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)

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)

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)

When making decisions, humans can observe many kinds of information about others' activities, but their effects on performance are not well understood. We investigated social learning strategies using a simple problem-solving task in which participants search a complex space, and each can view and imitate others' solutions. Results showed that participants combined multiple sources of information to guide learning, including payoffs of peers' solutions, popularity of solution elements among peers, similarity of peers' solutions to their own, and relative payoffs from (...) individual exploration. Furthermore, performance was positively associated with imitation rates at both the individual and group levels. When peers' payoffs were hidden, popularity and similarity biases reversed, participants searched more broadly and randomly, and both quality and equity of exploration suffered. We conclude that when peers' solutions can be effectively compared, imitation does not simply permit scrounging, but it can also facilitate propagation of good solutions for further cumulative exploration. (shrink)

INTRODUCTION Although the writings of Thomas Reid are very fertile and interesting, his life is biographically barren in comparison to such seventeenth - and ...

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)

THE NATURE OF ART is a collection of 29 seminal, historically-organized readings that are focused on a basic philosophical question: What is Art? Including writings from the Western tradition'both Continental and Analytic traditions'as well as non-Western, minority, and feminist writings, this volume provides students with a rich set of resources to explore this matter both broadly and deeply. Introductions to each reading situate the selection amidst each respective thinker's body of work and the greater philosophical context in which the remarks (...) arose. Reading questions accompany each selection, drawing students' attention to key points to be encountered. Hailed by reviewers and adopters for its clarity and rigor, Wartenberg's THE NATURE OF ART offers a lively and engaging introduction to the philosophy of art. (shrink)

The newly updated Right and Wrong 2nd Edition is an accessible introduction to the major traditions in western philosophical ethics, written in a lively and engaging style. It is designed for entry-level ethics courses and includes real-life ethical scenarios chosen to appeal directly to students. Greatly expanded and improved, this successful text introduces students to the major ethical traditions, and provides a simple methodology for resolving ethical dilemmas Treats teleological and deontological approaches to ethics as the two most important traditions, (...) but now includes chapters on virtue ethics and the ethics of care The very accessible writing style speaks directly to students’ own experience Draws examples from three types of real-life ethical scenarios submitted by students: academic dishonesty, partying, and personal relationships Provides a concise treatment of this notoriously complex subject, perfect for entry-level ethics and applied ethics courses. (shrink)

This chapter contains section titled: Personhood: A Start Are Dolphins Persons? Language and the Hand Personhood Redefined Conclusion: What Kind of Beings Are Dolphins?

David Ekdahl (2023), in a constructive and thoughtful commentary, outlines both points of agreement with and suggestions for further research arising from our paper ‘Crossing the Fictional Line: Moral Graveness, the Gamer’s Dilemma, and the Paradox of Fictionally Going Too Far’ (Montefiore & Formosa, 2023).

According to a widely held view, a Kantian intuition functions like a singular term. I argue that this view is false. Its apparent plausibility, both textual and philosophical, rests on attributing to Kant a Fregean conception of judgment. I show that Kant does not hold a Fregean conception of judgment and argue that, as a consequence, intuition cannot be understood on analogy with singular terms.

In this book Thomas Wren uncovers and assesses the largely hidden philosophical assumptions about human motivation that have shaped contemporary psychological ...

This interdisciplinary volume questions one of the most fundamental tenets of social theory by focusing on detachment, an important but neglected aspect of social life. Going against the grain of recent theoretical celebrations of engagement, this book challenges us to re-think the relational basis of social theory. In so, doing it brings to light the productive aspects of disconnection, distance and detachment. Rather than treating detachment simply as the moral inversion of compassion and engagement, the volume brings together empirical studies (...) and theoretical comments by leading anthropologists, sociologists and science studies scholars. Taken together, these illustrate the range of contexts within which distance and disconnection can offer meaningful frameworks for action. Positioned at the cutting edge of social theory, this landmark volume will be of great interest to students and academics across the social sciences and humanities. (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)

Some theories of goodness are descriptively rich: they have much to say about what makes things good. Neo-Aristotelian accounts, for instance, detail the various features that make a human being, a dog, a bee good relative to facts about those forms of life. Famously, such theories of relative goodness tend to be comparatively poor: they have little or nothing to say about what makes one kind of being better than another kind. Other theories of goodness—those that take there to be (...) absolute goodness—are comparatively rich: they offer grounds for judging some types of things better than others because they have more absolute goodness. Moorean accounts, for example, can tell us that humans and human experiences are superior to bees and blades of grass. But such theories tend to be descriptively poor: they struggle to tell us in virtue of what this is so. In this essay we motivate and flesh out a view that splits the difference between accounts of goodness as relative and accounts of goodness as absolute. Such a view holds promise only if the mechanics of this kind of metaphysics of goodness can be worked out. Here we present a view on which the paradigm for absolute goodness is God and the paradigm for each kind of relative goodness is a divine idea. (shrink)

Proceedings of a conference held in Apr. 2008 in Washington, D.C.

It is somewhat misleading to think of the Franciscans as forming a “school” in ethics, since there was a fair bit of diversity among Franciscans. Nonetheless, one can identify certain characteristic tendencies of Franciscan moral thought, and certain “celebrity” Franciscans whose views in ethics and moral psychology are particularly noteworthy. I shall first offer an overview of the general character of Franciscan moral thought in the late thirteenth and early fourteenth centuries and then turn to a more detailed examination of (...) the thought of John Duns Scotus (1265/66-1308) and William Ockham (c. 1288-1347) on three central matters of debate: the nature of the virtues, the relationship between intellect and will, and the relationship between moral requirements and the divine will. (shrink)