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I propose a relevance-based independence axiom on how to aggregate individual yes/no judgments on given propositions into collective judgments: the collective judgment on a proposition depends only on people’s judgments on propositions which are relevant to that proposition. This axiom contrasts with the classical independence axiom: the collective judgment on a proposition depends only on people’s judgments on the same proposition. I generalize the premise-based rule and the sequential-priority rule to an arbitrary priority order of the propositions, instead of a (...) |
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The Preface Paradox is often discussed for its implications for rational belief. Much less discussed is a variant of the Preface Paradox for knowledge. In this paper, I argue that the most plausible closure-friendly resolution to the Preface Paradox for Knowledge is to say that in any given context, we do not know much. I call this view “Socraticism”. I argue that Socraticism is the most plausible view on two accounts—(1) this view is compatible with the claim that most of (...) |
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Theories of rational decision making often abstract away from computational and other resource limitations faced by real agents. An alternative approach known as resource rationality puts such matters front and center, grounding choice and decision in the rational use of finite resources. Anticipated by earlier work in economics and in computer science, this approach has recently seen rapid development and application in the cognitive sciences. Here, the theory of rationality plays a dual role, both as a framework for normative assessment (...) |
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Traditionally epistemologists have taken doxastic states to come in three varieties—belief, disbelief, and suspension. Recently many epistemologists have taken our doxastic condition to be usefully represented by credences—quantified degrees of belief. Moreover, some have thought that this new credal picture is sufficient to account for everything we want to explain with the old traditional picture. Therefore, belief, disbelief, and suspension must map onto the new picture somehow. In this paper I challenge that possibility. Approaching the question from the angle of (...) |
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Uniqueness is the view that a body of evidence justifies a unique doxastic attitude toward any given proposition. Contemporary defenses and criticisms of Uniqueness are generally indifferent to whether we formulate the view in terms of the coarse-grained attitude of belief or the fine-grained attitude of credence. This paper articulates and discusses a hybrid view I call Hybrid Impermissivism that endorses Uniqueness about belief but rejects Uniqueness about credence. While Hybrid Impermissivism is an attractive position in several respects, I show (...) |
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– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) |
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There are many things—call them ‘experts’—that you should defer to in forming your opinions. The trouble is, many experts are modest: they’re less than certain that they are worthy of deference. When this happens, the standard theories of deference break down: the most popular (“Reflection”-style) principles collapse to inconsistency, while their most popular (“New-Reflection”-style) variants allow you to defer to someone while regarding them as an anti-expert. We propose a middle way: deferring to someone involves preferring to make any decision (...) |
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I argue that we should solve the Lottery Paradox by denying that rational belief is closed under classical logic. To reach this conclusion, I build on my previous result that (a slight variant of) McGee’s election scenario is a lottery scenario (see Lissia 2019). Indeed, this result implies that the sensible ways to deal with McGee’s scenario are the same as the sensible ways to deal with the lottery scenario: we should either reject the Lockean Thesis or Belief Closure. After (...) |
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This paper is about guessing: how people respond to a question when they aren’t certain of the answer. Guesses show surprising and systematic patterns that the most obvious theories don’t explain. We argue that these patterns reveal that people aim to optimize a tradeoff between accuracy and informativity when forming their guess. After spelling out our theory, we use it to argue that guessing plays a central role in our cognitive lives. In particular, our account of guessing yields new theories (...) |
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This guide accompanies the following article(s): Jackson, E., Philosophy Compass 15/6 (2020) pp. 1-13 10.1111/phc3.12668.x. |
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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 (...) |
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I show that the Lottery Paradox is just a version of the Sorites, and argue that this should modify our way of looking at the Paradox itself. In particular, I focus on what I call “the Cut-off Point Problem” and contend that this problem, well known by Sorites scholars, ought to play a key role in the debate on Kyburg’s puzzle. Very briefly, I show that, in the Lottery Paradox, the premises “ticket n°1 will lose”, “ticket n°2 will lose”… “ticket (...) |
