In a 2017 AJP paper, Cevolani and Schurz propose a novel solution to the Preface Paradox that appeals to the notion of expected truthlikeness. This discussion note extends and analyses their approach by applying it to the related Lottery Paradox.

It is a prevalent, if not popular, thesis in the metaphysics of belief that facts about an agent’s beliefs depend entirely upon facts about that agent’s underlying credal state. Call this thesis ‘credal reductivism’ and any view that endorses this thesis a ‘credal reductivist view’. An adequate credal reductivist view will accurately predict both when belief occurs and which beliefs are held appropriately, on the basis of credal facts alone. Several well-known—and some lesser known—objections to credal reductivism turn on the (...) inability of standard credal reductivist views to get the latter, normative, results right. This paper presents and defends a novel credal reductivist view according to which belief is a type of “imprecise credence” that escapes these objections by including an extreme credence of 1. (shrink)

An important trend in contemporary epistemology centers on elaborating an old idea of pragmatist pedigree: theory selection (and in general the process of changing view and fixing beliefs) presupposes epistemic values. This article focuses on analyzing the case where epistemic values are indeterminate or when the sources of valuation are multiple (epistemic values like coherence and simplicity need not order options in compatible ways). According to the theory that thus arises epistemic alternatives need not be fully ordered by an underlying (...) notion of information-value and therefore the usual economic techniques of optimization cannot be applied in order to compute optimal contractions. But in cases of this sort it is still rational to maximize, i.e. to deem an option as choosable when it is not known to be worse that any other. We present here basic results about a notion of liberal contraction based on maximizing quasi-orderings. This requires the previous solution of some open problems in the theory of rational choice functions, namely a full characterization of choice functions rationalizable in terms of maximization of quasi-transitive relations. We conclude by discussing the problem of what is the adequate feasible set for calculating maximizing solutions for contraction problems and by considering the epistemological roots of some counterexamples against the most fundamental axioms on choice functions (like α). While the first part of the paper shows how economic insights can be used to improve our understanding of the principles of belief formation and change, this final section reverses this strategy by showing the utility of epistemological insights and techniques for providing invariance conditions capable of regulating the applicability of the pure principles of choice. (shrink)

The article focuses on representing different forms of non-adjunctive inference as sub-Kripkean systems of classical modal logic, where the inference from □A and □B to □A ∧ B fails. In particular we prove a completeness result showing that the modal system that Schotch and Jennings derive from a form of non-adjunctive inference in (Schotch and Jennings, 1980) is a classical system strictly stronger than EMN and weaker than K (following the notation for classical modalities presented in Chellas, 1980). The unified (...) semantical characterization in terms of neighborhoods permits comparisons between different forms of non-adjunctive inference. For example, we show that the non-adjunctive logic proposed in (Schotch and Jennings, 1980) is not adequate in general for representing the logic of high probability operators. An alternative interpretation of the forcing relation of Schotch and Jennings is derived from the proposed unified semantics and utilized in order to propose a more fine-grained measure of epistemic coherence than the one presented in (Schotch and Jennings, 1980). Finally we propose a syntactic translation of the purely implicative part of Jaśkowski's system D₂ into a classical system preserving all the theorems (and non-theorems) explicilty mentioned in (Jaśkowski, 1969). The translation method can be used in order to develop epistemic semantics for a larger class of non-adjunctive (discursive) logics than the ones historically investigated by Jaśkowski. (shrink)

It can often be heard in the hallways, and occasionally read in print, that reliabilism runs into special trouble regarding lottery cases. My main aim in this paper is to argue that this is not so. Nevertheless, lottery cases do force us to pay close attention to the relation between justification and probability.

