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 (...) n°1000 will lose” are equivalent to soritical premises of the form “~(the winning ticket is in {…, (tn)}) ⊃ ~(the winning ticket is in {…, tn, (tn + 1)})” (where “⊃” is the material conditional, “~” is the negation symbol, “tn” and “tn + 1” are “ticket n°n” and “ticket n°n + 1” respectively, and “{}” identify the elements of the lottery tickets’ set. The brackets in “(tn)” and “(tn + 1)” are meant to point out that in the antecedent of the conditional we do not always have a “tn” (and, as a result, a “tn + 1” in the consequent): consider the conditional “~(the winning ticket is in {}) ⊃ ~(the winning ticket is in {t1})”). As a result, failing to believe, for some ticket, that it will lose comes down to introducing a cut-off point in a chain of soritical premises. In this paper I explore the consequences of the different ways of blocking the Lottery Paradox with respect to the Cut-off Point Problem. A heap variant of the Lottery Paradox is especially relevant for evaluating the different solutions. One important result is that the most popular way out of the puzzle, i.e., denying the Lockean Thesis, becomes less attractive. Moreover, I show that, along with the debate on whether rational belief is closed under classical logic, the debate on the validity of modus ponens should play an important role in discussions on the Lottery Paradox. -/- . (shrink)

It is valuable for inquiry to have researchers who are committed advocates of their own theories. However, in light of pervasive disagreement, such a commitment is not well explained by the idea that researchers believe their theories. Instead, this commitment, the rational attitude to take toward one’s favored theory during the course of inquiry, is what I call endorsement. Endorsement is a doxastic attitude, but one which is governed by a different type of epistemic rationality. This inclusive epistemic rationality is (...) sensitive to reasons beyond those to think the particular proposition in question is true. Instead, it includes extrinsic epistemic reasons, which concern the health of inquiry more generally. Such extrinsic reasons include the distribution of cognitive labor that a researcher will contribute to by endorsing a particular theory. Recognizing endorsement and inclusive epistemic rationality thus allows us to smooth a tension between individual rationality and collective rationality. It does so by showing how it can be epistemically rational to endorse a theory on the basis of the way this endorsement will benefit collective inquiry. I provide a decision theoretic treatment for inclusive epistemic rationality and endorsement which illustrates how this can be accomplished. (shrink)

Deductive Cogency holds that the set of propositions towards which one has, or is prepared to have, a given type of propositional attitude should be consistent and closed under logical consequence. While there are many propositional attitudes that are not subject to this requirement, e.g. hoping and imagining, it is at least prima facie plausible that Deductive Cogency applies to the doxastic attitude involved in propositional knowledge, viz. belief. However, this thought is undermined by the well-known preface paradox, leading a (...) number of philosophers to conclude that Deductive Cogency has at best a very limited role to play in our epistemic lives. I argue here that Deductive Cogency is still an important epistemic requirement, albeit not as a requirement on belief. Instead, building on a distinction between belief and acceptance introduced by Jonathan Cohen and recent developments in the epistemology of understanding, I propose that Deductive Cogency applies to the attitude of treating propositions as given in the context of attempting to understand a given phenomenon. I then argue that this simultaneously accounts for the plausibility of the considerations in favor of Deductive Cogency and avoids the problematic consequences of the preface paradox. (shrink)

According to Bas van Fraassen, scientific realists and anti-realists disagree about whether accepting a scientific theory involves believing that the theory is true. On van Fraassen’s own anti-realist empiricist position, accepting a theory involves believing only that the theory is correct in its claims about observable aspects of the world. However, a number of philosophers have argued that acceptance and belief cannot be distinguished and thus that the debate is either confused or trivially settled in favor of the realist. In (...) addition, another set of philosophers have argued that van Fraassen’s empiricist position appeals to an unmotivated distinction between observable and unobservable aspects of the world. This paper aims to reconstruct a van Fraassen-style empiricism about scientific acceptance that avoids these two objections – reconstructed empiricism. (shrink)

Certain philosophers maintain that there is a ‘constitutive threshold for belief’: to believe that p just is to have a degree of confidence that p above a certain threshold. On the basis of this view, these philosophers defend what is known as ‘the Lockean Thesis ’, according to which it is rational to believe that p just in case it is rational to have a degree of confidence that p above the constitutive threshold for belief. While not directly speaking to (...) the controversy over the Lockean Thesis, this paper defends the general idea behind it—namely, the thesis that there is some threshold such that it is rational to believe that p if and only if it is rational to have a degree of confidence great than that threshold. This paper identifies the threshold in question—not with the alleged constitutive threshold for belief—but with what I call ‘the practical threshold for rational belief’. Roughly, the thesis defended here is that it is rational to believe that p if and only if it is rational to have a degree of confidence that p that rationalizes engaging in certain types of practical reasoning. (shrink)

