We show that the Axiom of Choice is equivalent to each of the following statements: A product of closures of subsets of topological spaces is equal to the closure of their product ; A product of complete uniform spaces is complete.

Classical logic is traditionally introduced by itself, but that makes it seem arbitrary and unnatural. This text introduces classical alongside several nonclassical logics (relevant, constructive, quantative, paraconsistent).

Relevant logic is a proper subset of classical logic. It does not include among its theorems any ofpositive paradox A (B A).

There are several important arguments in metaethics that rely on explanatory considerations. Gilbert Harman has presented a challenge to the existence of moral facts that depends on the claim that the best explanation of our moral beliefs does not involve moral facts. The Reliability Challenge against moral realism depends on the claim that moral realism is incompatible with there being a satisfying explanation of our reliability about moral truths. The purpose of this chapter is to examine these and related arguments. (...) In particular, this chapter will discuss four kinds of arguments – Harman’s Challenge, evolutionary debunking arguments, irrelevant influence arguments, and the Reliability Challenge – understood as arguments against moral realism. The main goals of this chapter are (i) to articulate the strongest version of these arguments; (ii) to present and assess the central epistemological principles underlying these arguments; and (iii) to determine what a realist would have to do to adequately respond to these arguments. (shrink)

Here I consider the two most venerated arguments about the existence of God: the Ontological Argument and the Argument from Evil. The Ontological Argument purports to show that God’s nature guarantees that God exists. The Argument from Evil purports to show that God’s nature, combined with some plausible facts about the way the world is, guarantees (or is very compelling grounds for thinking) that God does not exist. Obviously, both arguments cannot be sound. But I argue here that they are (...) both unsound for the very same reason. (shrink)

There are many alleged problems with trusting another person’s moral testimony, perhaps the most prominent of which is that it fails to deliver moral understanding. Without moral understanding, one cannot do the right thing for the right reason, and so acting on trusted moral testimony lacks moral worth. This chapter, however, argues that moral advice differs from moral testimony, differs from it in a way that enables a defender of moral advice to parry this worry about moral worth. The basic (...) idea is that an advisor and an advisee can together constitute a joint agent, and that this joint agent’s action can indeed have moral worth. So while the advisee himself might not do the right thing for the right reason (this because all alone he lacks the right reason), and while the advisor herself might not do the right thing for the right reason (this because all alone she does not do the right thing), they together do the right for the right reason. (shrink)

In the first chapter of his Knowledge and Lotteries, John Hawthorne argues that thinkers do not ordinarily know lottery propositions. His arguments depend on claims about the intimate connections between knowledge and assertion, epistemic possibility, practical reasoning, and theoretical reasoning. In this paper, we cast doubt on the proposed connections. We also put forward an alternative picture of belief and reasoning. In particular, we argue that assertion is governed by a Gricean constraint that makes no reference to knowledge, and that (...) practical reasoning has more to do with rational degrees of belief than with states of knowledge. (shrink)

This paper argues that the classification of propositional attitudes into the de re, de dicto, and de se is incomplete. De se attitudes are widely agreed to be closely connected to de re attitudes. But there is a species of belief that is linked to agent-centered action in the way that de se beliefs are, but is also associated with entities, places, and especially times, under a description. These mark out a fourth kind. One way to think about what makes (...) them distinctive is that, despite being ‘essentially indexical’ they can be retained across different contexts of evaluation without having diagonal content. The paper also discusses the connection between such beliefs and the kinds of utterances (like ‘Don't put off for tomorrow what you can do today’) that are contested as examples of what David Kaplan called ‘monsters.’. (shrink)

No citizen should be denied the right to vote due solely to her age. We can see this by showing that all objections to it fail. It might be objected that it is not unjust to so deprive children because children as a group are unintelligent or irrational, have their interests already represented by the parents, or are justly deprived of many other rights, among other reasons. But all these objections fail because there is no evidence to support it, even (...) if true, this would not justify disenfranchisement, or, most prominently argued here, they deprive individuals of political rights based upon their membership in a group. The voting age should be abolished. (shrink)

This paper argues that under some conditions, when one person acts on the direction of another person, the two of them thereby act together, and that this explains why both the director and the directee can be responsible for what is done. In other words, a director and a directee can be a joint agent, one whose members are responsible for what they together do. This is most clearly so when the directive is a command. But it is also sometimes (...) so when the directive is a bit of advice. (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)