Disquotational theories of truth are often criticised for being too weak to prove interesting generalisations about truth. In this paper we will propose a certain formal theory to serve as a framework for a solution of the generalisation problem. In contrast with Horwich’s original proposal, our framework will eschew psychological notions altogether, replacing them with the epistemic notion of believability. The aim will be to explain why someone who accepts a given disquotational truth theory Th, should also accept various generalisations (...) not provable in Th. The strategy will consist of the development of an axiomatic theory of believability, one permitting us to show how to derive the believability of generalisations from basic axioms that characterise the believability predicate, together with the information that Th is a theory of truth that we accept. (shrink)

The so-called Preface Paradox seems to show that one can rationally believe two logically incompatible propositions. We address this puzzle, relying on the notions of truthlikeness and approximate truth as studied within the post-Popperian research programme on verisimilitude. In particular, we show that adequately combining probability, approximate truth, and truthlikeness leads to an explanation of how rational belief is possible in the face of the Preface Paradox. We argue that our account is superior to other solutions of the paradox, including (...) a recent one advanced by Hannes Leitgeb (Analysis 74.1). (shrink)

Formal models of appearance and reality have proved fruitful for investigating structural properties of perceptual knowledge. This paper applies the same approach to epistemic justification. Our central goal is to give a simple account of The Preface, in which justified belief fails to agglomerate. Following recent work by a number of authors, we understand knowledge in terms of normality. An agent knows p iff p is true throughout all relevant normal worlds. To model The Preface, we appeal to the normality (...) of error. Sometimes, it is more normal for reality and appearance to diverge than to match. We show that this simple idea has dramatic consequences for the theory of knowledge and justification. Among other things, we argue that a proper treatment of The Preface requires a departure from the internalist idea that epistemic justification supervenes on the appearances and the widespread idea that one knows most when free from error. (shrink)

Philosophy and Phenomenological Research, Volume 104, Issue 1, Page 19-49, January 2022.

Information received from different sources can be inconsistent. Even when the sources of information can be ordered on the basis of their trustworthiness, it turns out that extracting an acceptable notion of support for information is a non-trivial matter, as is the question what information a rational agent should accept. Here it is shown how a support ordering on the information can be generated and how it can be used to decide what information to accept and what not to accept. (...) This ordering, it turns out, is closely related to notions such as Epistemic Entrenchment and Grove spheres studied in belief revision. (shrink)

This paper is about the statics and dynamics of belief states that are represented by pairs consisting of an agent's credences (represented by a subjective probability measure) and her categorical beliefs (represented by a set of possible worlds). Regarding the static side, we argue that the latter proposition should be coherent with respect to the probability measure and that its probability should reach a certain threshold value. On the dynamic side, we advocate Jeffrey conditionalisation as the principal mode of changing (...) one's belief state. This updating method fits the idea of the Lockean Thesis better than plain Bayesian conditionalisation, and it affords a flexible method for adding and withdrawing categorical beliefs. We show that it fails to satisfy the traditional principles of Inclusion and Preservation for belief revision and the principle of Recovery for belief withdrawals{, as well as the Levi and Harper identities. We take this to be a problem for the latter principles rather than for the idea of coherent belief change. (shrink)

In this paper, I offer an analysis of the radical disagreement over the adequacy of string theory. The prominence of string theory despite its notorious lack of empirical support is sometimes explained as a troubling case of science gone awry, driven largely by sociological mechanisms such as groupthink (e.g. Smolin 2006). Others, such as Dawid (2013), explain the controversy by positing a methodological revolution of sorts, according to which string theorists have quietly turned to nonempirical methods of theory assessment given (...) the technological inability to directly test the theory. The appropriate response, according to Dawid, is to acknowledge this development and widen the canons of acceptable scientific methods. As I’ll argue, however, the current situation in fundamental physics does not require either of these responses. Rather, as I’ll suggest, much of the controversy stems from a failure to properly distinguish the “context of justification” from the “context of pursuit”. Both those who accuse string theorists of betraying the scientific method and those who advocate an enlarged conception of scientific methodology objectionably conflate epistemic justification with judgements of pursuit-worthiness. Once we get clear about this distinction and about the different norms governing the two contexts, the current situation in fundamental physics becomes much less puzzling. After defending this diagnosis of the controversy, I’ll show how the argument patterns that have been posited by Dawid as constituting an emergent methodological revolution in science are better off if reworked as arguments belonging to the context of pursuit. (shrink)

