to which certain imprecise agents are unable to engage in inductive learning. In addition, I answer the objection that that imprecise agents are doomed to violate the rational principle of Reflection.     

A forward looking decision rule for imprecise credences

Adam Elga (Philosophers’ Imprint, 10(5), 1–11, 2010) presents a diachronic puzzle to supporters of imprecise credences and argues that no acceptable decision rule for imprecise credences can deliver the intuitively correct result. Elga concludes that agents should not hold imprecise credences. In this paper, I argue for a two-part thesis. First, I show that Elga’s argument is incomplete: there is an acceptable decision rule that delivers the intuitive result. Next, I repair the argument by offering a more elaborate diachronic puzzle that is more difficult for imprecise Bayesians to avoid.     

A Theory of Bayesian Groups

A group is often construed as one agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated “Groupthink”, Russell et al. (2015) require group credences to undergo Bayesian revision whenever new information is learnt, i.e., whenever individual credences undergo Bayesian revision based on this information. To obtain a fully Bayesian group, one should often extend this requirement to non‐public or even private information (learnt by not all or just one individual), or to non‐representable information (not representable by any event in the domain where credences are held). I propose a taxonomy of six types of ‘group Bayesianism’. They differ in the information for which Bayesian revision of group credences is required: public representable information, private representable information, public non‐representable information, etc. Six corresponding theorems establish how individual credences must (not) be aggregated to ensure group Bayesianism of any type, respectively. Aggregating through standard averaging is never permitted; instead, different forms of geometric averaging must be used. One theorem—that for public representable information—is essentially Russell et al.'s central result (with minor corrections). Another theorem—that for public non‐representable information—fills a gap in the theory of externally Bayesian opinion pooling.     

Subjective causal networks and indeterminate suppositional credences

This paper has two main parts. In the first part, we motivate a kind of indeterminate, suppositional credences by discussing the prospect for a subjective interpretation of a causal Bayesian network (CBN), an important tool for causal reasoning in artificial intelligence. A CBN consists of a causal graph and a collection of interventional probabilities. The subjective interpretation in question would take the causal graph in a CBN to represent the causal structure that is believed by an agent, and interventional probabilities in a CBN to represent suppositional credences. We review a difficulty noted in the literature with such an interpretation, and suggest that a natural way to address the challenge is to go for a generalization of CBN that allows indeterminate credences. In the second part, we develop a decision-theoretic foundation for such indeterminate suppositional credences, by generalizing a theory of coherent choice functions to accommodate some form of act-state dependence. The upshot is a decision-theoretic framework that is not only rich enough to, so to speak, ground the probabilities in a subjectively interpreted causal network, but also interesting in its own right, in that it accommodates both act-state dependence and imprecise probabilities.

     

Imprecise Epistemic Values and Imprecise Credences

A number of recent arguments purport to show that imprecise credences are incompatible with accuracy-first epistemology. If correct, this conclusion suggests a conflict between evidential and alethic epistemic norms. In the first part of the paper, I claim that these arguments fail if we understand imprecise credences as indeterminate credences. In the second part, I explore why agents with entirely alethic epistemic values can end up in an indeterminate credal state. Following William James, I argue that there are many distinct alethic values that a rational agent can have. Furthermore, such an agent is rationally permitted not to have settled on one fully precise value function. This indeterminacy in value will sometimes result in indeterminacy in epistemic behaviour—that is, because the agent’s values aren’t settled, what she believes might not be.     

Agreement and Updating For Self-Locating Belief

In this paper, I argue that some plausible principles concerning which credences are rationally permissible for agents given information about one another’s epistemic and credal states have some surprising consequences for which credences an agent ought to have in light of self-locating information. I provide a framework that allows us to state these constraints and draw out these consequences precisely. I then consider and assess the prospects for rejecting these prima facie plausible principles.     

A Representation Theorem for Frequently Irrational Agents

The standard representation theorem for expected utility theory tells us that if a subject’s preferences conform to certain axioms, then she can be represented as maximising her expected utility given a particular set of credences and utilities—and, moreover, that having those credences and utilities is the only way that she could be maximising her expected utility (given her preferences). However, the kinds of agents these theorems seem apt to tell us anything about are highly idealised, being (amongst other things) always probabilistically coherent with infinitely precise degrees of belief and full knowledge of all a priori truths. Ordinary subjects do not look very rational when compared to the kinds of agents usually talked about in decision theory. In this paper, I will develop an expected utility representation theorem aimed at the representation of those who are neither probabilistically coherent, logically omniscient, nor expected utility maximisers across the board—that is, agents who are frequently irrational. The agents in question may be deductively fallible, have incoherent credences, limited representational capacities, and fail to maximise expected utility for all but a limited class of gambles.     

Explanation,updating, and accuracy

There is evidence that people update their credences partly on the basis of explanatory considerations. Philosophers have recently argued that to minimise the inaccuracy of their credences, people's updates also ought to be partly based on such considerations. However, there are many ways in which explanatory considerations can factor into updating, not all of which minimise inaccuracy. It is an open question whether in their updating, people take explanatory considerations into account in a way that philosophers would deem recommendable. To address this question, we re-analyse data from an experiment reported in Douven and Schupbach, “The role of explanatory considerations in updating” (Cognition, 2015).     

