Download or read book The Indispensability of Mathematics written by Mark Colyvan and published by . This book was released on 2001 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation. The Quine-Putnam indispensability argument in the philosophy of mathematics urges us to place mathematical entities on the same ontological footing as other theoretical entities essential to our best scientific theories. Recently, the argument has come under serious scrutiny, with manyinfluential philosophers unconvinced of its cogency. This book not only outlines the indispensability argument in considerable detail but also defends it against various challenges.
Download or read book An Introduction to the Philosophy of Mathematics written by Mark Colyvan and published by Cambridge University Press. This book was released on 2012-06-14 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.
Download or read book The Indispensability of Mathematics written by Mark Colyvan and published by Oxford University Press. This book was released on 2001-03-22 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Quine-Putnam indispensability argument in the philosophy of mathematics urges us to place mathematical entities on the same ontological footing as other theoretical entities essential to our best scientific theories. Recently, the argument has come under serious scrutiny, with many influential philosophers unconvinced of its cogency. This book not only outlines the indispensability argument in considerable detail but also defends it against various challenges.
Download or read book Deflating Existential Consequence written by Jody Azzouni and published by Oxford University Press, USA. This book was released on 2004 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: If we take mathematical statements to be true, must we also believe in the existence of abstract invisible mathematical objects? This text claims that the way to escape such a commitment is to accept true statements which are about objects that don't exist in any sense at all.
Download or read book Mathematics and Scientific Representation written by Christopher Pincock and published by Oxford University Press. This book was released on 2012-01-13 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. In this book Christopher Pincock tackles this perennial question in a new way by asking how mathematics contributes to the success of our best scientific representations. In the first part of the book this question is posed and sharpened using a proposal for how we can determine the content of a scientific representation. Several different sorts of contributions from mathematics are then articulated. Pincock argues that each contribution can be understood as broadly epistemic, so that what mathematics ultimately contributes to science is best connected with our scientific knowledge. In the second part of the book, Pincock critically evaluates alternative approaches to the role of mathematics in science. These include the potential benefits for scientific discovery and scientific explanation. A major focus of this part of the book is the indispensability argument for mathematical platonism. Using the results of part one, Pincock argues that this argument can at best support a weak form of realism about the truth-value of the statements of mathematics. The book concludes with a chapter on pure mathematics and the remaining options for making sense of its interpretation and epistemology. Thoroughly grounded in case studies drawn from scientific practice, this book aims to bring together current debates in both the philosophy of mathematics and the philosophy of science and to demonstrate the philosophical importance of applications of mathematics.
Download or read book Mathematics and Reality written by Mary Leng and published by OUP Oxford. This book was released on 2010-04-22 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mary Leng offers a defense of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at least approximately) true. But since claims whose truth would require the existence of mathematical objects are indispensable in formulating our best empirical theories, it follows that we have good reason to believe in the mathematical objects posited by those mathematical theories used in empirical science, and therefore to believe that the mathematical theories utilized in empirical science are true. Previous responses to the indispensability argument have focussed on arguing that mathematical assumptions can be dispensed with in formulating our empirical theories. Leng, by contrast, offers an account of the role of mathematics in empirical science according to which the successful use of mathematics in formulating our empirical theories need not rely on the truth of the mathematics utilized.
Download or read book Autonomy Platonism and the Indispensability Argument written by Russell Marcus and published by Lexington Books. This book was released on 2015-06-11 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical platonism is the view that mathematical statements are true of real mathematical objects like numbers, shapes, and sets. One central problem with platonism is that numbers, shapes, sets, and the like are not perceivable by our senses. In contemporary philosophy, the most common defense of platonism uses what is known as the indispensability argument. According to the indispensabilist, we can know about mathematics because mathematics is essential to science. Platonism is among the most persistent philosophical views. Our mathematical beliefs are among our most entrenched. They have survived the demise of millennia of failed scientific theories. Once established, mathematical theories are rarely rejected, and never for reasons of their inapplicability to empirical science. Autonomy Platonism and the Indispensability Argument is a defense of an alternative to indispensability platonism. The autonomy platonist believes that mathematics is independent of empirical science: there is purely mathematical evidence for purely mathematical theories which are even more compelling to believe than empirical science. Russell Marcus begins by contrasting autonomy platonism and indispensability platonism. He then argues against a variety of indispensability arguments in the first half of the book. In the latter half, he defends a new approach to a traditional platonistic view, one which includes appeals to a priori but fallible methods of belief acquisition, including mathematical intuition, and a natural adoption of ordinary mathematical methods. In the end, Marcus defends his intuition-based autonomy platonism against charges that the autonomy of mathematics is viciously circular. This book will be useful to researchers, graduate students, and advanced undergraduates with interests in the philosophy of mathematics or in the connection between science and mathematics.
