Jim buys a ticket in a million-ticket lottery. He knows it is a fair lottery, but, given the odds, he believes he will lose. When the winning ticket is chosen, it is not his. Did he know his ticket would lose? It seems that he did not. After all, if he knew his ticket would lose, why would he have bought it? Further, if he knew his ticket would lose, then, given that his ticket is no different in its chances (...) of winning from any other ticket, it seems that by parity of reasoning he should also know that every other ticket would lose. But of course he doesn’t know that; in fact, he knows that not every ticket will lose. (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)

Various theories try to give accounts of how measures of this confidence do or ought to behave, both as far as the internal mental consistency of the agent as ...

There are circumstances in which we want to predict a series of interrelated events. Faced with such a prediction task, it is natural to consider logically inconsistent predictions to be irrational. However, it is possible to find cases where an inconsistent prediction has higher expected accuracy than any consistent prediction. Predicting tournaments in sports provides a striking example of such a case and I argue that logical consistency should not be a norm of rational predictions in these situations.

In legal proceedings, a fact-finder needs to decide whether a defendant is guilty or not based on probabilistic evidence. We defend the thesis that the defendant should be found guilty just in case it is rational for the fact-finder to believe that the defendant is guilty. We draw on Leitgeb’s stability theory for an appropriate notion of rational belief and show how our thesis solves the problem of statistical evidence. Finally, we defend our account of legal proof against challenges from (...) Staffel and compare it to a recent competitor put forth by Moss. (shrink)

Additionally, the text shows how to develop computationally feasible methods to mesh with this framework.

The volume analyses and develops David Makinson’s efforts to make classical logic useful outside its most obvious application areas. The book contains chapters that analyse, appraise, or reshape Makinson’s work and chapters that develop themes emerging from his contributions. These are grouped into major areas to which Makinsons has made highly influential contributions and the volume in its entirety is divided into four sections, each devoted to a particular area of logic: belief change, uncertain reasoning, normative systems and the resources (...) of classical logic. Among the contributions included in the volume, one chapter focuses on the “inferential preferential method”, i.e. the combined use of classical logic and mechanisms of preference and choice and provides examples from Makinson’s work in non-monotonic and defeasible reasoning and belief revision. One chapter offers a short autobiography by Makinson which details his discovery of modern logic, his travels across continents and reveals his intellectual encounters and inspirations. The chapter also contains an unusually explicit statement on his views on the role of logic in philosophy. (shrink)

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

This volume concerns Rational Agents - humans, players in a game, software or institutions - which must decide the proper next action in an atmosphere of partial information and uncertainty. The book collects formal accounts of Uncertainty, Rationality and Agency, and also of their interaction. It will benefit researchers in artificial systems which must gather information, reason about it and then make a rational decision on which action to take.

Much of the literature on the relationship between belief and credence has focused on the reduction question: that is, whether either belief or credence reduces to the other. This debate, while important, only scratches the surface of the belief-credence connection. Even on the anti-reductive dualist view, belief and credence could still be very tightly connected. Here, I explore questions about the belief-credence connection that go beyond reduction. This paper is dedicated to what I call the independence question: just how independent (...) are belief and credence? I look at this question from two angles: a descriptive one (as a psychological matter, how much can belief and credence come apart?) and a normative one (for a rational person, how closely connected are belief and credence?) Ultimately, I suggest that the two attitudes are more independent than one might think. (shrink)

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 (...) non-skeptical. We compare these proposals with each other and with the Lockean thesis, in particular with regard to the question of how much we gain by adopting any one of them instead of the probability 1 requirement, that is, of how likely it is that one believes more than the things one is fully certain of. (shrink)

This paper explores the nature of curiosity from an epistemological point of view. First it motivates this exploration by explaining why epistemologists do and should care about what curiosity is. Then it surveys the relevant literature and develops a particular approach.

