This paper explores the set theoretic assumptions used in the current published proof of Fermat's Last Theorem, how these assumptions figure in the methods Wiles uses, and the currently known prospects for a proof using weaker assumptions.

According to epistemological internalism, the rationality of a belief supervenes purely on "internal facts" about the thinker's mind. But what are "internal facts"? Why does the rationality of a belief supervene on them? The standard answers are unacceptable. This paper proposes new answers. "Internal facts" are facts about the thinker's nonfactive mental states. The rationality of a belief supervenes on such internal facts because we need rules of belief revision that we can follow directly, not by means of following any (...) other rules, and the proximate explanation of any belief revision always consists of such internal facts. (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)

Closure for justification is the claim that thinkers are justified in believing the logical consequences of their justified beliefs, at least when those consequences are competently deduced. Many have found this principle to be very plausible. Even more attractive is the special case of Closure known as Single-Premise Closure. In this paper, I present a challenge to Single-Premise Closure. The challenge is based on the phenomenon of rational self-doubt – it can be rational to be less than fully confident in (...) one's beliefs and patterns of reasoning. In rough outline, the argument is as follows: Consider a thinker who deduces a conclusion from a justified initial premise via an incredibly long sequence of small competent deductions. Surely, such a thinker should suspect that he has made a mistake somewhere. And surely, given this, he should not believe the conclusion of the deduction even though he has a justified belief in the initial premise. (shrink)

Virtually all philosophers agree that for a belief to be epistemically justified, it must satisfy certain conditions. Perhaps it must be supported by evidence. Or perhaps it must be reliably formed. Or perhaps there are some other "good-making" features it must have. But does a belief's justification also require some sort of awareness of its good-making features? The answer to this question has been hotly contested in contemporary epistemology, creating a deep divide among its practitioners. Internalists, who tend to focus (...) on scientific or theoretical beliefs as the ideal, insist that such awareness is required for justification. Externalists, who think children's ordinary beliefs in obvious facts are paradigm cases of justified belief, say it isn't required. Michael Bergmann's book offers a decisive refutation of internalism and a sustained defense of externalism. (shrink)

A stellar line-up of leading philosophers from around the world offer new treatments of a topic which has long been central to philosophical debate, and in ...

This book defends a form of ethical intuitionism, according to which (i) there are objective moral truths; (ii) we know some of these truths through a kind of immediate, intellectual awareness, or "intuition"; and (iii) our knowledge of moral truths gives us reasons for action independent of our desires. The author rebuts all the major objections to this theory and shows that the alternative theories about the nature of ethics all face grave difficulties.

Ernest Sosa argues for two levels of knowledge, the animal and the reflective, each viewed as a distinctive human accomplishment.

This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.

The Realm of Reason develops a new, general theory of what it is for a thinker to be entitled to form a given belief. The theory locates entitlement in the nexus of relations between truth, content, and understanding. Peacocke formulates three principles of rationalism that articulate this conception. The principles imply that all entitlement has a component that is justificationally independent of experience. The resulting position is thus a form of rationalism, generalized to all kinds of content. To show how (...) these principles are realized in specific domains, Peacocke applies the theory in detail to several classical problems of philosophy, including the nature of perceptual entitlement, induction, and the status of moral thought. These discussions involve an elaboration of the structure of entitlement in ways that have applications in many other areas of philosophy. He also relates the theory to classical and recent rationalist thought, and to current issues in the theory of meaning, reference and explanation. In the course of these discussions, he proposes a general theory of the a priori. The focus of the work lies in the intersection of epistemology, metaphysics, and the theory of meaning, and will be of interest both to students and researchers in these areas, and to anyone concerned with the idea of rationality. (shrink)

Knowledge and its Limits presents a systematic new conception of knowledge as a kind of mental stage sensitive to the knower's environment. It makes a major contribution to the debate between externalist and internalist philosophies of mind, and breaks radically with the epistemological tradition of analyzing knowledge in terms of true belief. The theory casts new light on such philosophical problems as scepticism, evidence, probability and assertion, realism and anti-realism, and the limits of what can be known. The arguments are (...) illustrated by rigorous models based on epistemic logic and probability theory. The result is a new way of doing epistemology and a notable contribution to the philosophy of mind. (shrink)

In this companion volume to Warrant: The Current Debate, Plantinga develops an original approach to the question of epistemic warrant; that is what turns true belief into knowledge. He argues that what is crucial to warrant is the proper functioning of one's cognitive faculties in the right kind of cognitive environment.

