'Knowledge and its Limits' starts its exposition of the knowledge-first approach to epistemology with a structural analogy between knowledge and action as the two key relations between mind and world (Williamson 2000: 1, 6-8). This chapter aims to reconsider the relation between knowledge and action, and refine the analogy.

We study decision under uncertainty in an Anscombe–Aumann framework. Two binary relations characterize a decision-maker: one incomplete relation, reflecting her objective rationality, and a second complete relation, reflecting her subjective rationality. We require the latter to be an extension of the former. Our key axiom is a dominance condition. Our main theorem provides a representation of the two relations. The objectively rational relation has a Bewley-style multiple prior representation. Using this set of priors, we fully characterize the subjectively rational relation (...) in terms of the most optimistic and most pessimistic expected utilities. (shrink)

Sarah Moss’ thesis that we have probabilistic knowledge is from some perspectives unsurprising and from other perspectives hard to make sense of. The thesis is potentially transformative, but not yet elaborated in sufficient detail for epistemologists. This paper interprets Mossean probabilistic knowledge in a suitably-modified Kripke framework, thus filling in key details. It argues that probabilistic knowledge looks natural and plausible when so interpreted, and shows how the most pressing challenges to the thesis can be overcome. Most importantly, probabilistic knowledge (...) can satisfy factivity in the framework, though we are not forced to accept a specific account of probabilistic “facts”. The framework also reflects Moss’ claim that old-fashioned propositional knowledge is just a limiting case of probabilistic knowledge, and all knowledge is fundamentally probabilistic. Finally, Moss endorses a failure of contraposition: for example, p implies probably p, but not probably p does not imply not p. The framework makes clear the sense in which the valid inferences regarding probably p are as Moss claims. (shrink)

Philosophy and Phenomenological Research, EarlyView.

This is the classic work upon which modern-day game theory is based. What began as a modest proposal that a mathematician and an economist write a short paper together blossomed, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry (...) it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences. (shrink)

Traditional philosophical discussions of knowledge have focused on the epistemic status of full beliefs. In this book, Moss argues that in addition to full beliefs, credences can constitute knowledge. For instance, your .4 credence that it is raining outside can constitute knowledge, in just the same way that your full beliefs can. In addition, you can know that it might be raining, and that if it is raining then it is probably cloudy, where this knowledge is not knowledge of propositions, (...) but of probabilistic contents. -/- The notion of probabilistic content introduced in this book plays a central role not only in epistemology, but in the philosophy of mind and language as well. Just as tradition holds that you believe and assert propositions, you can believe and assert probabilistic contents. Accepting that we can believe, assert, and know probabilistic contents has significant consequences for many philosophical debates, including debates about the relationship between full belief and credence, the semantics of epistemic modals and conditionals, the contents of perceptual experience, peer disagreement, pragmatic encroachment, perceptual dogmatism, and transformative experience. In addition, accepting probabilistic knowledge can help us discredit negative evaluations of female speech, explain why merely statistical evidence is insufficient for legal proof, and identify epistemic norms violated by acts of racial profiling. Hence the central theses of this book not only help us better understand the nature of our own mental states, but also help us better understand the nature of our responsibilities to each other. (shrink)

It has been claimed that, in response to certain kinds of evidence, agents ought to adopt imprecise credences: doxastic states that are represented by sets of credence functions rather than single ones. In this paper I argue that, given some plausible constraints on accuracy measures, accuracy-centered epistemologists must reject the requirement to adopt imprecise credences. I then show that even the claim that imprecise credences are permitted is problematic for accuracy-centered epistemology. It follows that if imprecise credal states are permitted (...) or required in the cases that their defenders appeal to, then the requirements of rationality can outstrip what would be warranted by an interest in accuracy. (shrink)

The aim of this paper is to sketch a theory of justified belief. What I have in mind is an explanatory theory, one that explains in a general way why certain beliefs are counted as justified and others as unjustified. Unlike some traditional approaches, I do not try to prescribe standards for justification that differ from, or improve upon, our ordinary standards. I merely try to explicate the ordinary standards, which are, I believe, quite different from those of many classical, (...) e. g., ‘Cartesian’, accounts. (shrink)