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Agents are often assumed to have degrees of belief (“credences”) and also binary beliefs (“beliefs simpliciter”). How are these related to each other? A much-discussed answer asserts that it is rational to believe a proposition if and only if one has a high enough degree of belief in it. But this answer runs into the “lottery paradox”: the set of believed propositions may violate the key rationality conditions of consistency and deductive closure. In earlier work, we showed that this problem (...) |
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Belief-credence dualism is the view that we have both beliefs and credences and neither attitude is reducible to the other. Pragmatic encroachment is the view that practical stakes can affect the epistemic rationality of states like knowledge or justified belief. In this paper, I argue that dualism offers a unique explanation of pragmatic encroachment cases. First, I explain pragmatic encroachment and what motivates it. Then, I explain dualism and outline a particular argument for dualism. Finally, I show how dualism can (...) |
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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 (...) |
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According to the Lockean thesis, a proposition is believed just in case it is highly probable. While this thesis enjoys strong intuitive support, it is known to conflict with seemingly plausible logical constraints on our beliefs. One way out of this conflict is to make probability 1 a requirement for belief, but most have rejected this option for entailing what they see as an untenable skepticism. Recently, two new solutions to the conflict have been proposed that are alleged to be (...) |
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According to an increasingly popular epistemological view, people need outright beliefs in addition to credences to simplify their reasoning. Outright beliefs simplify reasoning by allowing thinkers to ignore small error probabilities. What is outright believed can change between contexts. It has been claimed that thinkers manage shifts in their outright beliefs and credences across contexts by an updating procedure resembling conditionalization, which I call pseudo-conditionalization (PC). But conditionalization is notoriously complicated. The claim that thinkers manage their beliefs via PC is (...) |
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In this article, I argue that faith’s going beyond the evidence need not compromise faith’s epistemic rationality. First, I explain how some of the recent literature on belief and credence points to a distinction between what I call B-evidence and C-evidence. Then, I apply this distinction to rational faith. I argue that if faith is more sensitive to B-evidence than to C-evidence, faith can go beyond the evidence and still be epistemically rational. |
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So-called “traditional epistemology” and “Bayesian epistemology” share a word, but it may often seem that the enterprises hardly share a subject matter. They differ in their central concepts. They differ in their main concerns. They differ in their main theoretical moves. And they often differ in their methodology. However, in the last decade or so, there have been a number of attempts to build bridges between the two epistemologies. Indeed, many would say that there is just one branch of philosophy (...) |
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In this paper we propose and analyze a game-theoretic model of the epistemology of peer disagreement. In this model, the peers' rationality is evaluated in terms of their probability of ending the disagreement with a true belief. We find that different strategies---in particular, one based on the Steadfast View and one based on the Conciliatory View---are rational depending on the truth-sensitivity of the individuals involved in the disagreement. Interestingly, the Steadfast and the Conciliatory Views can even be rational simultaneously in (...) |
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Many philosophers have argued that "degree of belief" or "credence" is a more fundamental state grounding belief. Many other philosophers have been skeptical about the notion of "degree of belief", and take belief to be the only meaningful notion in the vicinity. This paper shows that one can take belief to be fundamental, and ground a notion of "degree of belief" in the patterns of belief, assuming that an agent has a collection of beliefs that isn't dominated by some other (...) |
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The question I am addressing in this paper is the following: how is it possible to empirically test, or confirm, counterfactuals? After motivating this question in Section 1, I will look at two approaches to counterfactuals, and at how counterfactuals can be empirically tested, or confirmed, if at all, on these accounts in Section 2. I will then digress into the philosophy of probability in Section 3. The reason for this digression is that I want to use the way observable (...) |
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This essay develops a joint theory of rational (all-or-nothing) belief and degrees of belief. The theory is based on three assumptions: the logical closure of rational belief; the axioms of probability for rational degrees of belief; and the so-called Lockean thesis, in which the concepts of rational belief and rational degree of belief figure simultaneously. In spite of what is commonly believed, this essay will show that this combination of principles is satisfiable (and indeed nontrivially so) and that the principles (...) |
