Mathematics And Metaphilosophy PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Mathematics And Metaphilosophy PDF full book. Access full book title Mathematics And Metaphilosophy.
| Author | : Justin Clarke-Doane |
| Publisher | : Cambridge University Press |
| Total Pages | : 105 |
| Release | : 2022-06-30 |
| Genre | : Science |
| ISBN | : 1009002295 |
Download Mathematics and Metaphilosophy Book in PDF, ePub and Kindle
This Element discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the challenge to explain the (defeasible) justification of our mathematical beliefs ('the justificatory challenge'), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the challenge to explain their reliability ('the reliability challenge'), arises to the extent that we could have easily had different beliefs. The Element shows that mathematical facts are not, in general, empirically accessible, contra Quine, and that they cannot be dispensed with, contra Field. However, it argues that they might be so plentiful that our knowledge of them is unmysterious. The Element concludes with a complementary 'pluralism' about modality, logic and normative theory, highlighting its surprising implications. Metaphysically, pluralism engenders a kind of perspectivalism and indeterminacy. Methodologically, it vindicates Carnap's pragmatism, transposed to the key of realism.
| Author | : Justin Clarke-Doane |
| Publisher | : Oxford University Press |
| Total Pages | : 208 |
| Release | : 2020-03-12 |
| Genre | : Philosophy |
| ISBN | : 0192556800 |
Download Morality and Mathematics Book in PDF, ePub and Kindle
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.
| Author | : Stewart Shapiro |
| Publisher | : OUP Oxford |
| Total Pages | : 323 |
| Release | : 2000-07-13 |
| Genre | : Philosophy |
| ISBN | : 0192893068 |
Download Thinking about Mathematics Book in PDF, ePub and Kindle
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.
| Author | : Joel David Hamkins |
| Publisher | : MIT Press |
| Total Pages | : 350 |
| Release | : 2021-03-09 |
| Genre | : Mathematics |
| ISBN | : 0262542234 |
Download Lectures on the Philosophy of Mathematics Book in PDF, ePub and Kindle
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.
| Author | : |
| Publisher | : Elsevier |
| Total Pages | : 735 |
| Release | : 2009-07-08 |
| Genre | : Philosophy |
| ISBN | : 0080930581 |
Download Philosophy of Mathematics Book in PDF, ePub and Kindle
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
| Author | : James Robert Brown |
| Publisher | : Routledge |
| Total Pages | : 181 |
| Release | : 2005-08-09 |
| Genre | : Philosophy |
| ISBN | : 1134806442 |
Download Philosophy of Mathematics Book in PDF, ePub and Kindle
Philosophy of Mathematics is an excellent introductory text. This student friendly book discusses the great philosophers and the importance of mathematics to their thought. It includes the following topics: * the mathematical image * platonism * picture-proofs * applied mathematics * Hilbert and Godel * knots and nations * definitions * picture-proofs and Wittgenstein * computation, proof and conjecture. The book is ideal for courses on philosophy of mathematics and logic.
| Author | : Paul Benacerraf |
| Publisher | : Cambridge University Press |
| Total Pages | : 604 |
| Release | : 1984-01-27 |
| Genre | : Science |
| ISBN | : 1107268133 |
Download Philosophy of Mathematics Book in PDF, ePub and Kindle
The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.
| Author | : Nicholas Rescher |
| Publisher | : Lexington Books |
| Total Pages | : 256 |
| Release | : 2014-10-23 |
| Genre | : Philosophy |
| ISBN | : 0739199781 |
Download Metaphilosophy Book in PDF, ePub and Kindle
The definitive mission of metaphilosophy is to facilitate an understanding of how philosophy works—the aim of the enterprise, the instrumental and procedural resources for its work, and the prospect of its success. Nicholas Rescher unites two facets of metaphilosophy to show that historical perspective and forward-thinking normative, or systematic, metaphilosophy cannot be independent of one another. The descriptive, or historical, metaphilosophy provides an account of what has been thought regarding the conduct of philosophical inquiry, and the prescriptive, or normative, metaphilosophy which deliberates about what is to be thought regarding the conduct of philosophizing. Rescher argues that metaphilosophy forms a part of philosophy itself. This is a unique feature of the discipline since the philosophy of biology is not a part of biology and the philosophy of mathematics is not a part of mathematics. Ultimately, the salient features of philosophizing in general—including the inherently controversial and discordant nature of philosophical doctrines—are also bound to afflict metaphilosophy. Thus, only by a careful analysis of the central issues can a plausible view of the enterprise be developed. Metaphilosophy: Philosophy in Philosophical Perspective challenges the static, compartmentalized view of metaphilosophy, providing insight for scholars and students of all areas of philosophy.
| Author | : Mark Colyvan |
| Publisher | : Cambridge University Press |
| Total Pages | : 199 |
| Release | : 2012-06-14 |
| Genre | : Mathematics |
| ISBN | : 0521826020 |
Download An Introduction to the Philosophy of Mathematics Book in PDF, ePub and Kindle
A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.
| Author | : O. Bueno |
| Publisher | : Springer |
| Total Pages | : 330 |
| Release | : 2009-09-29 |
| Genre | : Philosophy |
| ISBN | : 0230245196 |
Download New Waves in Philosophy of Mathematics Book in PDF, ePub and Kindle
Thirteen promising young researchers write on what they take to be the right philosophical account of mathematics and discuss where the philosophy of mathematics ought to be going. New trends are revealed, such as an increasing attention to mathematical practice, a reassessment of the canon, and inspiration from philosophical logic.
