Crispin Wright tried to refute classical 'Cartesian' skepticism contending that its core argument is extendible to a reductio ad absurdum (_Mind<D>, 100, 87-116, 1991). We show both that Wright is mistaken and that his mistakes are philosophically illuminating. Wright's 'best version' of skepticism turns on a concept of warranted belief. By his definition, many of our well-founded beliefs about the external world and mathematics would not be warranted. Wright's position worsens if we take 'warranted belief' to be implicitly defined by (...) the general principles governing it. Those principles are inconsistent, as shown by a variant of Godel's argument. Thus the inconsistency Wright found has nothing to do with the special premises of Cartesian skepticism, but is embedded in his own conceptual apparatus. Lastly, we show how a Cartesian skeptic could avoid Wright's critique by reconstructing a skeptical argument that does not use the claims Wright ultimately finds objectionable. (shrink)

This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.

The nature of mathematical knowledge can be understood only by locating the knowing mathematician in an epistemic community. This claim is defended by extending Kripke's version of the Private Language Argument to include informal rules and using Godelian results to argue that such rules rules necessary in mathematics. A committed formalist might evade Kripke's original argument by positing internal mechanisms that determine rule -governed behavior. However, in the presence of informal rules, the formalist position collapses into the extreme skepticism that (...) the Private Language Argument works against. The existence of a community of rule followers provides the only viable alternative to such skepticism. (shrink)

According to quasi-empiricism, mathematics is very like a branch of natural science. But if mathematics is like a branch of science, and science studies real objects, then mathematics should study real objects. Thus a quasi-empirical account of mathematics must answer the old epistemological question: How is knowledge of abstract objects possible? This paper attempts to show how it is possible.The second section examines the problem as it was posed by Benacerraf in Mathematical Truth and the next section presents a way (...) of looking at abstract objects that purports to demythologize them. In particular, it shows how we can have empirical knowledge of various abstract objects and even how we might causally interact with them. (shrink)

_Sweet Reason: A Field Guide to Modern Logic, 2nd Edition_ offers an innovative, friendly, and effective introduction to logic. It integrates formal first order, modal, and non-classical logic with natural language reasoning, analytical writing, critical thinking, set theory, and the philosophy of logic and mathematics. An innovative introduction to the field of logic designed to entertain as it informs Integrates formal first order, modal, and non-classical logic with natural language reasoning, analytical writing, critical thinking, set theory, and the philosophy of (...) logic and mathematics Addresses contemporary applications of logic in fields such as computer science and linguistics A web-site linked to the text features numerous supplemental exercises and examples, enlightening puzzles and cartoons, and insightful essays. (shrink)

Big Ideas for Little Kids includes everything a teacher, a parent, or a college student needs to teach philosophy to elementary school children from picture books. Written in a clear and accessible style, the book explains why it is important to allow young children access to philosophy during primary-school education. Wartenberg also gives advice on how to construct a "learner-centered" classroom, in which children discuss philosophical issues with one another as they respond to open-ended questions by saying whether they agree (...) or disagree with what others have said. (shrink)

v. 1. Editorial introduction -- v. 2. The English and Latin texts (i) -- v. 3. The English and Latin texts (ii).

In this book, T. M. Scanlon offers new answers to these questions, as they apply to the central part of morality that concerns what we owe to each other.

This paper is an exposition and evaluation of the Agustín Rayo's views about the epistemology and metaphysics of mathematics, as they are presented in his book The Construction of Logical Space.

This volume is a study of the influence of Timaeus on the development of Western cosmology in three axial periods of European culture: Late Antiquity, Middle Ages and Renaissance.

Thomas Reid is now recognized as one of the towering figures of the Enlightenment. Best known for his published writings on epistemology and moral theory, he was also an accomplished mathematician and natural philosopher, as an earlier volume of his manuscripts edited by Paul Wood for the Edinburgh Reid Edition, Thomas Reid on the Animate Creation, has shown. The Correspondence of Thomas Reid collects all of the known letters to and from Reid in a fully annotated form. (...) Letters already published by Sir William Hamilton and others have been reedited, and roughly half of the letters included appear in print for the first time. Writing in 1802, Reid's disciple and biographer Dugald Stewart doubted that Reid's correspondence &"would be generally interesting.&" This collection proves otherwise, for the letters illuminate virtually every aspect of Reid's life and career and, in some instances, provide us with invaluable evidence about activities otherwise undocumented in his manuscripts or published works. Through his correspondence we can trace Reid's relations with contemporaries such as David Hume and his colleagues at both King's College, Aberdeen, and the University of Glasgow, as well as his engagement with the most controversial philosophical, scientific, and political issues of his day. If anything, the letters assembled here serve as the starting point for understanding Reid and his place in the Enlightenment. (shrink)

Feeling good: four ways -- Finding that feeling -- The place of pleasure -- Knowing what's what -- Making things happen -- Being good -- Love and friendship -- Putting it together.