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Epistemology is the study of knowledge and justified belief. Belief is thus central to epistemology. It comes in a qualitative form, as when Sophia believes that Vienna is the capital of Austria, and a quantitative form, as when Sophia's degree of belief that Vienna is the capital of Austria is at least twice her degree of belief that tomorrow it will be sunny in Vienna. Formal epistemology, as opposed to mainstream epistemology (Hendricks 2006), is epistemology done in a formal way, (...) |
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This dissertation proposes and defends a hybrid view I call Hybrid Impermissivism, which combines the following two theses: Moderate Uniqueness and Credal Permissivism. Moderate Uniqueness says that no evidence could justify both believing a proposition and its negation. However, on Moderate Uniqueness, evidence could justify both believing and suspending judgement on a proposition (hence the adjective “Moderate”). And Credal Permissivism says that more than one credal attitude could be justified on the evidence. Hybrid Impermissisim is developed into a precise theory (...) |
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This essay discusses the difficulty to reconcile two paradigms about beliefs: the binary or categorical paradigm of yes/no beliefs and the probabilistic paradigm of degrees of belief. The possibility for someone to hold both types of belief simultaneously is challenged by the lottery paradox, and more recently by a general impossibility theorem by Dietrich and List (2018, 2021). The nature, relevance, and implications of the tension are explained and assessed. |
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Belief is a familiar attitude: taking something to be the case or regarding it as true. But we are more confident in some of our beliefs than in others. For this reason, many epistemologists appeal to a second attitude, called credence, similar to a degree of confidence. This raises the question: how do belief and credence relate to each other? On a belief-first view, beliefs are more fundamental and credences are a species of beliefs, e.g. beliefs about probabilities. On a (...) |
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Many moral theories are committed to the idea that some kinds of moral considerations should be respected, whatever the cost to ‘lesser’ types of considerations. A person's life, for instance, should not be sacrificed for the trivial pleasures of others, no matter how many would benefit. However, according to the decision-theoretic critique of lexical priority theories, accepting lexical priorities inevitably leads us to make unacceptable decisions in risky situations. It seems that to operate in a risky world, we must reject (...) |
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We derive a probabilistic account of the vagueness and context-sensitivity of scalar adjectives from a Bayesian approach to communication and interpretation. We describe an iterated-reasoning architecture for pragmatic interpretation and illustrate it with a simple scalar implicature example. We then show how to enrich the apparatus to handle pragmatic reasoning about the values of free variables, explore its predictions about the interpretation of scalar adjectives, and show how this model implements Edgington’s Vagueness: a reader, 1997) account of the sorites paradox, (...) |
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This paper explores the connective ‘because’, based on the idea that ‘_C_ because _A_’ implies the acceptance/truth of the antecedent _A_ as well as of the consequent _C_, and additionally that the antecedent makes a difference for the consequent. To capture this idea of difference-making a ‘relevantized’ version of the Ramsey Test for conditionals is employed that takes the antecedent to be relevant to the consequent in the following sense: a conditional is true/accepted in a state \(\sigma \) just in (...) |
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Active reasoning is the kind of reasoning that we do deliberately and consciously. In characterizing the nature of active reasoning and the norms it should obey, the question arises which attitudes we can reason with. Many authors take outright beliefs to be the attitudes we reason with. Others assume that we can reason with both outright beliefs and degrees of belief. Some think that we reason only with degrees of belief. In this paper I approach the question of what kinds (...) |
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Synchronic norms of theory choice, a traditional concern in scientific methodology, restrict the theories one can choose in light of given information. Diachronic norms of theory change, as studied in belief revision, restrict how one should change one’s current beliefs in light of new information. Learning norms concern how best to arrive at true beliefs. In this paper, we undertake to forge some rigorous logical relations between the three topics. Concerning, we explicate inductive truth conduciveness in terms of optimally direct (...) |
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In this article, I discuss three distinct but related puzzles involving lotteries: Kyburg’s lottery paradox, the statistical evidence problem, and the Harman-Vogel paradox. Kyburg’s lottery paradox is the following well-known problem: if we identify rational outright belief with a rational credence above a threshold, we seem to be forced to admit either that one can have inconsistent rational beliefs, or that one cannot rationally believe anything one is not certain of. The statistical evidence problem arises from the observation that people (...) |