Reliabilism and imprecise credences

Philosophical Studies - What is it for an imprecise credence to be justified? It might be thought that this is not a particularly urgent question for friends of imprecise credences to answer. For...     

The Accuracy and Rationality of Imprecise Credences

It has been claimed that, in response to certain kinds of evidence (“incomplete” or “non‐specific” evidence), agents ought to adopt imprecise credences: doxastic states that are represented by sets of credence functions rather than single ones. In this paper I argue that, given some plausible constraints on accuracy measures, accuracy‐centered epistemologists must reject the requirement to adopt imprecise credences. I then show that even the claim that imprecise credences are permitted is problematic for accuracy‐centered epistemology. It follows that if imprecise credal states are permitted or required in the cases that their defenders appeal to, then the requirements of rationality can outstrip what would be warranted by an interest in accuracy.     

Repugnant Accuracy

Accuracy‐first epistemology is an approach to formal epistemology which takes accuracy to be a measure of epistemic utility and attempts to vindicate norms of epistemic rationality by showing how conformity with them is beneficial. If accuracy‐first epistemology can actually vindicate any epistemic norms, it must adopt a plausible account of epistemic value. Any such account must avoid the epistemic version of Derek Parfit's “repugnant conclusion.” I argue that the only plausible way of doing so is to say that accurate credences in certain propositions have no, or almost no, epistemic value. I prove that this is incompatible with standard accuracy‐first arguments for probabilism, and argue that there is no way for accuracy‐first epistemology to show that all credences of all agents should be coherent.     

Can religious and secular belief be rationally combined?

Sometimes the cognitive part of the human mind is modelled in a simplified way by degrees of belief. E.g., in philosophy of science and in formal epistemology agents are often identified by their credences in a set of claims. This line of dealing with the individual mind is currently expanded to groups by attempts of finding adequate ways of pooling individual degrees of belief into an overall group credence or, more abstractly speaking, into a collective mind. In this paper, we model religious people’s minds as such a collective mind. Religious people are therein identified with a set of degrees of beliefs containing religious and secular credences. E.g., within a religious context a person may be sure that some statement is true, whereas the same person lacks non-religious support for such a credence and hence may doubt the truth of that statement within a secular context. We will also present two results on the adequacy of this model.     

Religious credence is not factual belief

I argue that psychology and epistemology should posit distinct cognitive attitudes of religious credence and factual belief, which have different etiologies and different cognitive and behavioral effects. I support this claim by presenting a range of empirical evidence that religious cognitive attitudes tend to lack properties characteristic of factual belief, just as attitudes like hypothesis, fictional imagining, and assumption for the sake of argument generally lack such properties. Furthermore, religious credences have distinctive properties of their own. To summarize: factual beliefs (i) are practical setting independent, (ii) cognitively govern other attitudes, and (iii) are evidentially vulnerable. By way of contrast, religious credences (a) have perceived normative orientation, (b) are susceptible to free elaboration, and (c) are vulnerable to special authority. This theory provides a framework for future research in the epistemology and psychology of religious credence.     

What Chance‐Credence Norms Should Not Be

A chance‐credence norm states how an agent's credences in propositions concerning objective chances ought to relate to her credences in other propositions. The most famous such norm is the Principal Principle (PP), due to David Lewis. However, Lewis noticed that PP is too strong when combined with many accounts of chance that attempt to reduce chance facts to non‐modal facts. Those who defend such accounts of chance have offered two alternative chance‐credence norms: the first is Hall's and Thau's New Principle (NP); the second is Ismael's General Recipe (IP). Thus, the question arises: Should we adopt NP or IP or both? In this paper, I argue that IP has unacceptable consequences when coupled with reductionism, so we must accept NP alone.     

The Representation of Belief

I derive a sufficient condition for a belief set to be representable by a probability function: if at least one comparative confidence ordering of a certain type satisfies Scott’s axiom, then the belief set used to induce that ordering is representable. This provides support for Kenny Easwaran’s project of analyzing doxastic states in terms of belief sets rather than credences.     

Akrasia,instincts and revealed preferences

Recently in epistemology a number of authors have mounted Bayesian objections to dogmatism. These objections depend on a Bayesian principle of evidential confirmation: Evidence E confirms hypothesis H just in case Pr(H|E) > Pr(H). I argue using Keynes’ and Knight’s distinction between risk and uncertainty that the Bayesian principle fails to accommodate the intuitive notion of having no reason to believe. Consider as an example an unfamiliar card game: at first, since you’re unfamiliar with the game, you assign credences based on the indifference principle. Later you learn how the game works and discover that the odds dictate you assign the very same credences. Examples like this show that if you initially have noreason to believe H, then intuitively E can give you reason to believe H even though Pr(H|E) ≤ Pr(H). I show that without the principle, the objections to dogmatism fail.