In this paper, we develop an account of the justification thinkers have for employing certain basic belief-forming methods. The guiding idea is inspired by Reichenbach's work on induction. There are certain projects in which thinkers are rationally required to engage. Thinkers are epistemically justified in employing any belief-forming method such that "if it doesn't work, nothing will" for successfully engaging in such a project. We present a detailed account based on this intuitive thought and address objections to it. We conclude (...) by commenting on the implications that our account may have for other important epistemological issues and debates. (shrink)

The essay addresses the well‐known idea that there has to be a place for intuition, thought of as a kind of non‐inferential rational insight, in the epistemology of basic logic if our knowledge of its principles is non‐empirical and is to allow of any finite, non‐circular reconstruction. It is argued that the error in this idea consists in its overlooking the possibility that there is, properly speaking, no knowledge of the validity of principles of basic logic. When certain important distinctions (...) are observed, for instance that between recognising that Modus Ponenes is sound and recognising that it is proof against the competent discovery of basic counterexamples, the case for thinking that there is indeed no space for genuine recognition of the validity of Modus Ponens becomes increasingly impressive. It is argued however that, the impossibility of knowledge notwithstanding, we are, in an important sense, entitled to take it that Modus Ponens is sound and that this notion of entitlement can help break the trichotomy ‐ intuition, inference, experience ‐ which imprisons our ordinary thinking about logical knowledge. (shrink)

Consider the skeptic about the external world. Let’s straightaway concede to such a skeptic that perception gives us no conclusive or certain knowledge about our surroundings. Our perceptual justification for beliefs about our surroundings is always defeasible—there are always possible improvements in our epistemic state which would no longer support those beliefs. Let’s also concede to the skeptic that it’s metaphysically possible for us to have all the experiences we’re now having while all those experiences are false. Some philosophers dispute (...) this, but I do not. The skeptic I want to consider goes beyond these familiar points to the much more radical conclusion that our perceptual experiences can’t give us any knowledge or even justification for believing that our surroundings are one way rather than another. (shrink)

A central issue in epistemology concerns the connection between truth and justification. The burden of our paper is to explain this connection. Reliabilism, defended by Goldman, assumes that the connection is one of reliability. We argue that this assumption is too strong. We argue that foundational theories, such as those articulated by Pollock and Chisholm fail to elucidate the connection. We consider the potentiality of coherence theories to explain the truth connection by means of higher level convictions about probabilities, which (...) we call doxastic ascent, and defend such a theory. Our defense appeals to the work of Reid and contemporary cognitive psychology in order to account for the psychological reality of higher level evaluations. (shrink)

The debate between externalists and internalists in epistemology can be viewed as a disagreement about whether there are epistemic rights without corresponding duties or obligations. Taking an epistemic right to believe P as an authorization to not only accept P as true but to use P as a positive reason for accepting other propositions, the debate is about whether there are unjustified justifiers. It is about whether there are propositions that provide for others what nothing need provide for them—viz., reasons (...) for thinking them true. (shrink)

Ernest Sosa's A Virtue Epistemology, Vol. I is arguably the single-most important monograph to be published in analytic epistemology in the last ten years. Sosa, the first in the field to employ the notion of intellectual virtue – in his ground-breaking ‘The Raft and the Pyramid’– is the leading proponent of reliabilist versions of virtue epistemology. In A Virtue Epistemology, he deftly defends an externalist account of animal knowledge as apt belief, argues for a distinction between animal and reflective knowledge, (...) contends that rational intuition is an intellectual virtue ; and offers responses to dream scepticism, the problem of the criterion and the value problem. Nearly all of these arguments are new, albeit consistent with Sosa's earlier work; that is, consistent with two notable exceptions. First, c ontra Sosa's ‘Replies’ in Ernest Sosa and His Critics, A Virtue Epistemology explicitly contends that safety is not required for animal knowledge. Second, unlike Sosa's Knowledge in Perspective, which arguably construes the intellectual virtues as merely instrumentally valuable, A Virtue Epistemology explicitly contends that the intellectual virtues are instrumentally and constitutively valuable. Best read in conjunction with the above monographs and Epistemic Justification, A Virtue Epistemology is mandatory reading for epistemologists and graduate students in the field. It will rightly set the standard for debates in analytic epistemology for years to come.I will summarize and raise objections to two key conclusions that are unique to A Virtue Epistemology: the ‘kaleidoscope-perceiver’ has animal knowledge but lacks reflective knowledge; unlike the k-perceiver, the ordinary perceiver has reflective knowledge. My objections …. (shrink)

Epistemic relativism has the contemporary academy in its grip. Not merely in the United States, but seemingly everywhere, most scholars working in the humanities and the social sciences seem to subscribe to some form of it. Even where the label is repudiated, the view is embraced. Sometimes the relativism in question concerns truth, sometimes justification. The core impulse appears to be a relativism about knowledge. The suspicion is widespread that what counts as knowledge in one cultural, or broadly ideological, setting (...) need not count as knowledge in another. (shrink)

The paper asks under what conditions deductive reasoning transmits justification from its premises to its conclusion. It argues that both standard externalist and standard internalist accounts of this phenomenon fail. The nature of this failure is taken to indicate the way forward: basic forms of deductive reasoning must justify by being instances of 'blind but blameless' reasoning. Finally, the paper explores the suggestion that an inferentialist account of the logical constants can help explain how such reasoning is possible.