This paper argues for two theses: that degrees of belief are context sensitive; that outright belief is belief to degree 1. The latter thesis is rejected quickly in most discussions of the relationship between credence and belief, but the former thesis undermines the usual reasons for doing so. Furthermore, identifying belief with credence 1 allows nice solutions to a number of problems for the most widely-held view of the relationship between credence and belief, the threshold view. I provide a sketch (...) of a formal framework on which both theses are true. This is a modified Bayesian framework; I argue that despite making credences context-sensitive, the framework lets Bayesians hold on to their signature explanatory successes. The sort of context-sensitivity claimed for credences here mirrors the sort of context-sensitivity I have elsewhere claimed for outright belief: one's credences depend, in part, on the space of alternative possibilities one takes seriously in a context. (shrink)

The Preface Paradox has led many philosophers to believe that, if it isassumed that high probability is necessary for rational acceptability, the principleaccording to which rational acceptability is closed under conjunction (CP)must be abandoned. In this paper we argue that the paradox is far less damaging to CP than is generally believed. We describe how, given certain plausibleassumptions, in a large class of cases in which CP seems to lead tocontradiction, it does not do so after all. A restricted version (...) of CP canthus be maintained. (shrink)

Is Bayesian decision theory a panacea for many of the problems in epistemology and the philosophy of science, or is it philosophical snake-oil? For years a debate had been waged amongst specialists regarding the import and legitimacy of this body of theory. Mark Kaplan had written the first accessible and non-technical book to address this controversy. Introducing a new variant on Bayesian decision theory the author offers a compelling case that, while no panacea, decision theory does in fact have the (...) most profound consequences for the way in which philosophers think about inquiry, criticism and rational belief. The new variant on Bayesian theory is presented in such a way that a non-specialist will be able to understand it. The book also offers new solutions to some classic paradoxes. It focuses on the intuitive motivations of the Bayesian approach to epistemology and addresses the philosophical worries to which it has given rise. (shrink)

This thesis defends an account of what it is to trust other people, and what gives matters of trust (i.e. situations where we trust/distrust others) a characteristic interpersonal, normative, or moral/ethical importance to us. In other words, it answers what the nature of betrayal (and being susceptible to betrayal) is. -/- Along the way I put forward/defend accounts of the following: the relationship between trust and reliance (chapter 4); an account of reliance itself (chapter 5); trust and distrust as one/two/three-place (...) attitudes (chapter 7); and the ethical/normative significance of trust and betrayal as a matter of attachment security (chapters 6 and 8). -/- In addition to these accounts, the thesis also gives (in chapter 2) a conceptual/historical overview of the dominant paradigm in philosophical understanding of trust: as a form of reliance 'plus' betrayal conditions (a la Baier 1986; Holton 1994; Hawley 2014, among others). It also offers a rebuttal of that dominant paradigm in chapter 3 and 4. Furthermore, it offers an overview of how trust is understood more generally across philosophical and some social scientific/psychological literature (chapter 1). It also offers a rebuttal of the rational choice/game-theoretic understanding of trust and economic rationality a la so-called 'trust games' (chapter 1). This carries the consequence that analysis of trust in these traditions is not really based on anything resembling interpersonal trust, as we would intuitively recognise it. (shrink)

The aim of this paper is to propose foundations for a formal model of representation and numerical evaluation of a possibly broad class of arguments, including those that occur in natural discourse. Since one of the most characteristic features of everyday argumentation is the occurrence of convergent reasoning, special attention should be paid to the operation ⊕, which allows us to calculate the logical force of convergent arguments with an accuracy not offered by other approaches.

This paper offers a new model of belief by embedding the Peircean account of belief into a formal dialogue system that uses argumentation schemes for practical reasoning and abductive reasoning. A belief is characterised as a stable proposition that is derived abductively by one agent in a dialogue from the commitment set (including commitments derived from actions and goals) of another agent. On the model (to give a rough summary), a belief is defined as a proposition held by an agent (...) that (1) is not easily changed (stable), (2) is a matter of degree (held more or less weakly or strongly), (3) guides the goals and actions of the agent, and (4) is habitually or tenaciously held in a manner that indicates a strong commitment to defend it. It is argued that the new model overcomes the pervasive conflict in artificial intelligence between the belief-desire-intention model of reasoning and the commitment model. (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)

Glymour’s theory of bootstrap confirmation is a purely qualitative account of confirmation; it allows us to say that the evidence confirms a given theory, but not that it confirms the theory to a certain degree. The present paper extends Glymour’s theory to a quantitative account and investigates the resulting theory in some detail. It also considers the question how bootstrap confirmation relates to justification.