Download or read book The Indispensability of Mathematics ebook written by Mark Colyvan and published by . This book was released on 2001 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Quine-Putnam indispensability argument in the philosophy of mathematics urges us to place mathematical entities on the same ontological footing as other theoretical entities indispenable to certain scientific theories. This text examines the issues.
Download or read book The Oxford Handbook of Philosophy of Mathematics and Logic written by Stewart Shapiro and published by OUP USA. This book was released on 2005-02-10 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the state of the art in the philosophy of maths and logic, giving the reader an overview of the major problems, positions, and battle lines. The chapters in this book contain both exposition and criticism as well as substantial development of their own positions. It also includes a bibliography.
Download or read book Platonism Naturalism and Mathematical Knowledge written by James Robert Brown and published by Routledge. This book was released on 2013-06-17 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. Not only does this engaging book present the Platonist-Naturalist debate over mathematics in a comprehensive fashion, but it also sheds considerable light on non-mathematical aspects of a dispute that is central to contemporary philosophy.
Download or read book Platonism and Anti Platonism in Mathematics written by Mark Balaguer and published by Oxford University Press, USA. This book was released on 2001 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible. (Philosophy)
Download or read book Lectures on the Philosophy of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-03-09 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.
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 Morality and Mathematics written by Justin Clarke-Doane and published by Oxford University Press. This book was released on 2020-03-12 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: To what extent are the subjects of our thoughts and talk real? This is the question of realism. In this book, Justin Clarke-Doane explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. He argues that, contrary to widespread belief, our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to being empirically justified than our moral beliefs. It is also incorrect that reflection on the genealogy of our moral beliefs establishes a lack of parity between the cases. In general, if one is a moral antirealist on the basis of epistemological considerations, then one ought to be a mathematical antirealist as well. And, yet, Clarke-Doane shows that moral realism and mathematical realism do not stand or fall together — and for a surprising reason. Moral questions, insofar as they are practical, are objective in a sense that mathematical questions are not, and the sense in which they are objective can only be explained by assuming practical anti-realism. One upshot of the discussion is that the concepts of realism and objectivity, which are widely identified, are actually in tension. Another is that the objective questions in the neighborhood of factual areas like logic, modality, grounding, and nature are practical questions too. Practical philosophy should, therefore, take center stage.
Download or read book An Aristotelian Realist Philosophy of Mathematics written by J. Franklin and published by Springer. This book was released on 2014-04-09 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.
Download or read book Philosophy of Mathematics written by and published by Elsevier. This book was released on 2009-07-08 with total page 735 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics. -Comprehensive coverage of all main theories in the philosophy of mathematics-Clearly written expositions of fundamental ideas and concepts-Definitive discussions by leading researchers in the field-Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included
Download or read book Philosophy of Mathematics written by Gerhard Preyer and published by Walter de Gruyter. This book was released on 2013-05-02 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: One main interest of philosophy is to become clear about the assumptions, premisses and inconsistencies of our thoughts and theories. And even for a formal language like mathematics it is controversial if consistency is acheivable or necessary like the articles in the firt part of the publication show. Also the role of formal derivations, the role of the concept of apriority, and the intuitions of mathematical principles and properties need to be discussed. The second part is a contribution on nominalistic and platonistic views in mathematics, like the "indispensability argument" of W. v. O. Quine H. Putnam and the "makes no difference argument" of A. Baker. Not only in retrospect, the third part shows the problems of Mill, Frege's and the unity of mathematics and Descartes's contradictional conception of mathematical essences. Together, these articles give us a hint into the relationship between mathematics and world, that is, one of the central problems in philosophy of mathematics and philosophy of science.
