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.     

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.     

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.

     

Rationality and indeterminate probabilities

We argue that indeterminate probabilities are not only rationally permissible for a Bayesian agent, but they may even be rationally required. Our first argument begins by assuming a version of interpretivism: your mental state is the set of probability and utility functions that rationalize your behavioral dispositions as well as possible. This set may consist of multiple probability functions. Then according to interpretivism, this makes it the case that your credal state is indeterminate. Our second argument begins with our describing a world that plausibly has indeterminate chances. Rationality requires a certain alignment of your credences with corresponding hypotheses about the chances. Thus, if you hypothesize the chances to be indeterminate, your will inherit their indeterminacy in your corresponding credences. Our third argument is motivated by a dilemma. Epistemic rationality requires you to stay open-minded about contingent matters about which your evidence has not definitively legislated. Practical rationality requires you to be able to act decisively at least sometimes. These requirements can conflict with each other-for thanks to your open-mindedness, some of your options may have undefined expected utility, and if you are choosing among them, decision theory has no advice to give you. Such an option is playing Nover and Hájek??s Pasadena Game, and indeed any option for which there is a positive probability of playing the Pasadena Game. You can serve both masters, epistemic rationality and practical rationality, with an indeterminate credence to the prospect of playing the Pasadena game. You serve epistemic rationality by making your upper probability positive-it ensures that you are open-minded. You serve practical rationality by making your lower probability 0-it provides guidance to your decision-making. No sharp credence could do both.     

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.     

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 Determinable-Based Account of Metaphysical Indeterminacy

Many phenomena appear to be indeterminate, including material macro-object boundaries and certain open future claims. Here I provide an account of indeterminacy in metaphysical, rather than semantic or epistemic, terms. Previous accounts of metaphysical indeterminacy (MI) have typically taken this to involve its being indeterminate which of various determinate (precise) states of affairs obtain. On my alternative account, MI involves its being determinate (or just plain true) that an indeterminate (imprecise) state of affairs obtains. I more specifically suggest that MI involves an object's (i) having a determinable property, but (ii) not having any unique determinate of that determinable. I motivate the needed extension of the traditional understanding of determinables, then argue that a determinable-based account of MI accommodates, in illuminating fashion, both ‘glutty’ and ‘gappy’ cases of MI, while satisfactorily treating concerns about MI stemming from Evans’ argument and the problem of the many.     

Metaphysically indeterminate existence

Sider (Four-dimensionalism 2001; Philos Stud 114:135–146, 2003; Nous 43:557–567, 2009) has developed an influential argument against indeterminacy in existence. In what follows, I argue that the defender of metaphysical forms of indeterminate existence has a unique way of responding to Sider’s argument. The response I’ll offer is interesting not only for its applicability to Sider’s argument, but also for its broader implications; responding to Sider helps to show both how we should think about precisification in the context of metaphysical indeterminacy and how we should understand commitment to metaphysically indeterminate existence. And if I’m right that metaphysical indeterminacy can allow for indeterminate existence in a way that semantic indeterminacy can’t, indeterminate existence might actually give us a reason to accept metaphysical indeterminacy (rather than a reason to reject it, as is commonly assumed).     

Two Notions of Scientific Justification

Scientific claims can be assessed epistemically in either of two ways: according to scientific standards, or by means of philosophical arguments such as the no-miracle argument in favor of scientific realism. This paper investigates the basis of this duality of epistemic assessments. It is claimed that the duality rests on two different notions of epistemic justification that are well-known from the debate on internalism and externalism in general epistemology: a deontological and an alethic notion. By discussing the conditions for the scientific acceptability of empirical results, it is argued that intrascientific justification employs the deontological notion. Philosophical disputes such as those on scientific realism can by contrast be shown to rest on the alethic notion. The implications of these findings both for the nature of the respective epistemic projects and for their interrelation are explored.     

What Is Bayesian Confirmation for?