In this article I attempt to provide a conceptual framework for thinking about reliance in a systematic way. I argue that reliance is a cognitive attitude that has a tighter connection to the guidance of our thought and action than ordinary belief does. My main thesis is that reliance has a ‘constitutive aim’: namely, it aims at guiding our thought and action in a way that is sensible from the standpoint of practical or theoretical ends. This helps explain why reliance (...) is, in contrast to belief, typically formed and revised in response to pragmatic considerations. (shrink)

Many have the intuition that the right response to the Lottery Paradox is to deny that one can justifiably believe of even a single lottery ticket that it will lose. The paper shows that from any theory of justification that solves the paradox in accordance with this intuition, a theory not of that kind can be derived that also solves the paradox but is more conducive to our epistemic goal than the former. It is argued that currently there is no (...) valid reason not to give preference to the derived accounts over the accounts from which they come. (shrink)

An area in the theory of action that has received little attention is how mental agency and world-directed agency interact. The purpose of the present contribution is to clarify the rational conditions of such interaction, through an analysis of the central case of acceptance. There are several problems with the literature about acceptance. First, it remains unclear how a context of acceptance is to be construed. Second, the possibility of conjoining, in acceptance, an epistemic component, which is essentially mind-to-world, and (...) a utility component, which requires a world-to-mind direction of fit, is merely posited rather than derived from the rational structure of acceptance. Finally, the norm of acceptance is generally seen as related to truth, which turns out to be inapplicable in a number of cases. We will argue, first, that the specific context-dependence of acceptances is derived from their being mental actions, each embedded in a complex hierarchy of acceptances composing, together, a planning sequence. Second, that acceptances come in several varieties, corresponding to the specific epistemic norm(s) that constitute them. The selection of a particular norm for accepting answers to considerations of utility – to the association of an epistemic goal with an encompassing world-directed action. Once a type of acceptance is selected, however, the epistemic norm constitutive for that acceptance strictly applies. Third, we argue that context-dependence superimposes a decision criterion on the output of the initial epistemic acceptance. Strategic acceptance is regulated by instrumental norms of expected utility, which may rationally lead an agent to screen off her initial epistemic acceptance. (shrink)

An impossibility result pertaining to the aggregation of individual judgements is thought by many to have significant implications for political theory, social epistemology and metaphysics. When members of a group hold a rational set of judgments on some interconnected questions, the theorem shows, it isn't always (logically) possible for them to aggregate their judgements into a collective one in conformity with seemingly very plausible constraints. I reject one of the constraints which engender the dilemma. The analogy with the lottery paradox, (...) I argue, shows that rational belief needn't be consistent. So the alleged implications of the dilemma are dispelled. (shrink)

There is a duality in our everyday view of belief. On the one hand, we sometimes speak of credence as a matter of degree. We talk of having some level of confidence in a claim (that a certain course of action is safe, for example, or that a desired event will occur) and explain our actions by reference to these degrees of confidence – tacitly appealing, it seems, to a probabilistic calculus such as that formalized in Bayesian decision theory. On (...) the other hand, we also speak of belief as an unqualified, or flat-out, state (‘plain belief’ as it is sometimes called), which is either categorically present or categorically absent. We talk of simply believing or thinking that something is the case, and we cite these flat-out attitudes in explanation of our actions – appealing to classical practical reasoning of the sort formalized in the so-called ‘practical syllogism’.1 This tension in everyday discourse is reflected in the theoretical literature on belief. In formal epistemology there is a division between those in the Bayesian tradition, who treat credence as graded, and those who think of it as a categorical attitude of some kind. The Bayesian perspective also contrasts with the dominant view in philosophy of mind, where belief is widely regarded as a categorical state (a token sentence of a mental language, inscribed in a functionally defined ‘belief box’, according to one popular account). A parallel duality is present in our everyday view of desire. Sometimes we talk of having degrees of preference or desirability; sometimes we speak simply of wanting or desiring something tout court, and, again, this tension is reflected in the theoretical literature. What should we make of these dualities? Are there two different types of belief and desire – partial and flat-out, as they are sometimes called? If so, how are they related? And how could both have a role in guiding rational action, as the everyday view has it? The last question poses a particular challenge in relation to flat-out belief and desire.. (shrink)

This chapter outlines a new argument for the view that language has a cognitive role. I suggest that humans exhibit two distinct kinds of belief state, one passively formed, the other actively formed. I argue that actively formed beliefs (_virtual beliefs_, as I call them) can be identified with _premising policies_, and that forming them typically involves certain linguistic operations. I conclude that natural language has at least a limited cognitive role in the formation and manipulation of virtual beliefs.

As part of an exceptionally lucid analysis of the Lottery Paradox, Dana Nelkin castigates the solutions to that paradox put forward by Laurence Bonjour and Sharon Ryan. According to her, these are “so finely tailored to lottery-like cases that they are limited in their ability to explain [what seem the intuitively right responses to such cases]”. She then offers a solution to the Lottery Paradox that allegedly has the virtue of being independently motivated by our intuitions regarding certain non-lottery-like cases. (...) This note argues that Nelkin fails to show that her solution applies to other than lottery-like cases or in any event that it is more general than Bonjour’s and Ryan’s solutions. (shrink)

As part of an exceptionally lucid analysis of the Lottery Paradox, Dana Nelkin castigates the solutions to that paradox put forward by Laurence Bonjour and Sharon Ryan. According to her, these are “so finely tailored to lottery-like cases that they are limited in their ability to explain [what seem the intuitively right responses to such cases]”. She then offers a solution to the Lottery Paradox that allegedly has the virtue of being independently motivated by our intuitions regarding certain non-lottery-like cases. (...) This note argues that Nelkin fails to show that her solution applies to other than lottery-like cases or in any event that it is more general than Bonjour’s and Ryan’s solutions. (shrink)