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Michele Friend provides an introduction to the standard theories of mathematics - platonism and realism, logicism, formalism, constructivism, and structuralism - as well as to some of the less standard theories, such as psychologism, fictionalism, and Meinongian philosophy of mathematics. The author explains what characterises each theory, the differences between them, and some of the arguments in favour of and against the different positions. Introducing Philosophy of Mathematics also explores questions that occupy present-day philosophers and mathematicians, such as the relationship between good reasoning and mathematics, the problem of infinity, and whether we are more certain of mathematics than we are of everyday sense experience or science. Friend strikes a nice balance between conceptual accessibility and clear representation of the issues to enable readers to challenge existing positions.
Michele Friend is Assistant Professor of Philosophy at George Washington University, Washington DC
Table of Contents
Potential versus actual infinity
The ordinal notion of infinity
The cardinal notion of infinity
Mathematical Platonism and realism
Realism in general
General problems with set-theoretic realism
Frege's logicism: technical accomplishments
Frege's logicism: philosophical accomplishments
Problems with Frege's logicism
Whitehead and Russell's logicism
Philosophically, what is wrong with Whitehead and Russell's type theory?
Other attempts at logicism
The motivation for structuralism: Benacerraf's puzzle
The philosophy of structuralism: Hellman
The philosophy of structuralism: Resnik and Shapiro
Prima facie motivations for constructivism
Deeper motivations for constructivism
The semantics of intuitionist logic: Dummett
Problems with constructivism
A pot-pourri of philosophies of mathematics
Empiricism and naturalism
Meinongian Philosophy of Mathematics
Proof: ex falso quod libet
Guide to further reading
Table of Contents provided by Ingram. All Rights Reserved.