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.
On the Philosophy of Logic
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.
Introducing Philosophy of Mathematics
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.
Wisdom, Knowledge and Rationality
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.
The Moral Magic of Consent
Abstract: We regularly wield powers that, upon close scrutiny, appear remarkably magical. By sheer exercise of will, we bring into existence things that have never existed before. With but a nod, we effect the disappearance of things that have long served as barriers to the actions of others. And, by mere resolve, we generate things that pose significant obstacles to others’ exercise of liberty. What is the nature of these things that we create and destroy by our mere decision to do so? The answer: the rights and obligations of others. And by what seemingly magical means do we alter these rights and obligations? By making promises and issuing or revoking consent When we make promises, we generate obligations for ourselves, and when we give consent, we create rights for others. Since the rights and obligations that are affected by means of promising and consenting largely define the boundaries of permissible action, our exercise of these seemingly magical powers can significantly affect the lives and liberties of others
Obligation and Consent – I
Introduction: One might suppose that if political theorists are by now clear about anything at all, they should be clear about the problem of political obligation and the solution to it most commonly offered, the doctrine of consent. The greatest modern political theorists took up this problem and formulated this answer. The resulting theories are deeply imbedded in our American political tradition; as a consequence we are al- ready taught a sort of rudimentary consent theory in high school. And yet I want to suggest that we are not even now clear on what “the problem of political obligation” is, what sorts of “answers” are appropriate to it, what the con- sent answer really says, or whether it is a satis- factory answer. This essay is designed to point up the extent of our confusion, to explore some of the ground anew as best it can, and to invite further effort by others. That such effort is worthwhile, that such political theory is still worth considering and that it can be made genuinely relevant to our world, are the assump- tions on which this essay rests and the larger message it is meant to convey
Theories of Vagueness
Publisher’s Note: Most expressions in natural language are vague. But what is the best semantic treatment of terms like ‘heap’, ‘red’ and ‘child’? And what is the logic of arguments involving this kind of vague expression? These questions are receiving increasing philosophical attention, and in this timely book Rosanna Keefe explores the questions of what we should want from an account of vagueness and how we should assess rival theories. Her discussion ranges widely and comprehensively over the main theories of vagueness and their supporting arguments, and she offers a powerful and original defence of a form of supervaluationism, a theory that requires almost no deviation from standard logic yet can accommodate the lack of sharp boundaries to vague predicates and deal with the paradoxes of vagueness in a methodologically satisfying way. Her study will be of particular interest to readers in philosophy of language and of mind, philosophical logic, epistemology and metaphysics.
Symmetry and Symmetry Breaking
Introduction: Symmetry considerations dominate modern fundamental physics, both in quantum theory and in relativity. Philosophers are now beginning to devote increasing attention to such issues as the significance of gauge symmetry, quantum particle identity in the light of permutation symmetry, how to make sense of parity violation, the role of symmetry breaking, the empirical status of symmetry principles, and so forth. These issues relate directly to traditional problems in the philosophy of science, including the status of the laws of nature, the relationships between mathematics, physical theory, and the world, and the extent to which mathematics suggests new physics.
This entry begins with a brief description of the historical roots and emergence of the concept of symmetry that is at work in modern science. It then turns to the application of this concept to physics, distinguishing between two different uses of symmetry: symmetry principles versus symmetry arguments. It mentions the different varieties of physical symmetries, outlining the ways in which they were introduced into physics. Then, stepping back from the details of the various symmetries, it makes some remarks of a general nature concerning the status and significance of symmetries in physics.
Understanding and The Facts
Abstract: If understanding is factive, the propositions that express an understanding are true. I argue that a factive conception of understanding is unduly restrictive. It neither reflects our practices in ascribing understanding nor does justice to contemporary science. For science uses idealizations and models that do not to mirror the facts. Strictly speaking, they are false. By appeal to exemplification, I devise a more generous, flexible conception of understanding that accommodates science, reflects our practices, and shows a sufficient but not slavish sensitivity to the facts.
White Ignorance
<strong>Abstract:</strong> The development of social epistemology in recent decades is a welcome turn away from Cartesian individualism. But the centrality of oppression to societies in general is still insufficiently recognized in this literature. This chapter looks at “white ignorance†as an example of a particular kind of systemic group-based miscognition that has been hugely influential over the past few hundred years. After a ten-point clarification of the concept, it turns to an examination of white ignorance as it plays itself out in the complex interaction of Eurocentric perception and categorization, white normativity, social memory and social amnesia, the derogation of non-white testimony, racial group interests, and motivated irrationality.