Peter Brössel and Franz Huber in 2015 argued that the Bayesian concept of confirmation had no use. I will argue that it has both the uses they discussed—it can be used for making claims about how worthy of belief various hypotheses are, and it can be used to measure the epistemic value of experiments. Furthermore, it can be useful in explanations. More generally, I will argue that more coarse-grained concepts (like confirmation) can be useful, even when we have more fine-grained concepts (like credences).     

Indeterminacy and the principle of need

The principle of need—the idea that resources should be allocated according to need—is often invoked in priority setting in the health care sector. In this article, I argue that a reasonable principle of need must be indeterminate, and examine three different ways that this can be dealt with: appendicizing the principle with further principles, imposing determinacy, or empowering decision makers. I argue that need must be conceptualized as a composite property composed of at least two factors: health shortfall and capacity to benefit. When one examines how the different factors relate to each other, one discovers that this is sometimes indeterminate. I illustrate this indeterminacy in this article by applying the small improvement argument. If the relation between the factors are always determinate, the comparative relation changes by a small adjustment. Yet, if two needs are dissimilar but of seemingly equal magnitude, the comparative relation does not change by a small adjustment of one of the factors. I then outline arguments in favor of each of the three strategies for dealing with indeterminacy, but also point out that all strategies have significant shortcomings. More research is needed concerning how to deal with this indeterminacy, and the most promising path seems to be to scrutinize the position of the principle of need among a plurality of relevant principles for priority setting in the health care sector.     

Radical Interpretation and Logical Pluralism

I examine Quine’s and Davidson’s arguments to the effect that classical logic is the one and only correct logic. This conclusion is drawn from their views on radical translation and interpretation, respectively. I focus on the latter, but I first address, independently, Quine’s argument to the effect that the ‘deviant’ logician, who departs from classical logic, is merely changing the subject. Regarding logical pluralism, the question is whether there is more than one correct logic. I argue that bivalence may be subject matter dependent, but that distribution and the law of excluded middle can probably not be dropped whilst maintaining the standard meanings of the connectives. In discussing the ramifications of the indeterminacy of interpretation, I ask whether it forces Davidsonian interpreters to adopt Dummett’s epistemic conception of truth vis-à-vis their interpretations. And, if so, does this cohere with their attributing a nonepistemic notion of truth to their interpretees? This would be a form of logical pluralism. In addition, I discuss Davidson’s arguments against conceptual schemes. Schemes incommensurable with our own could be construed as wholesale deviant logics, or so I argue. And, if so, their possibility would yield, in turn, the possibility of a radical logical pluralism. I also address Davidson’s application of Tarski’s definition of truth.

     

Qeauty and the books: a response to Lewis’s quantum sleeping beauty problem

In his 2007 paper “Quantum Sleeping Beauty”, Peter Lewis poses a problem for the supporters’ of the Everett interpretation of quantum mechanics appeal to subjective probability. Lewis’s argument hinges on parallels between the traditional “sleeping beauty” problem in epistemology and a quantum variant. These two cases, Lewis argues, advocate different treatments of credences even though they share important epistemic similarities, leading to a tension between the traditional solution to the sleeping beauty problem (typically called the “thirder” solution) and Everettian quantum mechanics. In this paper I examine the metaphysical and epistemological differences between Lewis’s two cases, and, in particular, I show how diachronic Dutch book arguments support both the thirder solution in the traditional case and the Everettian’s solution in the variant case. These Dutch books, I argue, reveal an important disanalogy between Lewis’s two cases such that Lewis’s argument does not reveal an inconsistency in either the Everettian’s or the thirder’s assignment of credences.     

Radical quotation and real repetition

In this essay I argue for a constructivist account of the entities composing the object languages of Davidsonian truth theories and a quotational account of the reference from metalinguistic expressions to interpreted utterances. I claim that ‘radical quotation’ requires an ontology of repeatable events with strong similarities to Derrida's account of iterable events. In part one I summarise Davidson's account of interpretation and Olav Gjelsivk's arguments to the effect that the syntactic individuation of linguistic objects is only workable if interpreters make richer assumptions about semantic properties than Davidson can tolerate. In part two I show that the objectivist account of syntactic objects which Gjelsivk's arguments presuppose is incompatible with one corollary of Davidsonian semantic indeterminacy: namely, the relativity of language to interpretative scheme. In place of this an account of radical interpretation is presented in which a quotational theory of metalinguistic reference furnishes the requisite relativity. In part three I argue that this account requires that particular utterance events must be repeatable to be radically quotable and give reasons why particularity and repeatability are not incompatible.     