In this paper, I consider the relationship between Inference to the Best Explanation and Bayesianism, both of which are well-known accounts of the nature of scientific inference. In Sect. 2, I give a brief overview of Bayesianism and IBE. In Sect. 3, I argue that IBE in its most prominently defended forms is difficult to reconcile with Bayesianism because not all of the items that feature on popular lists of “explanatory virtues”—by means of which IBE ranks competing explanations—have confirmational import. (...) Rather, some of the items that feature on these lists are “informational virtues”—properties that do not make a hypothesis \ more probable than some competitor \ given evidence E, but that, roughly-speaking, give that hypothesis greater informative content. In Sect. 4, I consider as a response to my argument a recent version of compatibilism which argues that IBE can provide further normative constraints on the objectively correct probability function. I argue that this response does not succeed, owing to the difficulty of defending with any generality such further normative constraints. Lastly, in Sect. 5, I propose that IBE should be regarded, not as a theory of scientific inference, but rather as a theory of when we ought to “accept” H, where the acceptability of H is fixed by the goals of science and concerns whether H is worthy of commitment as research program. In this way, IBE and Bayesianism, as I will show, can be made compatible, and thus the Bayesian and the proponent of IBE can be friends. (shrink)

There are currently two robust traditions in philosophy dealing with doxastic attitudes: the tradition that is concerned primarily with all-or-nothing belief, and the tradition that is concerned primarily with degree of belief or credence. This paper concerns the relationship between belief and credence for a rational agent, and is directed at those who may have hoped that the notion of belief can either be reduced to credence or eliminated altogether when characterizing the norms governing ideally rational agents. It presents a (...) puzzle which lends support to two theses. First, that there is no formal reduction of a rational agent’s beliefs to her credences, because belief and credence are each responsive to different features of a body of evidence. Second, that if our traditional understanding of our practices of holding each other responsible is correct, then belief has a distinctive role to play, even for ideally rational agents, that cannot be played by credence. The question of which avenues remain for the credence-only theorist is considered. (shrink)

What does logic tells us how about we ought to reason? If P entails Q, and I believe P, should I believe Q? I will argue that we should embed the issue in an independently motivated contextualist semantics for ‘ought’, with parameters for a standard and set of propositions. With the contextualist machinery in hand, we can defend a strong principle expressing how agents ought to reason while accommodating conflicting intuitions. I then show how our judgments about blame and guidance (...) can be handled by this machinery. (shrink)

Decision-making typically requires judgments about causal relations: we need to know the causal effects of our actions and the causal relevance of various environmental factors. We investigate how several individuals' causal judgments can be aggregated into collective causal judgments. First, we consider the aggregation of causal judgments via the aggregation of probabilistic judgments, and identify the limitations of this approach. We then explore the possibility of aggregating causal judgments independently of probabilistic ones. Formally, we introduce the problem of causal-network aggregation. (...) Finally, we revisit the aggregation of probabilistic judgments when this is constrained by prior aggregation of qualitative causal judgments. (shrink)

According to the so-called Lockean thesis, a rational agent believes a proposition just in case its probability is sufficiently high, i.e., greater than some suitably fixed threshold. The Preface paradox is usually taken to show that the Lockean thesis is untenable, if one also assumes that rational agents should believe the conjunction of their own beliefs: high probability and rational belief are in a sense incompatible. In this paper, we show that this is not the case in general. More precisely, (...) we consider two methods of computing how probable must each of a series of propositions be in order to rationally believe their conjunction under the Lockean thesis. The price one has to pay for the proposed solutions to the paradox is what we call “quasi-dogmatism”: the view that a rational agent should believe only those propositions which are “nearly certain” in a suitably defined sense. (shrink)

