Publisher's Note: This teaching book is designed to help its readers to reason systematically, reliably, and to some extent self-consciously, in the course of their ordinary pursuits-primarily in inquiry and in decision making. The principles and techniques recommended are explained and justified - not just stated; the aim is to teach orderly thinking, not the manipulation of symbols. The structure of material follows that of Quine's Methods of Logic, and may be used as an introduction to that work, with sections on truth-functional logic, predicate logic, relational logic, and identity and description. Exercises are based on problems designed by authors including Quine, John Cooley, Richard Jeffrey, and Lewis Carroll.

Publisher's Note: Jennifer Fisher's On the Philosophy of Logic explores questions about logic often overlooked by philosophers. Which of the many different logics available to us is right? How would we know? What makes a logic right in the first place? Is logic really a good guide to human reasoning? An ideal companion text for any course in symbolic logic, this lively and accessible book explains important logical concepts, introduces classical logic and its problems and alternatives, and reveals the rich and interesting philosophical issues that arise in exploring the fundamentals of logic.

Publisher's Note: What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.

Abstract: Temporal logic as a modern discipline is separate from classical logic; it is seen as an addition or expansion of the more basic propositional and predicate logics. This approach is in contrast with logic in the Middle Ages, which was primarily intended as a tool for the analysis of natural language. Because all natural language sentences have tensed verbs, medieval logic is inherently a temporal logic. This fact is most clearly exemplified in medieval theories of supposition. As a case study, we look at the supposition theory of Lambert of Lagny (Auxerre), extracting from it a temporal logic and providing a formalization of that logic.

Abstract: This paper deals with the adequacy of the model-theoretic definition of logical consequence. Logical consequence is commonly described as a necessary relation that can be determined by the form of the sentences involved. In this paper, necessity is assumed to be a metaphysical notion, and formality is viewed as a means to avoid dealing with complex metaphysical questions in logical investigations. Logical terms are an essential part of the form of sentences and thus have a crucial role in determining logical consequence. Gila Sher and Stewart Shapiro each propose a formal criterion for logical terms within a model-theoretic framework, based on the idea of invariance under isomorphism. The two criteria are formally equivalent, and thus we have a common ground for evaluating and comparing Sher and Shapiro philosophical justification of their criteria. It is argued that Shapiro's blended approach, by which models represent possible worlds under interpretations of the language, is preferable to Sher’s formal-structural view, according to which models represent formal structures. The advantages and disadvantages of both views’ reliance on isomorphism are discussed.

Abstract: In his paper on 'The Concept of Voluntariness', Ben Colburn helpfully takes up the task of developing my view about the sense of voluntariness that is relevant for judgments of substantive responsibility, or judgments about individuals' liability to pick up some costs of their choices. On my view, a necessary condition for holding people responsible for their choices is that those choices be voluntary in the sense that they are not made because there is no acceptable alternative, where the standard for the acceptability of options is an objective standard of well-being. [...] Colburn's first point is entirely well-taken. By way of endorsing it, I ask whether we are justified in taking some but not all kinds of beliefs to affect the voluntariness of choice, as his elaboration of my view suggests. However, I find Colburn's second point less convincing, and argue that we should allow for the moral character of options to affect the voluntariness of choice.

Abstract: After surveying the strengths and weaknesses of several well-known approaches to wisdom, I argue for a new theory of wisdom that focuses on being epistemically, practically, and morally rational. My theory of wisdom, The Deep Rationality Theory of Wisdom, claims that a wise person is a person who is rational and who is deeply committed to increasing his or her level of rationality. This theory is a departure from theories of wisdom that demand practical and/or theoretical knowledge. The Deep Rationality Theory salvages all that is attractive, and avoids all that is problematic, about theories of wisdom that require wise people to be knowledgeable.

Publisher's Note: Philosophy long sought to set knowledge on a firm foundation, through derivation of indubitable truths by infallible rules. For want of such truths and rules, the enterprise foundered. Nevertheless, foundationalism's heirs continue their forbears' quest, seeking security against epistemic misfortune, while their detractors typically espouse unbridled coherentism or facile relativism. Maintaining that neither stance is tenable, Catherine Elgin devises a via media between the absolute and the arbitrary, reconceiving the nature, goals, and methods of epistemology. In Considered Judgment, she argues for a reconception that takes reflective equilibrium as the standard of rational acceptability. A system of thought is in reflective equilibrium when its components are reasonable in light of one another, and the account they comprise is reasonable in light of our antecedent convictions about the subject it concerns. Many epistemologists now concede that certainty is a chimerical goal. But they continue to accept the traditional conception of epistemology's problematic. Elgin suggests that in abandoning the quest for certainty we gain opportunities for a broader epistemological purview - one that comprehends the arts and does justice to the sciences. She contends that metaphor, fiction, emotion, and exemplification often advance understanding in science as well as in art. The range of epistemology is broader and more variegated than is usually recognized. Tenable systems of thought are neither absolute nor arbitrary. Although they afford no guarantees, they are good in the way of belief.

Introduction: In A Theory of Justice John Rawls tells us he is presenting a social contract theory: "My aim," he writes, "is to present a conception of justice which generalizes and carries to a higher level of abstraction the familiar theory of the social contract as found in say, Locke, Rousseau, and Kant". And indeed his many and various critics have generally assumed he has a contractarian position and have criticized him on that basis. However, it will be my contention in this paper that a contractual agreement on the two principles not only does not but ought not to occur in the original position, and that, although Rawls uses contract language in his book, there is another procedure outlined in Part One of A Theory of Justice through which the two principles are selected.

Introduction: There was once a luck egalitarian school of thought, according to which disadvantage arising due to bad luck was unjust—at the bar of egalitarian justice—while disadvantage arising due to choice was just, at least if the choice was exercised against the background of equal options. “Choice” in this context needed to be “genuine choice”—which, for some, meant “voluntary,” and for others, also “freely willed”—but if it was genuine, then it did not matter whether it was a silly mistake or a considered course of action: if it led to disadvantage, its presence was deemed sufficient to justify leaving the agent to bear the disadvantage. Let's call the view that choice leading to disadvantage is sufficient to justify the disadvantage, at least if choice was exercised against the background of equal options, the inflated view of choice. [...] The inflated view was so crude that in the face of criticism pointing out its crudeness, its supporters have adopted more sophisticated views, and no recent luck egalitarian has defended the crude version. These more sophisticated views recognize that the mere fact that an outcome has been chosen does not make the outcome just—not even by the standards of egalitarian justice alone. In what follows, I will argue that this dominant reading of early luck egalitarianism as committed to the inflated view is, at best, a one-sided interpretation of the iconic writings of the luck egalitarian literature advanced by its most famous proponents, namely Arneson, Cohen, and Dworkin. Their writings did not unambiguously point toward the inflated view; if the early texts were interpreted more charitably, we could have, perhaps, avoided associating luck egalitarianism with the inflated view, arriving immediately at the sophisticated versions of luck egalitarianism dominating the field today.