This paper concerns the epistemology of difficult moral cases where the difficulty is not traceable to ignorance about non-moral matters. The paper first argues for a principle concerning the epistemic status of moral beliefs about difficult moral cases. The basic idea behind the principle is that one’s belief about the moral status of a potential action in a difficult moral case is not justified unless one has some appreciation of what the relevant moral considerations are and how they bear on (...) the moral status of the potential action. The paper then argues that this principle has important ramifications for moral epistemology and moral metaphysics. It puts pressure on some views of the justification of moral belief, such as ethical intuitionism and reliabilism. It puts pressure on some antirealist views of moral metaphysics, including simple versions of relativism. It also provides some direct positive support for broadly realist views of morality. (shrink)

The paper challenges the inferentialist account of concept possession that Paul Boghossian takes as a premise in his account of the transmission of justification by deductive reasoning in his paper 'Blind Reasoning'. Unorthodox speakers who reject the inferences in an alleged possession condition can still have the concept by understanding a word for it. In that sense, the inferences are not analytic. Inferentialist accounts of logical constants, theoretical terms (using the Ramsey-Carnap-Lewis method) and pejorative expressions such as 'Boche' are examined (...) and rejected. It is suggested that epistemological questions cannot be reduced to questions in the theory of thought and meaning. (shrink)

One of the key supposed 'platitudes' of contemporary epistemology is the claim that knowledge excludes luck. One can see the attraction of such a claim, in that knowledge is something that one can take credit for - it is an achievement of sorts - and yet luck undermines genuine achievement. The problem, however, is that luck seems to be an all-pervasive feature of our epistemic enterprises, which tempts us to think that either scepticism is true and that we don't know (...) very much, or else that luck is compatible with knowledge after all. In this book, Duncan Pritchard argues that we do not need to choose between these two austere alternatives, since a closer examination of what is involved in the notion of epistemic luck reveals varieties of luck that are compatible with knowledge possession and varieties that aren't. Moreover, Pritchard shows that a more nuanced understanding of the relationship between luck and knowledge can cast light on many of the most central topics in contemporary epistemology. These topics include: the externalism/internalism distinction; virtue epistemology; the problem of scepticism; metaepistemological scepticism; modal epistemology; and the problem of moral luck. All epistemologists will need to come to terms with Pritchard's original and incisive contribution. (shrink)

Intuition is sometimes derided as an abstruse or esoteric phenomenon akin to crystal-ball gazing. Such derision appears to be fuelled primarily by the suggestion, evidently endorsed by traditional rationalists such as Plato and Descartes, that intuition is a kind of direct, immediate apprehension akin to perception. This paper suggests that although the perceptual analogy has often been dismissed as encouraging a theoretically useless metaphor, a quasi-perceptualist view of intuition may enable rationalists to begin to meet the challenge of supplying a (...) theoretically satisfying treatment of their favoured epistemic source. It is argued, first, that intuitions and perceptual experiences are at a certain level of abstraction the same type of mental state, presentations, which are distinct from beliefs, hunches, inclinations, attractions, and seemings. The notion of a presentation is given a positive explication, which identifies its characteristic features, accounts for several of its substantive psychological roles, and systematically locates it in a threefold division among types of contentful states. Subsequently, it is argued that presentations, intuitive no less than sensory, are by their nature poised to play a distinctive epistemic role. Specifically, in the case of intuition, we encounter an intellectual state that is so structured as to provide justification without requiring justification in turn—something which may, thus, be thought of as ‘given’. (shrink)

Elijah Chudnoff elaborates and defends a view of intuition according to which intuition purports to, and reveals, how matters stand in abstract reality by making us aware of that reality through the intellect. He explores the experience of having an intuition; justification for beliefs that derives from intuition; and contact with abstract reality.

