Introduction to Mathematical Philosophy
Title | Introduction to Mathematical Philosophy PDF eBook |
Author | Bertrand Russell |
Publisher | |
Pages | 224 |
Release | 1920 |
Genre | Mathematics |
ISBN |
An Introduction to the Philosophy of Mathematics
Title | An Introduction to the Philosophy of Mathematics PDF eBook |
Author | Mark Colyvan |
Publisher | Cambridge University Press |
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.
Introduction to Mathematical Philosophy
Title | Introduction to Mathematical Philosophy PDF eBook |
Author | Bertrand Russell |
Publisher | |
Pages | 0 |
Release | 1963 |
Genre | Mathematics |
ISBN |
Thinking about Mathematics
Title | Thinking about Mathematics PDF eBook |
Author | Stewart Shapiro |
Publisher | OUP Oxford |
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.
Lectures on the Philosophy of Mathematics
Title | Lectures on the Philosophy of Mathematics PDF eBook |
Author | Joel David Hamkins |
Publisher | MIT Press |
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.
Principia Mathematica
Title | Principia Mathematica PDF eBook |
Author | Alfred North Whitehead |
Publisher | |
Pages | 688 |
Release | 1910 |
Genre | Logic, Symbolic and mathematical |
ISBN |
Set Theory and its Philosophy
Title | Set Theory and its Philosophy PDF eBook |
Author | Michael Potter |
Publisher | Clarendon Press |
Pages | 362 |
Release | 2004-01-15 |
Genre | Philosophy |
ISBN | 0191556432 |
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.