Reconhecido centro de formação profissional em carreiras jurídicas, o IDC oferece Especialização, preparação para Exame de Ordem e Cursos de Extensão em mais de 20 áreas do Direito, aprofundando os conhecimentos de advogados e bacharéis. Possui também graduação em Filosofia, além de promover Cursos Preparatórios para Concursos em diversas áreas, obtendo excelentes resultados de aprovação graças à preocupação constante na qualificação e excelência de seu corpo docente e infra-estrutura.

It is widely held that Bayesian decision theory is the final word on how a rational person should make decisions. However, Leonard Savage--the inventor of Bayesian decision theory--argued that it would be ridiculous to use his theory outside the kind of small world in which it is always possible to "look before you leap." If taken seriously, this view makes Bayesian decision theory inappropriate for the large worlds of scientific discovery and macroeconomic enterprise. When is it correct to use Bayesian (...) decision theory--and when does it need to be modified? Using a minimum of mathematics, Rational Decisions clearly explains the foundations of Bayesian decision theory and shows why Savage restricted the theory's application to small worlds. The book is a wide-ranging exploration of standard theories of choice and belief under risk and uncertainty. Ken Binmore discusses the various philosophical attitudes related to the nature of probability and offers resolutions to paradoxes believed to hinder further progress. In arguing that the Bayesian approach to knowledge is inadequate in a large world, Binmore proposes an extension to Bayesian decision theory--allowing the idea of a mixed strategy in game theory to be expanded to a larger set of what Binmore refers to as "muddled" strategies. Written by one of the world's leading game theorists, Rational Decisions is the touchstone for anyone needing a concise, accessible, and expert view on Bayesian decision making. (shrink)

Unspecific evidence calls for imprecise credence. My aim is to vindicate this thought. First, I will pin down what it is that makes one's imprecise credences more or less epistemically valuable. Then I will use this account of epistemic value to delineate a class of reasonable epistemic scoring rules for imprecise credences. Finally, I will show that if we plump for one of these scoring rules as our measure of epistemic value or utility, then a popular family of decision rules (...) recommends imprecise credences. In particular, a range of Hurwicz criteria, which generalise the Maximin decision rule, recommend imprecise credences. If correct, the moral is this: an agent who adopts precise credences, rather than imprecise ones, in the face of unspecific and incomplete evidence, goes wrong by gambling with the epistemic utility of her doxastic state in too risky a fashion. Precise credences represent an overly risky epistemic bet, according to the Hurwicz criteria. (shrink)

According to a tradition reaching back to Plato, questions about the nature of knowledge are to be answered by offering an analysis in terms of truth, belief, justification, and other factors presumed to be in some sense more basic than knowledge itself. In light of the apparent failure of this approach, knowledge first philosophy instead takes knowledge as the starting point in epistemology and related areas of the philosophies of language and mind. Knowledge cannot be analyzed in the traditional sense, (...) but this does not make it mysterious or unimportant. On the contrary, we are freed to use our grasp of what knowledge is to elucidate the nature of belief, justification, evidence, the speech act of assertion, and the demands on action and practical reasoning, and to treat knowledge as a purely mental state in its own right. Knowledge First? offers the first overview and critical evaluation of knowledge first philosophy as a whole. (shrink)

There has been much recent interest in imprecise probabilities, models of belief that allow unsharp or fuzzy credence. There have also been some influential criticisms of this position. Here we argue, chiefly against Elga (2010), that subjective probabilities need not be sharp. The key question is whether the imprecise probabilist can make reasonable sequences of decisions. We argue that she can. We outline Elga's argument and clarify the assumptions he makes and the principles of rationality he is implicitly committed to. (...) We argue that these assumptions are too strong and that rational imprecise choice is possible in the absence of these overly strong conditions. (shrink)