Efficient voice leading, in which melodic lines move by short distances from chord to chord, is a hallmark of many different Western musical styles. Although musicians can often find maximally efficient voice leadings with relative ease, theorists have not adequately described general principles or procedures for doing so. This article formalises the notion of voice leading, shows how to classify voice leadings according to transpositional and inversional equivalence and supplies algorithms for identifying maximally efficient voice leadings between arbitrarily chosen chords. (...) The article also includes analytical and theoretical discussions of neo-Riemannian theory, the 'tritone substitution' in contemporary jazz, the music of Wagner and Debussy, the relation between harmony and counterpoint and the connections between scale theory and serial theory. (shrink)

This book is a fiftieth anniversary republication of Thomas Nagel's "What Is It Like to Be a Bat?", a classic in the philosophy of mind. Through its argument for the irreducible subjectivity of consciousness, it played an essential role in making the study of consciousness a central part of philosophy, psychology, and neuroscience. It also spurred the now flourishing scientific attention to the consciousness of non-human creatures: mammals, birds, fish, mollusks, and insects. The book also includes a second essay (...) offering Nagel's more recent thoughts on the most promising positive response to the mind-body problem, as posed in the original essay. (shrink)

Thomas Hill, a leading figure in the recent development of Kantian moral philosophy, presents a set of essays exploring the implications of basic Kantian ideas for practical issues. The first part of the book provides background in central themes in Kant's ethics; the second part discusses questions regarding human welfare; the third focuses on moral worth-the nature and grounds of moral assessment of persons as deserving esteem or blame. Hill shows moral, political, and social philosophers just how valuable moral (...) theory can be in addressing practical matters. (shrink)

Respect, Pluralism, and Justice is a series of essays which sketches a broadly Kantian framework for moral deliberation, and then uses it to address important social and political issues. Hill shows how Kantian theory can be developed to deal with questions about cultural diversity, punishment, political violence, responsibility for the consequences of wrongdoing, and state coercion in a pluralistic society.

The word “emotion” has named a psychological category and a subject for systematic enquiry only since the 19th century. Before then, relevant mental states were categorised variously as “appetites,” “passions,” “affections,” or “sentiments.” The word “emotion” has existed in English since the 17th century, originating as a translation of the French émotion, meaning a physical disturbance. It came into much wider use in 18th-century English, often to refer to mental experiences, becoming a fully fledged theoretical term in the following century, (...) especially through the influence of two Scottish philosopher-physicians, Thomas Brown and Charles Bell. This article relates this intellectual and semantic history to contemporary debates about the usefulness and meaning of “emotion” as a scientific term. (shrink)

Nietzsche is often regarded as a paradigmatically anti-theoretical philosopher. Bernard Williams has said that Nietzsche is so far from being a theorist that his text “is booby-trapped not only against recovering theory from it, but, in many cases, against any systematic exegesis that assimilates it to theory.” Many would apply this view especially to Nietzsche’s moral philosophy. They would say that even when he is making positive normative claims, as against just criticizing existing morality, his claims have neither the content (...) nor the organization characteristic of moral theory. (shrink)

Existing research suggests that people's judgments of actual causation can be influenced by the degree to which they regard certain events as normal. We develop an explanation for this phenomenon that draws on standard tools from the literature on graphical causal models and, in particular, on the idea of probabilistic sampling. Using these tools, we propose a new measure of actual causal strength. This measure accurately captures three effects of normality on causal judgment that have been observed in existing studies. (...) More importantly, the measure predicts a new effect ("abnormal deflation"). Two studies show that people's judgments do, in fact, show this new effect. Taken together, the patterns of people's causal judgments thereby provide support for the proposed explanation. (shrink)