At least some of us, at least some of the time—when not in the grip of radical sceptical doubt—are inclined to believe that we know, for example, that if we infer a conclusion from two true premises, one a conditional whose consequent is that conclusion and the other the antecedent of that conditional, then our conclusion must be true, or that we know similar things about other simple patterns of inference. If we do indeed have knowledge of this sort, it (...) is what I mean by logical knowledge. Logical knowledge is, roughly speaking, knowledge about logic—such as knowledge that a certain principle of inference necessarily preserves truth, or that every proposition of a certain form must be true—and so is not the same thing as knowledge that is gained by using logic, i.e. inferential knowledge. That is not to say, of course, that logical knowledge can't be inferential. On the contrary, it is barely open to question that—if there is any logical knowledge at all—there is a lot of inferential logical knowledge. For example, if we know that the introduction and elimination principles for the conditional are truth-preserving, we can surely get to know, by inference, that the principle of hypothetical syllogism is so too, not to mention other, less obvious and more recondite, examples of putative logical knowledge. (shrink)

Paul Boghossian defends a meaning‐based approach to the apriority of the propositions of logic. His model is based on the idea that the logical constants are implicitly defined by some of the axioms and inference rules in which they are involved, thereby offering an alternative to those theories that deny that grasp of meaning can contribute to the explanation of a thinker's entitlement to a particular type of transition or belief.

In section 1, I develop epistemic communism, my view of the function of epistemically evaluative terms such as ‘rational’. The function is to support the coordination of our belief-forming rules, which in turn supports the reliable acquisition of beliefs through testimony. This view is motivated by the existence of valid inferences that we hesitate to call rational. I defend the view against the worry that it fails to account for a function of evaluations within first-personal deliberation. In the rest of (...) the paper, I then argue, on the basis of epistemic communism, for a view about rationality itself. I set up the argument in section 2 by saying what a theory of rational deduction is supposed to do. I claim that such a theory would provide a necessary, sufficient, and explanatorily unifying condition for being a rational rule for inferring deductive consequences. I argue in section 3 that, given epistemic communism and the conventionality that it entails, there is no such theory. Nothing explains why certain rules for deductive reasoning are rational. (shrink)

We are reliable about logic in the sense that we by-and-large believe logical truths and disbelieve logical falsehoods. Given that logic is an objective subject matter, it is difficult to provide a satisfying explanation of our reliability. This generates a significant epistemological challenge, analogous to the well-known Benacerraf-Field problem for mathematical Platonism. One initially plausible way to answer the challenge is to appeal to evolution by natural selection. The central idea is that being able to correctly deductively reason conferred a (...) heritable survival advantage upon our ancestors. However, there are several arguments that purport to show that evolutionary accounts cannot even in principle explain how it is that we are reliable about logic. In this paper, I address these arguments. I show that there is no general reason to think that evolutionary accounts are incapable of explaining our reliability about logic. (shrink)

This highly acclaimed book is a major contribution to the philosophy of language as well as a systematic interpretation of Frege, indisputably the father of ...

The paper outlines a view of normativity that combines elements of relativism and expressivism, and applies it to normative concepts in epistemology. The result is a kind of epistemological anti-realism, which denies that epistemic norms can be (in any straightforward sense) correct or incorrect; it does allow some to be better than others, but takes this to be goal-relative and is skeptical of the existence of best norms. It discusses the circularity that arises from the fact that we need to (...) use epistemic norms to gather the facts with which to evaluate epistemic norms; relatedly, it discusses how epistemic norms can rationally evolve. It concludes with some discussion of the impact of this view on "ground level" epistemology. (shrink)

This new work provides an approachable introduction to the complex system that Making It Explicit mapped out.

Such a conception, says Dummett, will form "a base camp for an assault on the metaphysical peaks: I have no greater ambition in this book than to set up a base ...

Two opposing tendencies in the philosophy of language go by the names of ‘referentialism’ and ‘inferentialism’ respectively. In the crudest version of the contrast, the referentialist account of meaning gives centre stage to the referential semantics for a language, which is then used to explain the inference rules for the language, perhaps as those which preserve truth on that semantics (since a referential semantics for a language determines the truth-conditions of its sentences). By contrast, the inferentialist account of meaning gives (...) centre stage to the inference rules for the language, which are then used to explain its referential semantics, perhaps as the semantics on which the rules preserve truth. On pain of circularity, we cannot combine both directions of explanation. (shrink)

Intuitively, it seems that some belief-forming practices have the following three properties: 1. They are rational practices, and the beliefs that we form by means of these practices are themselves rational or justified beliefs. 2. Even if in most cases these practices reliably lead to correct beliefs (i.e., beliefs in true propositions), they are not infallible: it is possible for beliefs that are formed by means of these practices to be incorrect (i.e., to be beliefs in false propositions). 3. The (...) rationality of these practices is basic or primitive. That is, the rationality of these practices is not due simply to the availability, by means of some process of reasoning that relies purely on other practices, of a rational or justified belief in the reliability of these practices. -/- How can there be such practices? This paper offers an answer to that question. (shrink)