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Lin and Kelly :957–981, 2012) and Leitgeb :1338–1389, 2013, Philos Rev 123:131–171, 2014), offer similar solutions to the Lottery Paradox, defining acceptance rules which determine a rational agent’s beliefs in terms of broader features of her credal state than just her isolated credences in individual propositions. I express each proposal as a method for obtaining an ordering over a partition from a credence function, and then a belief set from the ordering. Although these proposals avoid the original Lottery Paradox, I (...) |
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There are two prominent ways of formally modelling human belief. One is in terms of plain beliefs, i.e., sets of propositions. The second one is in terms of degrees of beliefs, which are commonly taken to be representable by subjective probability functions. In relating these two ways of modelling human belief, the most natural idea is a thesis frequently attributed to John Locke: a proposition is or ought to be believed just in case its subjective probability exceeds a contextually fixed (...) |
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Richard Bradley has initiated a new debate, with Brian Hill and Jake Chandler as further participants, about the implications of a number of so-called triviality results surrounding the Ramsey test for conditionals. I comment on this debate and argue that ‘Inclusion’ and ‘Preservation’, which were originally introduced as postulates for the rational revision of factual beliefs, have little to recommend them in the first place when extended to languages containing conditionals. I question the philosophical method of postulation that was applied (...) |
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A normative Bayesian theory of deliberation and judgement requires a procedure for merging the evidence of a collection of agents. In order to provide such a procedure, one needs to ask what the evidence is that grounds Bayesian probabilities. After finding fault with several views on the nature of evidence (the views that evidence is knowledge; that evidence is whatever is fully believed; that evidence is observationally set credence; that evidence is information), it is argued that evidence is whatever is (...) |
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A new justification of probabilism is developed that pays close attention to the structure of the underlying space of possibilities. Its central assumption is that rational numerical degrees of bel... |
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Kroedel has proposed a new solution, the permissibility solution, to the lottery paradox. The lottery paradox results from the Lockean thesis according to which one ought to believe a proposition just in case one’s degree of belief in it is sufficiently high. The permissibility solution replaces the Lockean thesis by the permissibility thesis according to which one is permitted to believe a proposition if one’s degree of belief in it is sufficiently high. This note shows that the epistemology of belief (...) |
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We argue that giving up on the closure of rational belief under conjunction comes with a substantial price. Either rational belief is closed under conjunction, or else the epistemology of belief has a serious diachronic deficit over and above the synchronic failures of conjunctive closure. The argument for this, which can be viewed as a sequel to the preface paradox, is called the ‘review paradox'; it is presented in four distinct, but closely related versions. |
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Synchronic norms of theory choice, a traditional concern in scientific methodology, restrict the theories one can choose in light of given information. Diachronic norms of theory change, as studied in belief revision, restrict how one should change one’s current beliefs in light of new information. Learning norms concern how best to arrive at true beliefs. In this paper, we undertake to forge some rigorous logical relations between the three topics. Concerning, we explicate inductive truth conduciveness in terms of optimally direct (...) |
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In this paper we compare Leitgeb’s stability theory of belief and Spohn’s ranking-theoretic account of belief. We discuss the two theories as solutions to the lottery paradox. To compare the two theories, we introduce a novel translation between ranking functions and probability functions. We draw some crucial consequences from this translation, in particular a new probabilistic belief notion. Based on this, we explore the logical relation between the two belief theories, showing that models of Leitgeb’s theory correspond to certain models (...) |
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In standard Bayesian probability revision, the adoption of full beliefs (propositions with probability 1) is irreversible. Once an agent has full belief in a proposition, no subsequent revision can remove that belief. This is an unrealistic feature, and it also makes probability revision incompatible with belief change theory, which focuses on how the set of full beliefs is modified through both additions and retractions. This problem in probability theory can be solved in a model that (i) lets the codomain of (...) |
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In this paper, we compare and contrast two methods for the revision of qualitative beliefs. The first method is generated by a simplistic diachronic Lockean thesis requiring coherence with the agent’s posterior credences after conditionalization. The second method is the orthodox AGM approach to belief revision. Our primary aim is to determine when the two methods may disagree in their recommendations and when they must agree. We establish a number of novel results about their relative behavior. Our most notable finding (...) |
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