It is widely held that Bayesian decision theory is the final word on how a rational person should make decisions. However, Leonard Savage--the inventor of Bayesian decision theory--argued that it would be ridiculous to use his theory outside the kind of small world in which it is always possible to "look before you leap." If taken seriously, this view makes Bayesian decision theory inappropriate for the large worlds of scientific discovery and macroeconomic enterprise. When is it correct to use Bayesian (...) decision theory--and when does it need to be modified? Using a minimum of mathematics, Rational Decisions clearly explains the foundations of Bayesian decision theory and shows why Savage restricted the theory's application to small worlds. The book is a wide-ranging exploration of standard theories of choice and belief under risk and uncertainty. Ken Binmore discusses the various philosophical attitudes related to the nature of probability and offers resolutions to paradoxes believed to hinder further progress. In arguing that the Bayesian approach to knowledge is inadequate in a large world, Binmore proposes an extension to Bayesian decision theory--allowing the idea of a mixed strategy in game theory to be expanded to a larger set of what Binmore refers to as "muddled" strategies. Written by one of the world's leading game theorists, Rational Decisions is the touchstone for anyone needing a concise, accessible, and expert view on Bayesian decision making. (shrink)

Lara Buchak sets out a new account of rational decision-making in the face of risk. She argues that the orthodox view is too narrow, and suggests an alternative, more permissive theory: one that allows individuals to pay attention to the worst-case or best-case scenario, and vindicates the ordinary decision-maker.

In “Knowledge Under Threat” (Philosophy and Phenomenological Research 2012), Tomas Bogardus proposes a counterexample to the safety condition for knowledge. Bogardus argues that the case demonstrates that unsafe knowledge is possible. I argue that the case just corroborates the well-known requirement that modal conditions like safety must be relativized to methods of belief formation. I explore several ways of relativizing safety to belief-forming methods and I argue that none is adequate: if methods were individuated in those ways, safety would fail (...) to explain several much-discussed cases. I then propose a plausible externalist principle of method individuation. On the one hand, relativizing safety to belief-forming methods in the way suggested allows the defender of safety to account for the cases. On the other hand, it shows that the target known belief of Bogardus’s example is safe. Finally, I offer a diagnosis of a common error about the kind of cases that are typically considered potential counterexamples to the necessity of the epistemic condition: proponents of the alleged counterexamples mistake a strong condition that I call super-safety for safety. (shrink)

Recent proposals that frame norms of action in terms of knowledge have been challenged by Bayesian decision theorists. Bayesians object that knowledge-based norms conflict with the highly successful and established view that rational action is rooted in degrees of belief. I argue that the knowledge-based and Bayesian pictures are not as incompatible as these objectors have made out. Attending to the mechanisms of practical reasoning exposes space for both knowledge and degrees of belief to play their respective roles.

Many contemporary epistemologists hold that a subject S’s true belief that p counts as knowledge only if S’s belief that p is also, in some important sense, safe. I describe accounts of this safety condition from John Hawthorne, Duncan Pritchard, and Ernest Sosa. There have been three counterexamples to safety proposed in the recent literature, from Comesaña, Neta and Rohrbaugh, and Kelp. I explain why all three proposals fail: each moves fallaciously from the fact that S was at epistemic risk (...) just before forming her belief to the conclusion that S’s belief was formed unsafely. In light of lessons from their failure, I provide a new and successful counterexample to the safety condition on knowledge. It follows, then, that knowledge need not be safe. Safety at a time depends counterfactually on what would likely happen at that time or soon after in a way that knowledge does not. I close by considering one objection concerning higher-order safety. (shrink)

This paper argues that just as full beliefs can constitute knowledge, so can properties of your credence distribution. The resulting notion of probabilistic knowledge helps us give a natural account of knowledge ascriptions embedding language of subjective uncertainty, and a simple diagnosis of probabilistic analogs of Gettier cases. Just like propositional knowledge, probabilistic knowledge is factive, safe, and sensitive. And it helps us build knowledge-based norms of action without accepting implausible semantic assumptions or endorsing the claim that knowledge is interest-relative.