This Element introduces the philosophical literature on models, with an emphasis on normative considerations relevant to models for decision-making. Chapter 1 gives an overview of core questions in the philosophy of modeling. Chapter 2 examines the concept of model adequacy for purpose, using three examples of models from the atmospheric sciences to describe how this sort of adequacy is determined in practice. Chapter 3 explores the significance of using models that are not adequate for purpose, including the purpose of informing (...) public decisions. Chapter 4 provides a basic framework for values in modelling, using a case study to highlight the ethical challenges in building models for decision making. It concludes by establishing the need for strategies to manage value judgments in modelling, including the potential for public participation in the process. (shrink)

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)

Autant d'études classiques qui accompagnent les grands ouvrages d'Eric Weil, Logique de la philosophie, Philosophie morale, Philosophie politique.

We think of logic as objective. We also think that we are reliable about logic. These views jointly generate a puzzle: How is it that we are reliable about logic? How is it that our logical beliefs match an objective domain of logical fact? This is an instance of a more general challenge to explain our reliability about a priori domains. In this paper, I argue that the nature of this challenge has not been properly understood. I explicate the challenge (...) both in general and for the particular case of logic. I also argue that two seemingly attractive responses – appealing to a faculty of rational insight or to the nature of concept possession – are incapable of answering the challenge. (shrink)

Elizabeth Schechter explores the implications of the experience of people who have had the pathway between the two hemispheres of their brain severed, and argues that there are in fact two minds, subjects of experience, and intentional agents inside each split-brain human being: right and left. But each split-brain subject is still one of us.

Since the publication of Timothy Williamson’s Knowledge and its Limits, knowledge-first epistemology has become increasingly influential within epistemology. This paper discusses the viability of the knowledge-first program. The paper has two main parts. In the first part, I briefly present knowledge-first epistemology as well as several big picture reasons for concern about this program. While this considerations are pressing, I concede, however, that they are not conclusive. To determine the viability of knowledge-first epistemology will require philosophers to carefully evaluate the (...) individual theses endorsed by knowledge-first epistemologists as well as to compare it with alternative packages of views. In the second part of the paper, I contribute to this evaluation by considering a specific thesis endorsed by many knowledge-first epistemologists – the knowledge norm of assertion. According to this norm, roughly speaking, one should assert that p only if one knows that p. I present and motivate this thesis. I then turn to a familiar concern with the norm: In many cases, it is intuitively appropriate for someone who has a strongly justified belief that p, but who doesn't know that p, to assert that p. Proponents of the knowledge norm of assertion typically explain away our judgments about such cases by arguing that the relevant assertion is improper but that the subject has an excuse and is therefore not blameworthy for making the assertion. I argue that that this response does not work. In many of the problem cases, it is not merely that the subject’s assertion is blameless. Rather, the subject positively ought to make the assertion. Appealing to an excuse cannot be used to adequately explain this fact. (Nor can we explain this fact by appealing to some other, quite different, consideration.) Finally, I conclude by briefly considering whether we should replace the knowledge norm of assertion with an alternative norm. I argue that the most plausible view is that there is no norm specifically tied to assertion. (shrink)

There are many domains about which we think we are reliable. When there is prima facie reason to believe that there is no satisfying explanation of our reliability about a domain given our background views about the world, this generates a challenge to our reliability about the domain or to our background views. This is what is often called the reliability challenge for the domain. In previous work, I discussed the reliability challenges for logic and for deductive inference. I argued (...) for four main claims: First, there are reliability challenges for logic and for deduction. Second, these reliability challenges cannot be answered merely by providing an explanation of how it is that we have the logical beliefs and employ the deductive rules that we do. Third, we can explain our reliability about logic by appealing to our reliability about deduction. Fourth, there is a good prospect for providing an evolutionary explanation of the reliability of our deductive reasoning. In recent years, a number of arguments have appeared in the literature that can be applied against one or more of these four theses. In this paper, I respond to some of these arguments. In particular, I discuss arguments by Paul Horwich, Jack Woods, Dan Baras, Justin Clarke-Doane, and Hartry Field. (shrink)

