Truth in Mathematics

Front Cover
Harold G. Dales, Gianluigi Oliveri
Clarendon Press, 1998 - Mathematics - 376 pages
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The nature of truth in mathematics is a problem which has exercised the minds of thinkers from at least the time of the ancient Greeks. The great advances in mathematics and philosophy in the twentieth centuryand in particular the proof of Godel's theorem and the development of the notion ofindependence in mathematicshave led to new viewpoints on this question in our era. This book is the result of the interaction of a number of outstanding mathematicians and philosophersincluding Yurii Manin, Vaughan Jones, and Per Martin-Lofand their discussions of this problem. It provides anoverview of the forefront of current thinking, and is a valuable introduction and reference for researchers in the area.
 

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Contents

Truth and the foundations of mathematics
1
Tarski
11
The realismantirealism debate and the question about math
20
Bibliography
34
Truth and objectivity from a verificationist point
41
Objectivity
48
Varieties of constructive mathematics
55
Complex analysis
63
Bibliography
214
Mathematical definability
233
4
235
Applications
242
Bibliography
249
Seeing or interpreting?
255
Truth
261
Bibliography
268

On founding the theory of algorithms
71
Abstract machines and implementations
79
Implementations
89
Infinitary algorithms
95
Bibliography
102
Proofs
120
Computers and mathematics
136
Conclusion
144
Truth rigour and common sense
147
Materials for three case studies
155
How to be a naturalist about mathematics
161
The naturalistic philosopher
172
Bibliography
179
The style of formalists
186
Arguments against realism
194
11
203
First and secondorder reflection
277
Higherorder reflection
283
quotient and direct limit types
289
Putnams Models and Reality and the concepts of finiteness
296
Notes
306
Two conceptions of natural number
311
Notes
318
Bibliography
326
Firstorder logic
332
The formula
338
Evidence 345
353
215
363
Index
371
219
372
Copyright

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References to this book

Naturalism in Mathematics
Penelope Maddy
No preview available - 1997
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About the author (1998)

Garth Dales is at University of Leeds. Gianluigi Oliveri is at Wolfson College, Oxford.

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