REPLIES TO HOUGH, BAUMANN AND BLAAUW

I reply to comments by Gerry Hough, Peter Baumann and Martijn Blaauw on my book Moral Skepticisms . The main issues concern whether modest justifiedness is epistemic and how it is related to extreme justifiedness; how contrastivists can handle crazy contrast classes, indeterminacy and common language; whether Pyrrhonian scepticism leads to paralysis in decision-making or satisfies our desires to evaluate beliefs as justified or not; and how contextualists can respond to my arguments against relevance of contrast classes.     

Problems for contrastive closure: resolved and regained

The standard contextualist solution to the skeptical paradox is intended to provide a way to retain epistemic closure while avoiding the excessive modesty of radical skepticism and the immodesty of Moorean dogmatism. However, contextualism’s opponents charge that its solution suffers from epistemic immodesty comparable to Moorean dogmatism. According to the standard contextualist solution, all contexts where an agent knows some ordinary proposition to be true are contexts where she also knows that the skeptical hypotheses are false. It has been hoped that contrastivist theories of knowledge can mirror the contextualist solution while avoiding this epistemic immodesty. I review the main problems for contrastive closure and argue that none of the arguments currently in the literature pose an insurmountable problem for the contrastivist solution. However, I argue that contrastivist theories of knowledge, like their contextualist rivals, are indeed committed to epistemic immodesty.     

Minimizing Inaccuracy for Self-Locating Beliefs

One's inaccuracy for a proposition is defined as the squared difference between the truth value (1 or 0) of the proposition and the credence (or subjective probability, or degree of belief) assigned to the proposition. One should have the epistemic goal of minimizing the expected inaccuracies of one's credences. We show that the method of minimizing expected inaccuracy can be used to solve certain probability problems involving information loss and self-locating beliefs (where a self-locating belief of a temporal part of an individual is a belief about where or when that temporal part is located). We analyze the Sleeping Beauty problem, the duplication version of the Sleeping Beauty problem, and various related problems.     

Future freedom and the fixity of truth: closing the road to limited foreknowledge open theism

Unlike versions of open theism that appeal to the alethic openness of the future, defenders of limited foreknowledge open theism (hereafter LFOT) affirm that some propositions concerning future contingents are presently true. Thus, there exist truths that are unknown to God, so God is not omniscient simpliciter. LFOT requires modal definitions of divine omniscience such that God knows all truths that are logically knowable. Defenders of LFOT have yet to provide an adequate response to Richard Purtill’s argument that fatalism logically follows from the omnitemporality of truth. Hasker believes a distinction between hard and soft facts prevents fatalism, but I argue that his defense fails in light of arguments involving divine necessity. Additionally, I point out that Hasker’s philosophy of language concerning divine names faces problems that cannot be overcome, given the versions of the dilemma of freedom and foreknowledge that motivate LFOT. Thus, contra Hasker, Swinburne, and van Inwagen, open theism necessitates the alethic openness of the future.     

A Non-factualist defense of the Reflection principle

Are there plausible synchronic constraints on how a subject thinks of herself extended over time? At first glance, Bas van Fraassen’s principle of Reflection seems to prescribe the sort of epistemic authority one’s future self should be taken by one to have over one’s current epistemic states. (The gist of this principle is that I should now believe what I’m convinced I will believe tomorrow.) There has been a general consensus that, as a principle concerning epistemic authority, Reflection does not apply to epistemically non-ideal agents. I agree with this, but argue here that it misses the point of Reflection. Rather than an epistemic principle concerning reasons for belief, Reflection concerns the semantics of belief avowal. I present a non-factual interpretation of Reflection, argue that the principle provides a constraint on the ways in which one can reflectively endorse one’s future epistemic self, and say something about the logic governing such an interpretation.