How should we understand validity? A standard way to characterize validity is in terms of the preservation of truth (or truth in a model). But there are several problems facing such characterizations. An alternative approach is to characterize validity epistemically, for instance in terms of the preservation of an epistemic status. In this paper, I raise a problem for such views. First, I argue that if the relevant epistemic status is factive, such as being in a position to know or (...) having conclusive evidence for, then the account runs into trouble if we endorse certain familiar logical principles. Second, I argue that if the relevant epistemic status is non-factive, such as is rationally committed to or has justification for believing, then a similar problem arises if we endorse the logical principles as well as a sufficiently strong epistemic “level-bridging” principle. Finally, I argue that an analogous problem arises for the most natural characterization of validity in terms of rational credence. (shrink)

This chapter discusses epistemic objections to non-naturalist moral realism. The goal of the chapter is to determine which objections are pressing and which objections can safely be dismissed. The chapter examines five families of objections: (i) one involving necessary conditions on knowledge, (ii) one involving the idea that the causal history of our moral beliefs reflects the significant impact of irrelevant influences, (iii) one relying on the idea that moral truths do not play a role in explaining our moral beliefs, (...) (iv) one involving the claim that if moral realism is true then our moral beliefs are unlikely to be reliable, and (v) one involving the claim that moral realism is incompatible with there being a plausible explanation of our reliability about morality. The overall conclusion of the chapter is that the final objection is by far the most pressing. (shrink)

We review and present a new meta‐analysis of research suggesting that ethicists in the United States appear to behave no morally better overall than do non‐ethicist professors. Measures include: returning library books, peer evaluation of overall moral behavior, voting participation, courteous and discourteous behavior at conferences, replying to student emails, paying conference registration fees and disciplinary society dues, staying in touch with one's mother, charitable giving, organ and blood donation, vegetarianism, and honesty in responding to survey questions. One multi‐measure study (...) found ethicists tending to embrace more stringent moral views, especially about meat eating and charitable donation. The same multi‐measure study found ethicists and other professors to show similarly small‐to‐medium correlations between their expressed normative attitudes and their self‐reported or directly measured behavior. (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)

In this paper, we present an account of in virtue of what thinkers are justified in 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 a belief‐forming method that is indispensable 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 debates. (shrink)

According to the analysis of concessive conditionals suggested by Crupi and Iacona, a concessive conditional $$p{{\,\mathrm{\hookrightarrow }\,}}q$$ p ↪ q is adequately formalized as a conjunction of conditionals. This paper presents a sound and complete axiomatic system for concessive conditionals so understood. The soundness and completeness proofs that will be provided rely on a method that has been employed by Raidl, Iacona, and Crupi to prove the soundness and completeness of an analogous system for evidential conditionals.

In virtue of what are we justified in employing the rule of inference Modus Ponens? One tempting approach to answering this question is to claim that we are justified in employing Modus Ponens purely in virtue of facts concerning meaning or concept-possession. In this paper, we argue that such meaning-based accounts cannot be accepted as the fundamental account of our justification.

We are justified in employing the rule of inference Modus Ponens (or one much like it) as basic in our reasoning. By contrast, we are not justified in employing a rule of inference that permits inferring to some difficult mathematical theorem from the relevant axioms in a single step. Such an inferential step is intuitively “too large” to count as justified. What accounts for this difference? In this paper, I canvass several possible explanations. I argue that the most promising approach (...) is to appeal to features like usefulness or indispensability to important or required cognitive projects. On the resulting view, whether an inferential step counts as large or small depends on the importance of the relevant rule of inference in our thought. (shrink)

A consequence relation is strongly classical if it has all the theorems and entailments of classical logic as well as the usual meta-rules (such as Conditional Proof). A consequence relation is weakly classical if it has all the theorems and entailments of classical logic but lacks the usual meta-rules. The most familiar example of a weakly classical consequence relation comes from a simple supervaluational approach to modelling vague language. This approach is formally equivalent to an account of logical consequence according (...) to which α1, ..., αn entails β just in case □α1, ..., □αn entails □β in the modal logic S5. This raises a natural question: If we start with a different underlying modal logic, can we generate a strongly classical logic? This paper explores this question. In particular, it discusses four related technical issues: (1) Which base modal logics generate strongly classical logics and which generate weakly classical logics? (2) Which base logics generate themselves? (3) How can we directly characterize the logic generated from a given base logic? (4) Given a logic that can be generated, which base logics generate it? The answers to these questions have philosophical interest. They can help us to determine whether there is a plausible supervaluational approach to modelling vague language that yields the usual meta-rules. They can also help us to determine the feasibility of other philosophical projects that rely on an analogous formalism, such as the project of defining logical consequence in terms of the preservation of an epistemic status. (shrink)

