Introducing Philosophy of Mathematics

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Routledge, Dec 5, 2014 - Philosophy - 240 pages
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.
 

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User Review  - mdreid - LibraryThing

Do you know your constructivists from your formalists. Your realists from your platonists? I certainly didn't but I'd seen these terms pop up whenever I skirted around the edges of the philosophy of ... Read full review

Contents

1 Infinity
1
2 Mathematical Platonism and realism
23
3 Logicism
49
4 Structuralism
81
5 Constructivism
101
6 A potpourri of philosophies of mathematics
127
Proof ex falso quod libet
167
Glossary
169
Notes
177
Guide to further reading
191
Bibliography
195
Index
201
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