Introduction to Mathematical Philosophy
Author | : Bertrand Russell |
Publisher | : |
Total Pages | : 224 |
Release | : 1920 |
Genre | : Mathematics |
ISBN | : |
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Author | : Bertrand Russell |
Publisher | : |
Total Pages | : 224 |
Release | : 1920 |
Genre | : Mathematics |
ISBN | : |
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 | : BERTRAND. RUSSELL |
Publisher | : |
Total Pages | : 0 |
Release | : 2018 |
Genre | : |
ISBN | : 9781033092989 |
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 | : Richard E. Hodel |
Publisher | : Courier Corporation |
Total Pages | : 514 |
Release | : 2013-01-01 |
Genre | : Mathematics |
ISBN | : 0486497852 |
This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.
Author | : Alfred North Whitehead |
Publisher | : |
Total Pages | : 696 |
Release | : 1910 |
Genre | : Logic, Symbolic and mathematical |
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 | : 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 | : Stewart Shapiro |
Publisher | : OUP Oxford |
Total Pages | : 323 |
Release | : 2000-07-13 |
Genre | : Philosophy |
ISBN | : 0192893068 |
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 | : Paolo Mancosu |
Publisher | : OUP Oxford |
Total Pages | : 460 |
Release | : 2008-06-19 |
Genre | : Philosophy |
ISBN | : 0191559091 |
Contemporary philosophy of mathematics offers us an embarrassment of riches. Among the major areas of work one could list developments of the classical foundational programs, analytic approaches to epistemology and ontology of mathematics, and developments at the intersection of history and philosophy of mathematics. But anyone familiar with contemporary philosophy of mathematics will be aware of the need for new approaches that pay closer attention to mathematical practice. This book is the first attempt to give a coherent and unified presentation of this new wave of work in philosophy of mathematics. The new approach is innovative at least in two ways. First, it holds that there are important novel characteristics of contemporary mathematics that are just as worthy of philosophical attention as the distinction between constructive and non-constructive mathematics at the time of the foundational debates. Secondly, it holds that many topics which escape purely formal logical treatment - such as visualization, explanation, and understanding - can nonetheless be subjected to philosophical analysis. The Philosophy of Mathematical Practice comprises an introduction by the editor and eight chapters written by some of the leading scholars in the field. Each chapter consists of short introduction to the general topic of the chapter followed by a longer research article in the area. The eight topics selected represent a broad spectrum of contemporary philosophical reflection on different aspects of mathematical practice: diagrammatic reasoning and representation systems; visualization; mathematical explanation; purity of methods; mathematical concepts; the philosophical relevance of category theory; philosophical aspects of computer science in mathematics; the philosophical impact of recent developments in mathematical physics.