In our thought, we employ rules of inference and belief-forming methods more generally. For instance, we (plausibly) employ deductive rules such as Modus Ponens, ampliative rules such as Inference to the Best Explanation, and perceptual methods that tell us to believe what perceptually appears to be the case. What explains our entitlement to employ these rules and methods? This chapter considers the motivations for broadly internalist answers to this question. It considers three such motivations—one based on simple cases, one based (...) on a general conception of epistemic responsibility, and one based on skeptical scenarios. The chapter argues that none of these motivations is successful. The first two motivations lead to forms of internalism—Extreme Method Internalism and Defense Internalism—that are too strong to be tenable. The third motivation motivates Mental Internalism (Mentalism), which does not fit with plausible accounts of entitlement. (shrink)

In 1970 a coalition of student activists opposing the Vietnam War circulated documents revealing the involvement of several prominent social scientists in U.S. counterinsurgency activities in Thailand--activities that could cause harm to the people who were the subject of the scholars' research. The disclosure of these materials, which detailed meetings with the Agency for International Development and the Defense Department, prompted two members of the Ethics Committee of the American Anthropological Association to issue an unauthorized rebuke of the accused. Over (...) the next two years, the AAA agonized over the allegations and the appropriate response to them. Within an academic community already polarized by the war, political and professional acrimony reached unprecedented levels. Although the association ultimately passed a code of ethics, the key issues raised in the process were never fully resolved. Now back in print, Eric Wakin's Anthropology Goes to War is the first comprehensive study of what became known as the Thailand Controversy--and a timely reminder of a debate whose echoes may be heard in our own time. (shrink)

Learning information about the etiology of one's beliefs can reduce the justification a thinker has for those beliefs. Learning information about the etiology of one's desires, emotions, or concepts can similarly have a debunking effect. In this chapter, I develop a unified account of etiological debunking that applies across these different kinds of cases. According to this account, etiological debunking arguments work by providing reason to think that there is no satisfying explanation of how it is that some part of (...) our mental life is fitting. The role that etiological information plays is to help to rule out (or render less plausible) potential explanations, given our background views about the world. This account suggests several potential morals for epistemology, the philosophy of mind, and metaethics. (shrink)

Many experimental findings with split-brain subjects intuitively suggest that each such subject has two minds. The conceptual and empirical basis of this duality intuition has never been fully articulated. This article fills that gap, by offering a reconstruction of early neuropsychological literature on the split-brain phenomenon. According to that work, the hemispheres operate independently of each other insofar as they interact via the mediation of effection and transduction—via behavior and sensation, essentially. This is how your mind and my mind interact (...) with each other, however, giving rise to the intuition that a split-brain subject has two minds. (shrink)

This article shows that there is a liar-like paradox that arises for rational credence that relies only on very weak logical and credal principles. The paradox depends on a weak rational reflection principle, logical principles governing conjunction, and principles governing the relationship between rational credence and proof. To respond to this paradox, we must either reject even very weak rational reflection principles or reject some highly plausible logical or credal principle.

: This paper argues for a distinction between possession of a unified consciousness and possession of a single stream of consciousness. Although the distinction has widespread applicability in discussions of the structure of consciousness and of pathologies of conscious experience, I will illustrate its importance primarily using the debate about consciousness in split-brain subjects, suggesting that those who have argued that split-brain subjects have two streams of consciousness apiece and those who have argued that they have a unified consciousness may (...) both be right. (shrink)