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)

Until now, antirealists have offered sketches of a theory of truth, at best. In this paper, we present a probabilist account of antirealist truth in some formal detail, and we assess its ability to deal with the problems that are standardly taken to beset antirealism.

The thesis that high probability suffices for rational belief, while initially plausible, is known to face the Lottery Paradox. The present paper proposes an amended version of that thesis which escapes the Lottery Paradox. The amendment is argued to be plausible on independent grounds.

Sometimes, we think of belief as a phenomenon that comes in degrees – that is, in the many different levels of confidence that a thinker might have in various different propositions. Sometimes, we think of belief as a simple two-place relation that holds between a thinker and a proposition – that is, as what I shall here call "outright belief".

Starting from John MacFarlane's recent survey of answers to the question ‘What is assertion?’, I defend an account of assertion that draws on elements of MacFarlane's and Robert Brandom's commitment accounts, Timothy Williamson's knowledge norm account, and my own previous work on the normative status of logic. I defend the knowledge norm from recent attacks. Indicative conditionals, however, pose a problem when read along the lines of Ernest Adams' account, an account supported by much work in the psychology of reasoning. (...) Furthermore, there seems to be no place for degrees of belief in the accounts of belief and assertion given here. Degrees of belief do have a role in decision‐making, but, again, there is much evidence that the orthodox theory of subjective utility maximization is not a good description of what we do in decision‐making and, arguably, neither is it a good normative guide to how we ought to make decisions. (shrink)

In making assertions one takes on commitments to the consistency of what one asserts and to the logical consequences of what one asserts. Although there is no quick link between belief and assertion, the dialectical requirements on assertion feed back into normative constraints on those beliefs that constitute one's evidence. But if we are not certain of many of our beliefs and that uncertainty is modelled in terms of probabilities, then there is at least prima facie incoherence between the normative (...) constraints on belief and the probability-like structure of degrees of belief. I suggest that the norm-governed practice relating to degrees of belief is the evaluation of betting odds. (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.

Conditionals somehow express conditional beliefs. However, conditional belief is a bi-propositional attitude that is generally not truth-evaluable, in contrast to unconditional belief. Therefore, this article opts for an expressivistic semantics for conditionals, grounds this semantics in the arguably most adequate account of conditional belief, that is, ranking theory, and dismisses probability theory for that purpose, because probabilities cannot represent belief. Various expressive options are then explained in terms of ranking theory, with the intention to set out a general interpretive scheme (...) that is able to account for the most variegated usage of conditionals. The Ramsey test is only the first option. Relevance is another, familiar, but little understood item, which comes in several versions. This article adds a further family of expressive options, which is able to subsume also counterfactuals and causal conditionals, and indicates at the end how this family allows for partial recovery of truth conditions for conditionals. (shrink)

In this paper, I’ll survey a number of closure principles of epistemic justification and find them all wanting. However, it’ll be my contention that there’s a novel closure principle of epistemic justification that has the virtues of its close cousin closure principles, without their vices. This closure principle of epistemic justification can be happily thought of as a multi-premise closure principle and it cannot be used in Cartesian skeptical arguments that employ a closure principle of epistemic justification. In this way, (...) then, it represents marked improvement over other contemporary closure principles of epistemic justification that require both sacrificing multi-premise closure and forcing anti-Cartesian skeptics who reject the closure principle employed in certain Cartesian skeptical arguments to cast aside justification closure. (shrink)

Although recent epistemology has been marked by several prominent disagreements – e.g., between foundationalists and coherentists, internalists and externalists – there has been widespread agreement that some form of fallibilism must be correct. According to a rough formulation of this view, it is possible for a subject to have knowledge even in cases where the justification or grounding for the knowledge is compatible with the subject’s being mistaken. In this paper, I examine the motivation for fallibilism before providing a fully (...) general account of the view. I conclude by looking at the two major difficulties for fallibilism: the Gettier problem and the lottery paradox. (shrink)

