Introducing Philosophy of Mathematics

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  • Edition: 1st
  • Format: Nonspecific Binding
  • Copyright: 2014-08-20
  • Publisher: Routledge
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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.

Author Biography

Michele Friend is Assistant Professor of Philosophy at George Washington University, Washington DC

Table of Contents

Acknowledgementsp. vii
Prefacep. ix
Infinityp. 1
Introductionp. 1
Zeno's paradoxesp. 2
Potential versus actual infinityp. 7
The ordinal notion of infinityp. 12
The cardinal notion of infinityp. 13
Summaryp. 22
Mathematical Platonism and realismp. 23
Introductionp. 23
Historical originsp. 23
Realism in generalp. 26
Kurt Godelp. 35
Penelope Maddyp. 37
General problems with set-theoretic realismp. 41
Conclusionp. 46
Summaryp. 47
Logicismp. 49
Introductionp. 49
Frege's logicism: technical accomplishmentsp. 52
Frege's logicism: philosophical accomplishmentsp. 58
Problems with Frege's logicismp. 63
Whitehead and Russell's logicismp. 66
Philosophically, what is wrong with Whitehead and Russell's type theory?p. 71
Other attempts at logicismp. 78
Conclusionp. 78
Summaryp. 79
Structuralismp. 81
Introductionp. 81
The motivation for structuralism: Benacerraf's puzzlep. 83
The philosophy of structuralism: Hellmanp. 85
The philosophy of structuralism: Resnik and Shapirop. 90
Critiquep. 96
Summaryp. 100
Constructivismp. 101
Introductionp. 101
Intuitionist logicp. 106
Prima facie motivations for constructivismp. 113
Deeper motivations for constructivismp. 114
The semantics of intuitionist logic: Dummettp. 121
Problems with constructivismp. 123
Summaryp. 124
A pot-pourri of philosophies of mathematicsp. 127
Introductionp. 127
Empiricism and naturalismp. 130
Fictionalismp. 134
Psychologismp. 137
Husserlp. 141
Formalismp. 147
Hilbertp. 153
Meinongian Philosophy of Mathematicsp. 157
Lakatosp. 163
Proof: ex falso quod libetp. 167
Glossaryp. 169
Notesp. 177
Guide to further readingp. 191
Bibliographyp. 195
Indexp. 201
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