According to infinitism, beliefs can be justified by an infinite chain of reasons. So far, infinitism has rarely been taken seriously and often even dismissed as inconsistent. However, Peijnenburg and Atkinson have recently argued that beliefs can indeed be justified by an infinite chain of reasons, if justification is understood probabilistically. In the following, I will discuss the formal result that has led to this conclusion. I will then introduce three probabilistic explications of justification and examine to which extent they (...) support Peijnenburg’s and Atkinson’s claim. (shrink)

We propose a new account of indicative conditionals, giving acceptability and logical closure conditions for them. We start from Adams’ Thesis: the claim that the acceptability of a simple indicative equals the corresponding conditional probability. The Thesis is widely endorsed, but arguably false and refuted by empirical research. To fix it, we submit, we need a relevance constraint: we accept a simple conditional 'If φ, then ψ' to the extent that (i) the conditional probability p(ψ|φ) is high, provided that (ii) (...) φ is relevant for ψ. How (i) should work is well-understood. It is (ii) that holds the key to improve our understanding of conditionals. Our account has (i) a probabilistic component, using Popper functions; (ii) a relevance component, given via an algebraic structure of topics or subject matters. We present a probabilistic logic for simple indicatives, and argue that its (in)validities are both theoretically desirable and in line with empirical results on how people reason with conditionals. (shrink)

Epistemologists focus primarily on cases of knowledge, belief, or credence where the evidence which one possesses, or on which one is relying, plays a fundamental role in the epistemic or normative status of one's doxastic state. Recent work in epistemology goes beyond the evidence one possesses to consider the relevance for such statuses of evidence which one does not possess, particularly when there is a sense in which one should have had some evidence. I focus here on Sanford Goldberg's approach (...) ("Should Have Known," Synthese, forthcoming; and "On the Epistemic Significance of Evidence You Should Have Had," Episteme 2016, this issue); but the discussion will interest anyone working on epistemic defeat. (shrink)

It is natural to regard understanding as having a rational dimension, in the sense that understanding seems to require having justification for holding certain beliefs about the world. Some philosophers however argue that justification is not required to gain understanding of phenomena. In the present paper, my intention is to provide a critical examination of the arguments that have been offered against the view that understanding requires justification in order to show that, contrary to what they purport to establish, justification (...) remains a plausible requirement on understanding. (shrink)

According to deontological approaches to justification, we can analyze justification in deontic terms. In this paper, I try to advance the discussion of deontological approaches by applying recent insights in the semantics of deontic modals. Specifically, I use the distinction between weak necessity modals and strong necessity modals to make progress on a question that has received surprisingly little discussion in the literature, namely: ‘What’s the best version of a deontological approach?’ The two most obvious hypotheses are the Permissive View, (...) according to which justified expresses permission, and the Obligatory View, according to which justified expresses some species of obligation. I raise difficulties for both of these hypotheses. In light of these difficulties, I propose a new position, according to which justified expresses a property I call faultlessness, defined as the dual of weak necessity modals. According to this view, an agent is justified in phi-ing iff it’s not the case that she should [/ought] not phi. I argue that this ‘Faultlessness View’ gives us precisely what’s needed to avoid the problems facing the Permissive and Obligatory Views. (shrink)

What is it to believe something might be the case? We develop a puzzle that creates difficulties for standard answers to this question. We go on to propose our own solution, which integrates a Bayesian approach to belief with a dynamic semantics for epistemic modals. After showing how our account solves the puzzle, we explore a surprising consequence: virtually all of our beliefs about what might be the case provide counterexamples to the view that rational belief is closed under logical (...) implication. (shrink)