According to what is now commonly referred to as “the Equation” in the literature on indicative conditionals, the probability of any indicative conditional equals the probability of its consequent of the conditional given the antecedent of the conditional. Philosophers widely agree in their assessment that the triviality arguments of Lewis and others have conclusively shown the Equation to be tenable only at the expense of the view that indicative conditionals express propositions. This study challenges the correctness of that assessment by (...) presenting data that cast doubt on an assumption underlying all triviality arguments. (shrink)

There was a long tradition in philosophy according to which good reasoning had to be deductively valid. However, that tradition began to be questioned in the 1960’s, and is now thoroughly discredited. What caused its downfall was the recognition that many familiar kinds of reasoning are not deductively valid, but clearly confer justification on their conclusions. Here are some simple examples.

The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely-held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single-premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent theory validating (...) all these principles by combining Hartry Field's theory of truth with a modal enrichment developed for a different purpose by Michael Caie. The only casualty is classical logic: the theory avoids paradox by using a weaker-than-classical K3 logic. I then assess the philosophical merits of this approach. I argue that, unlike the traditional semantic paradoxes involving extensional notions like truth, its plausibility depends on the way in which sentences are referred to--whether in natural languages via direct sentential reference, or in mathematical theories via indirect sentential reference by Gödel coding. In particular, I argue that from the perspective of natural language, my non-classical treatment of knowledge as a predicate is plausible, while from the perspective of mathematical theories, its plausibility depends on unresolved questions about the limits of our idealized deductive capacities. (shrink)

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 way (...) for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

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)

Plural definite descriptions across many languages display two well-known properties. First, they can give rise to so-called non-maximal readings, in the sense that they ‘allow for exceptions’. Second, while they tend to have a quasi-universal quantificational force in affirmative sentences, they tend to be interpreted existentially in the scope of negation. Building on previous works, we offer a theory in which sentences containing plural definite expressions trigger a family of possible interpretations, and where general principles of language use account for (...) their interpretation in various contexts and syntactic environments. Our theory solves a number of problems that these previous works encounter, and has broader empirical coverage in that it offers a precise analysis for sentences that display complex interactions between plural definites, quantifiers and bound variables, as well as for cases involving non-distributive predicates. The resulting proposal is briefly compared with an alternative proposal by Križ, which has similar coverage but is based on a very different architecture and sometimes makes subtly different predictions. (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)

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 (...) are jointly satisfied if and only if rational belief is equivalent to the assignment of a stably high rational degree of belief. Although the logical closure of belief and the Lockean thesis are attractive postulates in themselves, initially this may seem like a formal “curiosity”; however, as will be argued in the rest of the essay, a very reasonable theory of rational belief can be built around these principles that is not ad hoc and that has various philosophical features that are plausible independently. In particular, this essay shows that the theory allows for a solution to the Lottery Paradox, and it has nice applications to formal epistemology. The price that is to be paid for this theory is a strong dependency of belief on the context, where a context involves both the agent's degree of belief function and the partitioning or individuation of the underlying possibilities. But as this essay argues, that price seems to be affordable. 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, I will show that this combination of principles is satisfiable (and indeed nontrivially so) and that the principles are jointly satisfied if and only if rational belief is equivalent to the assignment of a stably high rational degree of belief. Although the logical closure of belief and the Lockean thesis are attractive postulates in themselves, initially this may seem like a formal “curiosity”; however, as I am going to argue in the rest of the essay, a very reasonable theory of rational belief can be built around these principles that is not ad hoc but that has various philosophical features that are plausible independently. (shrink)

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)

