Philosophies Of Mathematics
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| Author | : Øystein Linnebo |
| Publisher | : Princeton University Press |
| Total Pages | : 214 |
| Release | : 2020-03-24 |
| Genre | : Mathematics |
| ISBN | : 069120229X |
A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers Mathematics is a model of precision and objectivity, but it appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic, accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Øystein Linnebo, one of the world's leading scholars on the subject, introduces all of the classical approaches to the field as well as more specialized issues, including mathematical intuition, potential infinity, and the search for new mathematical axioms. Sophisticated but clear and approachable, this is an essential book for all students and teachers of philosophy and of mathematics.
| Author | : Michele Friend |
| Publisher | : Routledge |
| Total Pages | : 294 |
| Release | : 2014-12-05 |
| Genre | : Philosophy |
| ISBN | : 1317493788 |
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.
| Author | : Mark Colyvan |
| Publisher | : Cambridge University Press |
| Total Pages | : 199 |
| Release | : 2012-06-14 |
| Genre | : Mathematics |
| ISBN | : 0521826020 |
A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.
| Author | : Joel David Hamkins |
| Publisher | : MIT Press |
| Total Pages | : 350 |
| Release | : 2021-03-09 |
| Genre | : Mathematics |
| ISBN | : 0262542234 |
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 | : Alexander L. George |
| Publisher | : Wiley-Blackwell |
| Total Pages | : 244 |
| Release | : 2001-12-03 |
| Genre | : Science |
| ISBN | : 9780631195443 |
This book provides an accessible, critical introduction to the three main approaches that dominated work in the philosophy of mathematics during the twentieth century: logicism, intuitionism and formalism.
| Author | : Bertrand Russell |
| Publisher | : |
| Total Pages | : 224 |
| Release | : 1920 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Paul Benacerraf |
| Publisher | : Cambridge University Press |
| Total Pages | : 604 |
| Release | : 1984-01-27 |
| Genre | : Science |
| ISBN | : 1107268133 |
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 | : Reuben Hersh |
| Publisher | : Oxford University Press |
| Total Pages | : 368 |
| Release | : 1997-08-21 |
| Genre | : Mathematics |
| ISBN | : 0198027362 |
Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.
| Author | : David Corfield |
| Publisher | : Cambridge University Press |
| Total Pages | : 300 |
| Release | : 2003-04-24 |
| Genre | : Philosophy |
| ISBN | : 1139436392 |
In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics, to the use of analogy, the prospects for a Bayesian confirmation theory, the notion of a mathematical research programme and the ways in which new concepts are justified. His inspiring book challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines and points clearly to the ways in which this can be done.
| Author | : Jacqueline Feke |
| Publisher | : Princeton University Press |
| Total Pages | : 250 |
| Release | : 2020-10-13 |
| Genre | : Mathematics |
| ISBN | : 069121039X |
A stimulating intellectual history of Ptolemy's philosophy and his conception of a world in which mathematics reigns supreme The Greco-Roman mathematician Claudius Ptolemy is one of the most significant figures in the history of science. He is remembered today for his astronomy, but his philosophy is almost entirely lost to history. This groundbreaking book is the first to reconstruct Ptolemy’s general philosophical system—including his metaphysics, epistemology, and ethics—and to explore its relationship to astronomy, harmonics, element theory, astrology, cosmology, psychology, and theology. In this stimulating intellectual history, Jacqueline Feke uncovers references to a complex and sophisticated philosophical agenda scattered among Ptolemy’s technical studies in the physical and mathematical sciences. She shows how he developed a philosophy that was radical and even subversive, appropriating ideas and turning them against the very philosophers from whom he drew influence. Feke reveals how Ptolemy’s unique system is at once a critique of prevailing philosophical trends and a conception of the world in which mathematics reigns supreme. A compelling work of scholarship, Ptolemy’s Philosophy demonstrates how Ptolemy situated mathematics at the very foundation of all philosophy—theoretical and practical—and advanced the mathematical way of life as the true path to human perfection.