There are many ordinary propositions we think we know. Almost every ordinary proposition entails some "lottery proposition" which we think we do not know but to which we assign a high probability of being true (for instance: “I will never be a multi-millionaire” entails “I will not win this lottery”). How is this possible - given that some closure principle is true? This problem, also known as “the Lottery puzzle”, has recently provoked a lot of discussion. In this paper I (...) discuss one of the most promising answers to the problem: Stewart Cohen’s contextualist solution which is based on ideas about the salience of chances of error. After presenting some objections to it I sketch an alternative solution which is still contextualist in spirit. (shrink)

This article discusses Keith DeRose’s treatment of the lottery problem in Chapter 5 of his recent The Appearance of Ignorance. I agree with a lot of it but also raise some critical points and questions and make some friendly proposals. I discuss different ways to set up the problem, go into the difference between knowing and ending inquiry, propose to distinguish between two different kinds of lotteries, add to the defense of the idea that one can know lottery propositions, give (...) a critical discussion of DeRose’s contextualist solution to the problem, and support his defense against an absurdity objection with additional arguments. (shrink)

Is self-knowledge a requirement of rationality, like consistency, or means-ends coherence? Many claim so, citing the evident impropriety of asserting, and the alleged irrationality of believing, Moore-paradoxical propositions of the form < p, but I don't believe that p>. If there were nothing irrational about failing to know one's own beliefs, they claim, then there would be nothing irrational about Moore-paradoxical assertions or beliefs. This article considers a few ways the data surrounding Moore's paradox might be marshaled to support rational (...) requirements to know one's beliefs, and finds that none succeed. (shrink)

Why ever assert clarity? If It is clear that p is true, then saying so should be at best superfluous. Barker and Taranto (2003) and Taranto (2006) suggest that asserting clarity reveals information about the beliefs of the discourse participants, specifically, that they both believe that p . However, mutual belief is not sufficient to guarantee clarity ( It is clear that God exists ). I propose instead that It is clear that p means instead (roughly) 'the publicly available evidence (...) justifies concluding that p '. Then what asserting clarity reveals is information concerning the prevailing epistemic standard that determines whether a body of evidence is sufficient to justify a claim. If so, the semantics of clarity constitutes a grammatical window into the discourse dynamics of inference and skepticism. (shrink)

The primary objective of this paper is to introduce a new epistemic paradox that puts pressure on the claim that justification is closed under multi premise deduction. The first part of the paper will consider two well-known paradoxes—the lottery and the preface paradox—and outline two popular strategies for solving the paradoxes without denying closure. The second part will introduce a new, structurally related, paradox that is immune to these closure-preserving solutions. I will call this paradox, The Paradox of the Pill. (...) Seeing that the prominent closure-preserving solutions do not apply to the new paradox, I will argue that it presents a much stronger case against the claim that justification is closed under deduction than its two predecessors. Besides presenting a more robust counterexample to closure, the new paradox also reveals that the strategies that were previously thought to get closure out of trouble are not sufficiently general to achieve this task as they fail to apply to similar closure-threatening paradoxes in the same vicinity. (shrink)

Following the pioneer work of Bruno De Finetti [12], conditional probability spaces (allowing for conditioning with events of measure zero) have been studied since (at least) the 1950's. Perhaps the most salient axiomatizations are Karl Popper's in [31], and Alfred Renyi's in [33]. Nonstandard probability spaces [34] are a well know alternative to this approach. Vann McGee proposed in [30] a result relating both approaches by showing that the standard values of infinitesimal probability functions are representable as Popper functions, and (...) that every Popper function is representable in terms of the standard real values of some infinitesimal measure. Our main goal in this article is to study the constraints on (qualitative and probabilistic) change imposed by an extended version of McGee's result. We focus on an extension capable of allowing for iterated changes of view. Such extension, we argue, seems to be needed in almost all considered applications. Since most of the available axiomatizations stipulate (definitionally) important constraints on iterated change, we propose a non-questionbegging framework, Iterative Probability Systems (IPS) and we show that every Popper function can be regarded as a Bayesian IPS. A generalized version of McGee's result is then proved and several of its consequences considered. In particular we note that our proof requires the imposition of Cumulativity, i.e. the principle that a proposition that is accepted at any stage of an iterative process of acceptance will continue to be accepted at any later stage. The plausibility and range of applicability of Cumulativity is then studied. In particular we appeal to a method for defining belief from conditional probability (first proposed in [42] and then slightly modified in [6] and [3]) in order to characterize the notion of qualitative change induced by Cumulative models of probability kinematics. The resulting cumulative notion is then compared with existing axiomatizations of belief change and probabilistic supposition. We also consider applications in the probabilistic accounts of conditionals [1] and [30]. (shrink)