The applicability of Bayesian conditionalization in setting one’s posterior probability for a proposition, α, is limited to cases where the value of a corresponding prior probability, PPRI(α|∧E), is available, where ∧E represents one’s complete body of evidence. In order to extend probability updating to cases where the prior probabilities needed for Bayesian conditionalization are unavailable, I introduce an inference schema, defeasible conditionalization, which allows one to update one’s personal probability in a proposition by conditioning on a proposition that represents a (...) proper subset of one’s complete body of evidence. While defeasible conditionalization has wider applicability than standard Bayesian conditionalization (since it may be used when the value of a relevant prior probability, PPRI(α|∧E), is unavailable), there are circumstances under which some instances of defeasible conditionalization are unreasonable. To address this difficulty, I outline the conditions under which instances of defeasible conditionalization are defeated. To conclude the article, I suggest that the prescriptions of direct inference and statistical induction can be encoded within the proposed system of probability updating, by the selection of intuitively reasonable prior probabilities. (shrink)

According to Michael Friedman’s theory of explanation, a law X explains laws Y1, Y2, …, Yn precisely when X unifies the Y’s, where unification is understood in terms of reducing the number of independently acceptable laws. Philip Kitcher criticized Friedman’s theory but did not analyze the concept of independent acceptability. Here we show that Kitcher’s objection can be met by modifying an element in Friedman’s account. In addition, we argue that there are serious objections to the use that Friedman makes (...) of the concept of independent acceptability. (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)

Conditioning can make imprecise probabilities uniformly more imprecise. We call this effect "dilation". In a previous paper (1993), Seidenfeld and Wasserman established some basic results about dilation. In this paper we further investigate dilation on several models. In particular, we consider conditions under which dilation persists under marginalization and we quantify the degree of dilation. We also show that dilation manifests itself asymptotically in certain robust Bayesian models and we characterize the rate at which dilation occurs.

The present article illustrates a conflict between the claim that rational belief sets are closed under deductive consequences, and a very inclusive claim about the factors that are sufficient to determine whether it is rational to believe respective propositions. Inasmuch as it is implausible to hold that the factors listed here are insufficient to determine whether it is rational to believe respective propositions, we have good reason to deny that rational belief sets are closed under deductive consequences.

The bootstrapping problem poses a general challenge, afflicting even strongly internalist theories. Even if one must always know that one’s source is reliable to gain knowledge from it, bootstrapping is still possible. I survey some solutions internalists might offer and defend the one I find most plausible: that bootstrapping involves an abuse of inductive reasoning akin to generalizing from a small or biased sample. I also argue that this solution is equally available to the reliabilist. The moral is that the (...) issues raised by bootstrapping are orthogonal to questions about internalism and basic knowledge, having more to do with the nature of good inductive reasoning. (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)

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 (...) debate thus far. (shrink)

In Chapter 12 of Warrant and Proper Function, Alvin Plantinga constructs two arguments against evolutionary naturalism, which he construes as a conjunction E&N .The hypothesis E says that “human cognitive faculties arose by way of the mechanisms to which contemporary evolutionary thought directs our attention (p.220).”1 With respect to proposition N , Plantinga (p. 270) says “it isn’t easy to say precisely what naturalism is,” but then adds that “crucial to metaphysical naturalism, of course, is the view that there is (...) no such person as the God of traditional theism.” Plantinga tries to cast doubt on the conjunction E&N in two ways.His “preliminary argument” aims to show that the conjunction is probably false, given the fact (R) that our psychological mechanisms for forming beliefs about the world are generally reliable.His “main argument” aims to show that the conjunction E&N is self-defeating — if you believe E&N , then you should stop believing that conjunction.Plantinga further develops the main argument in his unpublished paper “Naturalism Defeated” (Plantinga 1994).We will try to show that both arguments contain serious errors. (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)

Everyday life reasoning and argumentation is defeasible and uncertain. I present a probability logic framework to rationally reconstruct everyday life reasoning and argumentation. Coherence in the sense of de Finetti is used as the basic rationality norm. I discuss two basic classes of approaches to construct measures of argument strength. The first class imposes a probabilistic relation between the premises and the conclusion. The second class imposes a deductive relation. I argue for the second class, as the first class is (...) problematic if the arguments involve conditionals. I present a measure of argument strength that allows for dealing explicitly with uncertain conditionals in the premise set. (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)