Introducing Philosophy of Mathematics
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A01=Michele Friend
Actual Infinity
Author_Michele Friend
Category=PBB
Category=QDTL
Classical Logic
constructivist approaches
Dedekind Axioms
diff
Double Negation Elimination
epistemology of mathematics
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
erent
Frege's Basic Law
Husserl's Phenomenological Approach
infi
Infinite Cardinal
Infinite Ordinals
Intuitionist Logic
logic foundations
mathematical
Mathematical Intuition
mathematical ontology
mathematical structuralism
Meinongian Philosophy
Meta Language
Natural Numbers
nite
nity
number
Numbers Principle
object
Ordinal Numbers
philosophical analysis of mathematical knowledge
Potential Infinity
psychologism in mathematics
Rational Intuition
set
Set Theoretic Hierarchy
Set Theoretic Paradoxes
Set Theoretic Realism
Set Theoretic Universe
Set Theory
Sophisticated Platonist
Struc Tures
theory
Vice Versa
Product details
- ISBN 9781844650606
- Weight: 460g
- Dimensions: 156 x 234mm
- Publication Date: 22 Feb 2007
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Hardback
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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.
Michele Friend is Assistant Professor of Philosophy at George Washington University, Washington DC.
