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.

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)

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)

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 volume brings together for the first time a significant number of Reid's manuscript papers on natural history, physiology and materialist metaphysics. An important contribution not only to Reid studies but also to our understanding of eighteenth-century science and its context.

Thomas Reid was a philosopher who founded the Scottish school of 'common sense'. Much of Reid's work is a critique of his contemporary, David Hume, whose empiricism he rejects. In this work, written after Reid's appointment to a professorship at the university of Glasgow, and published in 1785, he turns his attention to ideas about perception, memory, conception, abstraction, judgement, reasoning and taste. He examines the work of his predecessors and contemporaries, arguing that 'when we find philosophers maintaining that (...) there is no heat in the fire, nor colour in the rainbow … we may be apt to think the whole to be only a dream of fanciful men, who have entangled themselves in cobwebs spun out of their own brain'. Written by one of the Scottish Enlightenment's most important thinkers, this work brings to life the intellectual debates of the time. (shrink)

Thomas Aquinas produced a voluminous body of work on moral theory, and much of that work is on virtue, particularly the status and value of the virtues as principles of virtuous acts, and the way in which a moral life can be organized around them schematically. Thomas Osborne presents Aquinas's account of virtue in its historical, philosophical and theological contexts, to show the reader what Aquinas himself wished to teach about virtue. His discussion makes the complexities of Aquinas's (...) moral thought accessible to readers despite the differences between Thomas's texts themselves, and the distance between our background assumptions and his. The book will be valuable for scholars and students in ethics, medieval philosophy, and theology. (shrink)

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

There has been an explosion of interest in the metaphysics of fundamentality in recent decades. The consensus view, called metaphysical foundationalism, maintains that there is something absolutely fundamental in reality upon which everything else depends. However, a number of thinkers have chal- lenged the arguments in favor of foundationalism and have proposed competing non-foundationalist ontologies. This paper provides a systematic and critical introduction to metaphysical foundationalism in the current literature and argues that its relation to ontological dependence and substance should (...) be qualified in important ways. (shrink)

In a recent paper Weinberg (2007) claims that there is an essential mark of trustworthiness which typical sources of evidence as perception or memory have, but philosophical intuitions lack, namely that we are able to detect and correct errors produced by these “hopeful” sources. In my paper I will argue that being a hopeful source isn't necessary for providing us with evidence. I then will show that, given some plausible background assumptions, intuitions at least come close to being hopeful, if (...) they are reliable. If this is true, Weinberg's new challenge comes down to the claim that philosophical intuitions are not reliable since they are significantly unstable. In the second part of my paper I will argue that and why the experimentally established instability of folk intuitions about philosophical cases does not show that philosopher's expert intuitions about these cases are instable. (shrink)

I critically examine some deflationary theories of properties, according to which properties are ‘shadows of predicates’ and quantification over them serves a mere quasi-logical function. I start by considering Hofweber’s internalist theory, and pose a problem for his account of inexpressible properties. I then introduce a theory of properties that closely resembles Horwich’s minimalist theory of truth. This theory overcomes the problem of inexpressible properties, but its formulation presupposes the existence of various kinds of abstract objects. I discuss some ways (...) to reduce these existence assumptions, but ultimately suggest that deflationists can hardly avoid quantification over abstract objects of one sort or another. I conclude that property deflationism is perhaps not as deflationary as some philosophers want it to be, but that it’s still apt to call the position ‘deflationary’. (shrink)

Looking back on it, it seems almost incredible that so many equally educated, equally sincere compatriots and contemporaries, all drawing from the same limited stock of evidence, should have reached so many totally different conclusions---and always with complete certainty.

Issues concerning patients' rights are at the center of bioethics, but the political basis for these rights has rarely been examined. In Bioethics in a Liberal Society: The Political Framework of Bioethics Decision Making , Thomas May offers a compelling analysis of how the political context of liberal constitutional democracy shapes the rights and obligations of both patients and health care professionals. May focuses on how a key feature of liberal society -- namely, an individual's right to make independent (...) decisions -- has an impact on the most important relational facets of health care, such as patients' autonomy and professionals' rights of conscience. Although a liberal political framework protects individual judgments, May asserts that this right is based on the assumption of an individual's competency to make sound decisions. May uses case studies to examine society's approach to medical decision making when, for reasons ranging from age to severe mental disorder, a person lacks sufficient competency to make independent and fully informed choices. To protect the autonomy of these vulnerable patients, May emphasizes the need for health care ethics committees and ethics consultants to help guide the decision-making process in clinical settings. Bioethics in a Liberal Society is essential reading for all those interested in understanding how bioethics is practiced within our society. (shrink)

What are the truth conditions of want ascriptions? According to an influential approach, they are intimately connected to the agent’s beliefs: ⌜S wants p⌝ is true iff, within S’s belief set, S prefers the p worlds to the not-p worlds. This approach faces a well-known problem, however: it makes the wrong predictions for what we call (counter)factual want ascriptions, wherein the agent either believes p or believes not-p—for example, ‘I want it to rain tomorrow and that is exactly what is (...) going to happen’ or ‘I want this weekend to last forever, but of course it will end in a few hours’. We solve this problem. The truth conditions for want ascriptions are, we propose, connected to the agent’s conditional beliefs. We substantiate this connection by pursuing a striking parallel between (counter)factual and non-(counter)factual want ascriptions on the one hand and counterfactual and indicative conditionals on the other. (shrink)

T. H. Green's Prolegomena to Ethics is a classic of modern philosophy. It begins with Green's idealist attack on empiricist metaphysics and epistemology and develops a perfectionist ethical theory that aims to bring together the best elements in the ancient and modern traditions, and that provides the moral foundations for Green's own distinctive brand of liberalism. David Brink's new edition will restore this great work to prominence, after two decades in which it has been hard to obtain. The present edition (...) uses the text of the fifth edition, accompanied by a new introductory essay, bibliographical essay, and index. Translations are provided for Green's quotations from other languages. Of particular importance is the editor's extended introductory essay, which situates the Prolegomena in its intellectual context, sympathetically but critically engages its main themes, and explains Green's enduring significance for the history of philosophy and contemporary ethical theory. Students and scholars of the history of ethics, ethical theory, political philosophy, and nineteenth century philosophy will find this new edition an invaluable resource. (shrink)

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 paper presents a new approach to the class-theoretic paradoxes. In the first part of the paper, I will distinguish classes from sets, describe the function of class talk, and present several reasons for postulating type-free classes. This involves applications to the problem of unrestricted quantification, reduction of properties, natural language semantics, and the epistemology of mathematics. In the second part of the paper, I will present some axioms for type-free classes. My approach is loosely based on the Gödel–Russell idea (...) of limited ranges of significance. It is shown how to derive the second-order Dedekind–Peano axioms within that theory. I conclude by discussing whether the theory can be used as a solution to the problem of unrestricted quantification. In an appendix, I prove the consistency of the class theory relative to Zermelo–Fraenkel set theory. (shrink)