Graphs are among the most frequently used structures in Computer Science. Some of the properties that must be checked in many applications are connectivity, acyclicity and the Eulerian and Hamiltonian properties. In this work, we analyze how we can express these four properties with modal logics. This involves two issues: whether each of the modal languages under consideration has enough expressive power to describe these properties and how complex it is to use these logics to actually test whether a given (...) graph has some desired property. First, we show that these properties are not definable in a basic modal logic or in any bisimulation-invariant extension of it, like the modal μ-calculus. We then show that it is possible to express some of the above properties in a basic hybrid logic. Unfortunately, the Hamiltonian and Eulerian properties still cannot be efficiently checked. In a second attempt, we propose an extension of CTL* with nominals and show that the Hamiltonian property can be more efficiently checked in this logic than in the previous one. In a third attempt, we extend the basic hybrid logic with the ↓ operator and show that we can check the Hamiltonian property with optimal complexity in this logic. Finally, we tackle the Eulerian property in two different ways. First, we develop a generic method to express edge-related properties in hybrid logics and use it to express the Eulerian property. Second, we express a necessary and sufficient condition for the Eulerian property to hold using a graded modal logic. (shrink)

This paper develops a new framework for combining propositional logics, called "juxtaposition". Several general metalogical theorems are proved concerning the combination of logics by juxtaposition. In particular, it is shown that under reasonable conditions, juxtaposition preserves strong soundness. Under reasonable conditions, the juxtaposition of two consequence relations is a conservative extension of each of them. A general strong completeness result is proved. The paper then examines the philosophically important case of the combination of classical and intuitionist logics. Particular attention is (...) paid to the phenomenon of collapse. It is shown that there are logics with two stocks of classical or intuitionist connectives that do not collapse. Finally, the paper briefy investigates the question of which rules, when added to these logics, lead to collapse. (shrink)

This paper discusses Ernest Sosa's account of knowledge and epistemic normativity. The paper has two main parts. The first part identifies places where Sosa's account requires supplementation if it is going to capture important epistemic phenomena. In particular, additional theoretical resources are needed to explain the way in which epistemic aims are genuinely good aims, and the way in which some forms of reasoning can be epistemically better than others even when they are equally conducive to attaining the truth. The (...) second part focuses on Sosa's claim that there is a kind of belief – judgmental belief – that doesn't merely aim at truth but also aims at aptness, and that this kind of belief is central to our mental lives. The paper raises several concerns about this part of Sosa's account, including the concern that aiming at aptness is overly self-directed, and so is more closely tied to vice than epistemic virtue. (shrink)

There are well-known quasi-formal arguments that identity is a "strict" relation in at least the following three senses: (1) There is a single identity relation and a single distinctness relation; (2) There are no contingent cases of identity or distinctness; and (3) There are no vague or indeterminate cases of identity or distinctness. However, the situation is less clear cut than it at first may appear. There is a natural formal theory of identity that is very close to the standard (...) classical theory but which does not validate the formal analogues of (1)-(3). The core idea is simple: We weaken the Principle of the Indiscernibility of Identicals from a conditional to an entailment and we adopt a weakly classical logic. This paper investigates this weakly classical theory of identity (and related theories) and discusses its philosophical ramifications. It argues that we can accept a reasonable theory of identity without committing ourselves to the uniqueness, necessity, or determinacy of identity. (shrink)

Expanded version of a commentary on Adam Elga's "Lucky to be Rational" delivered at the 2008 Bellingham Summer Philosophy Conference.

The attempt to model the structure of consciousness in split-brain subjects is ongoing. This paper concerns the recently proposed ?switch model? of split-brain consciousness, according to which a split-brain subject possesses only a single stream of consciousness, unified at and across time, that shifts from one hemisphere to the other from moment to moment. The paper argues that while the central explanatory element of the switch model may account for some aspects of split-brain consciousness, the best general picture of split-brain (...) consciousness is still offered by some version of the ?conscious duality model.? (shrink)

This paper concerns the role that reference to subjects of experience can play in individuating streams of consciousness, and the relationship between the subjective and the objective structure of consciousness. A critique of Tim Bayne’s recent book indicates certain crucial choices that works on the unity of consciousness must make. If one identifies the subject of experience with something whose consciousness is necessarily unified, then one cannot offer an account of the objective structure of consciousness. Alternatively, identifying the subject of (...) experience with an animal means forgoing the conceptual connection between being a subject of experience and having a single phenomenal perspective. (shrink)