This paper distinguishes two ways to ?put knowledge first?. One way affirms a knowledge norm. For example, Williamson [2000] argues that one must only assert that which one knows. Hawthorne and Stanley [2008] argue that one must only treat as a reason for action that which one knows. Another way to put knowledge first affirms a determination thesis. For example, Williamson [2000] argues that what one knows determines what one is justified in believing. Hawthorne and Stanley [2008] argue that what (...) one knows determines what it is rational for one to do. This paper argues that the defender of the knowledge norms can and should reject the determination theses. For example, the rationality of acting on a partial belief cannot be explained in terms of the subject's knowledge. That's no problem for the knowledge norm, which only governs acting on full belief. (Analogously, the knowledge norm of flat-out assertion does not govern hedged assertion.) One might worry that rejecting the determination theses undermines the importance of knowing. I reply that the knowledge norms set the standard for epistemic success. The importance of success is not undermined by loosening its ties to justification and rationality. (shrink)

Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought.

An examination of topics involved in statistical reasoning with imprecise probabilities. The book discusses assessment and elicitation, extensions, envelopes and decisions, the importance of imprecision, conditional previsions and coherent statistical models.

Many have claimed that unspecific evidence sometimes demands unsharp, indeterminate, imprecise, vague, or interval-valued probabilities. Against this, a variant of the diachronic Dutch Book argument shows that perfectly rational agents always have perfectly sharp probabilities.

Eighteen leading philosophers offer critical assessments of Timothy Williamson's ground-breaking work on knowledge and its impact on philosophy today. They discuss epistemological issues concerning evidence, defeasibility, scepticism, testimony, assertion, and perception, and debate Williamson's central claim that knowledge is a mental state.

This paper argues that the interest-relativity of knowledge cannot be explained by the interest-relativity of belief. The discussion starts with an argument that knowledge plays a key pair of roles in decision theory. It is then argued that knowledge cannot play that role unless knowledge is interest-relative. The theory of the interest-relativity of belief is reviewed and revised. That theory can explain some of the cases that are used to suggest knowledge is interest-relative. But it can’t explain some cases involving (...) ignorance, or mistake, about the odds at which a bet is offered. The paper ends with an argument that these cases require positing interest-relative defeaters, which affect whether an agent knows something without affecting whether she believes it, or is justified in believing it. (shrink)

What is the normative role of knowledge? I argue that knowledge plays an important role as a norm of assertion and action, which is explained and unified by its more fundamental role as a norm of belief. Moreover, I propose a distinctive account of what this normative role consists in. I argue that knowledge is the aim of belief, which sets a normative standard of correctness and a corresponding normative standard of justification. According to my proposal, it is correct to (...) believe, assert and act on a proposition if and only if one is in a position to know it, but one has justification to believe, assert and act on a proposition if and only if one has justification to believe that one is in a position to know it. (shrink)

I develop an approach to action and practical deliberation according to which the degree of epistemic warrant required for practical rationality varies with practical context. In some contexts of practical deliberation, very strong warrant is called for. In others, less will do. I set forth a warrant account, (WA), that captures this idea. I develop and defend (WA) by arguing that it is more promising than a competing knowledge account of action due to John Hawthorne and Jason Stanley. I argue (...) that cases of warranted false belief speak in favor of (WA) and against the knowledge account. Moreover, I note some problems with an “excuse maneuver” that proponents of the knowledge account frequently invoke in response to cases of warranted false belief. Finally, I argue that (WA) may provide a strict invariantist account of cases that have been thought to motivate interest-relative or subject-sensitive theories of knowledge and warrant. (shrink)

"[This book] proposes new foundations for the Bayesian principle of rational action, and goes on to develop a new logic of desirability and probabtility."—Frederic Schick, _Journal of Philosophy_.

Degrees of belief; Dempster's rule of combination; Simple and separable support functions; The weights of evidence; Compatible frames of discernment; Support functions; The discernment of evidence; Quasi support functions; Consonance; Statistical evidence; The dual nature of probable reasoning.