"Rationality: Contexts and Constraints" is an interdisciplinary reappraisal of the nature of rationality. In method, it is pluralistic, drawing upon the analytic approaches of philosophy, linguistics, neuroscience, and more. These methods guide exploration of the intersection between traditional scholarship and cutting-edge philosophical or scientific research. In this way, the book contributes to development of a suitably revised, comprehensive understanding of rationality, one that befits the 21st century, one that is adequately informed by recent investigations of science, pathology, non-human thought, emotion, (...) and even enigmatic Chinese texts that might previously have seemed to be expressions of irrationalism. Addresses recent challenges and Identifies a direction for future research on rationalityInvestigates the relationship between rationality and mental disorders, such as delusion and depressionAssesses reasoning in artificial intelligence and nonhuman animalsReflects on ancient Chinese Philosophy and possible cultural differences in human psychology Employs philosophical reflection, along with linguistic, probabilistic, and logical techniques. (shrink)

How much does rationality constrain what we should believe on the basis of our evidence? According to this book, not very much. For most people and most bodies of evidence, there is a wide range of beliefs that rationality permits them to have in response to that evidence. The argument, which takes inspiration from William James' ideas in 'The Will to Believe', proceeds from two premises. The first is a theory about the basis of epistemic rationality. It's called epistemic utility (...) theory, and it says that what it is epistemically rational for you to believe is what it would be rational for you to choose if you were given the chance to pick your beliefs and, when picking them, you were to care only about their epistemic value. So, to say which beliefs are permitted, we must say how to measure epistemic value, and which decision rule to use when picking your beliefs. The second premise is a claim about attitudes to epistemic risk, and it says that rationality permits many different such attitudes. These attitudes can show up in epistemic utility theory in two ways: in the way you measure epistemic value; and in the decision rule you use to pick beliefs. This book explores the latter. The result is permissivism about epistemic rationality: different attitudes to epistemic risk lead to different choices of prior beliefs; given most bodies of evidence, different priors lead to different posteriors; and even once we fix your attitudes to epistemic risk, if they are at all risk-inclined, there is a range of different priors and therefore different posteriors they permit. (shrink)

We conducted five experiments that reveal some main contours of the folk epistemology of lotteries. The folk tend to think that you don't know that your lottery ticket lost, based on the long odds ("statistical cases"); by contrast, the folk tend to think that you do know that your lottery ticket lost, based on a news report ("testimonial cases"). We evaluate three previous explanations for why people deny knowledge in statistical cases: the justification account, the chance account, and the statistical (...) account. None of them seems to work. We then propose a new explanation of our own, the formulaic account, according to which some people deny knowledge in statistical cases due to formulaic expression. (shrink)

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 (...) recalling my argument to this conclusion, I demonstrate that a McGee-like example (which is just, in fact, Carroll’s barbershop paradox) can be provided in which the Lockean Thesis plays no role: this proves that denying Belief Closure is the right way to deal with both McGee’s scenario and the Lottery Paradox. A straightforward consequence of my approach is that Carroll’s puzzle is solved, too. (shrink)