Download or read book Metaphysical Myths Mathematical Practice written by Jody Azzouni and published by Cambridge University Press. This book was released on 1994-02-25 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This original and exciting study offers a completely new perspective on the philosophy of mathematics. Most philosophers of mathematics try to show either that the sort of knowledge mathematicians have is similar to the sort of knowledge specialists in the empirical sciences have or that the kind of knowledge mathematicians have, although apparently about objects such as numbers, sets, and so on, isn't really about those sorts of things at all. Jody Azzouni argues that mathematical knowledge is a special kind of knowledge that must be gathered in its own unique way. He analyzes the linguistic pitfalls and misperceptions philosophers in this field are often prone to, and explores the misapplications of epistemic principles from the empirical sciences to the exact sciences. What emerges is a picture of mathematics sensitive both to mathematical practice and to the ontological and epistemological issues that concern philosophers. The book will be of special interest to philosophers of science, mathematics, logic, and language. It should also interest mathematicians themselves.
Download or read book Metaphysical Myths Mathematical Practice written by Jody Azzouni and published by . This book was released on 1994 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of the History and Philosophy of Mathematical Practice written by Bharath Sriraman and published by Springer Nature. This book was released on with total page 3221 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Perspectives on Mathematical Practices written by Bart van Kerkhove and published by Springer Science & Business Media. This book was released on 2007-06-01 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the eyes of the editors, this book will be considered a success if it can convince its readers of the following: that it is warranted to dream of a realistic and full-fledged theory of mathematical practices, in the plural. If such a theory is possible, it would mean that a number of presently existing fierce oppositions between philosophers, sociologists, educators, and other parties involved, are in fact illusory.
Download or read book The Rule Following Paradox and its Implications for Metaphysics written by Jody Azzouni and published by Springer. This book was released on 2017-03-08 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents Azzouni’s new approach to the rule-following paradox. His solution leaves intact an isolated individual’s capacity to follow rules, and it simultaneously avoids replacing the truth conditions for meaning-talk with mere assertability conditions for that talk. Kripke’s influential version of Wittgenstein’s rule-following paradox—and Wittgenstein’s views more generally—on the contrary, make rule-following practices and assertions about those practices subject to community norms without which they lose their cogency. Azzouni summarizes and develops Kripke’s original version of Wittgenstein’s rule-following paradox to make salient the linchpin assumptions of the paradox. By doing so, Azzouni reveals how compelling Kripke’s earlier work on the paradox was. Objections raised over the years by Fodor, Forbes Ginsborg, Goldfarb, Tait, Wright, and many others, are all shown to fail. No straight solution (a solution that denies an assumption of the paradox) can be made to work. Azzouni illustrates this in detail by showing that a popular family of straight solutions due to Lewis and refined by Williams, “reference magnetism,” fail as well. And yet an overlooked sceptical solution is still available in logical space. Azzouni describes a series of “disposition-meaning” private languages that he shows can be successfully used by a population of speakers to communicate with one another despite their ideolectical character. The same sorts of languages enable solitary “Robinson Crusoes” to survive and flourish in their island habitats. These languages—sufficiently refined—have the same properties normal human languages have; and this is the key to solving the rule-following paradox without sacrificing the individual’s authority over her self-imposed rules or her ability to follow those rules. Azzouni concludes this unusual monograph by uncovering a striking resemblance between the rule-following paradox and Hume’s problem of induction: he shows the rule-following paradox to be a corollary of Hume’s problem that arises when the problem of induction is applied to an individual’s own abilities to follow rules. “The book is clearly and engagingly written, and the conclusions are well-argued-for. (Depressingly well-argued-for in the case of Chapter 3, as I've always been partial to Lewisian responses to Putnam's model-theoretic argument--I'm rethinking that now.) And the proposed solution to the rule-following paradox really is novel.” Joshua Brown - Gustavus Adolphus College
Download or read book Philosophy of Mathematics Oxford Bibliographies Online Research Guide written by Otavio Bueno and published by Oxford University Press. This book was released on 2010-06 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ebook is a selective guide designed to help scholars and students of social work find reliable sources of information by directing them to the best available scholarly materials in whatever form or format they appear from books, chapters, and journal articles to online archives, electronic data sets, and blogs. Written by a leading international authority on the subject, the ebook provides bibliographic information supported by direct recommendations about which sources to consult and editorial commentary to make it clear how the cited sources are interrelated related. This ebook is a static version of an article from Oxford Bibliographies Online: Philosophy, a dynamic, continuously updated, online resource designed to provide authoritative guidance through scholarship and other materials relevant to the study Philosophy. Oxford Bibliographies Online covers most subject disciplines within the social science and humanities, for more information visit www.oxfordbibligraphies.com.
Download or read book Abstract Objects written by José L. Falguera and published by Springer Nature. This book was released on 2020-05-08 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume examines the question “Do abstract objects exist?”, presenting new work from contributing authors across different branches of philosophy. The introduction overviews philosophical debate which considers: what objects qualify as abstract, what do we mean by the word "exist” and indeed, what evidence should count in favor or against the thesis that abstract objects exist. Through subsequent chapters readers will discover the ubiquity of abstract objects as each philosophical field is considered. Given the ubiquitous use of expressions that purportedly refer to abstract objects, we think that it is relevant to attend to the controversy between those who want to advocate the existence of abstract objects and those who stand against them. Contributions to this volume depict positions and debates that directly or indirectly involve taking one position or other about abstract objects of different kinds and categories. The volume provides a variety of samples of how positions for or against abstract objects can be used in different areas of philosophy in relation to different matters.
Download or read book Proof and Other Dilemmas written by Bonnie Gold and published by MAA. This book was released on 2008 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sixteen original essays exploring recent developments in the philosophy of mathematics, written in a way mathematicians will understand.
Download or read book God and Abstract Objects written by William Lane Craig and published by Springer. This book was released on 2017-09-05 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an exploration and defense of the coherence of classical theism’s doctrine of divine aseity in the face of the challenge posed by Platonism with respect to abstract objects. A synoptic work in analytic philosophy of religion, the book engages discussions in philosophy of mathematics, philosophy of language, metaphysics, and metaontology. It addresses absolute creationism, non-Platonic realism, fictionalism, neutralism, and alternative logics and semantics, among other topics. The book offers a helpful taxonomy of the wide range of options available to the classical theist for dealing with the challenge of Platonism. It probes in detail the diverse views on the reality of abstract objects and their compatibility with classical theism. It contains a most thorough discussion, rooted in careful exegesis, of the biblical and patristic basis of the doctrine of divine aseity. Finally, it challenges the influential Quinean metaontological theses concerning the way in which we make ontological commitments.
Download or read book The Human a Priori written by A. W. Moore and published by Oxford University Press. This book was released on 2023-08-08 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Human A Priori is a collection of essays by A.W. Moore, one of them previously unpublished and the rest all revised. These essays are all concerned, more or less directly, with something ineliminably anthropocentric in our systematic pursuit of a priori sense-making. Part I deals with the nature, scope, and limits of a priori sense-making in general. Parts II, III, and IV deal with what are often thought to be the three great exemplars of the systematic pursuit of such sense-making: philosophy in the case of Part II, ethics in the case of Part III, and mathematics in the case of Part IV. Much of the attention throughout is devoted to the work of other philosophers: Kant and Wittgenstein feature prominently, and five of the essays take the form of reviews or critical notices of recent work in philosophy. But the interest in never purely exegetical. One of the lessons that emerges from the essays, either in opposition to the views of these other philosophers or by invocation of their views, is that we humans achieve nothing of real significance in philosophy, ethics, or mathematics except from a human point of view, and hence that all three of these pursuits can be said to betoken what may reasonably be called 'the human a priori'.
Download or read book Philosophy in an Age of Science written by Hilary Putnam and published by Harvard University Press. This book was released on 2012-04-17 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilary Putnam's unceasing self-criticism has led to the frequent changes of mind he is famous for, but his thinking is also marked by considerable continuity. A simultaneous interest in science and ethicsÑunusual in the current climate of contentionÑhas long characterized his thought. In Philosophy in an Age of Science, Putnam collects his papers for publicationÑhis first volume in almost two decades. Mario De Caro and David Macarthur's introduction identifies central themes to help the reader negotiate between Putnam past and Putnam present: his critique of logical positivism; his enduring aspiration to be realist about rational normativity; his anti-essentialism about a range of central philosophical notions; his reconciliation of the scientific worldview and the humanistic tradition; and his movement from reductive scientific naturalism to liberal naturalism. Putnam returns here to some of his first enthusiasms in philosophy, such as logic, mathematics, and quantum mechanics. The reader is given a glimpse, too, of ideas currently in development on the subject of perception. Putnam's work, contributing to a broad range of philosophical inquiry, has been said to represent a Òhistory of recent philosophy in outline.Ó Here it also delineates a possible future.
Download or read book Wittgenstein in America written by Timothy G. McCarthy and published by Oxford University Press. This book was released on 2001 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This remarkable collection explores the legacy of Wittgenstein's work in contemporary American philosophy. The contributors (including several celebrated philosophers) take a variety of approaches to Wittgenstein; they discuss such topics as rule-following, realism about mathematics, the method of the Tractatus, the relation between style and content in Wittgenstein, and his distinction between sense and nonsense. Wittgenstein also is discussed in relation to subsequent philosophers such as Quine and Kripke.
Download or read book Making and Breaking Mathematical Sense written by Roi Wagner and published by Princeton University Press. This book was released on 2017-01-10 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications? Roi Wagner uniquely combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on ancient, medieval, and modern case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics' claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, Wagner challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics’ exceptional consensus is due to the subject’s underlying reality. The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike.
Download or read book 18 Unconventional Essays on the Nature of Mathematics written by Reuben Hersh and published by Springer Science & Business Media. This book was released on 2006-01-16 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistry Interdisciplinary book that will be useful in several fields—with a cross-disciplinary subject area, and contributions from researchers of various disciplines
Download or read book Essays on the Foundations of Mathematics and Logic written by Giandomenico Sica and published by Polimetrica s.a.s.. This book was released on 2005 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Thinking about Mathematics written by Stewart Shapiro and published by OUP Oxford. This book was released on 2000-07-13 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.
Download or read book A Companion to Relativism written by Steven D. Hales and published by John Wiley & Sons. This book was released on 2011-03-21 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Companion to Relativism presents original contributions from leading scholars that address the latest thinking on the role of relativism in the philosophy of language, epistemology, ethics, philosophy of science, logic, and metaphysics. Features original contributions from many of the leading figures working on various aspects of relativism Presents a substantial, broad range of current thinking about relativism Addresses relativism from many of the major subfields of philosophy, including philosophy of language, epistemology, ethics, philosophy of science, logic, and metaphysics
