Mathematics and the Image of Reason

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Psychology Press, 1991 - Mathematics - 188 pages
A thorough account of the philosophy of mathematics. In a cogent account the author argues against the view that mathematics is solely logic.
 

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Contents

INTRODUCTION
1
AXIOMATIZATION RIGOUR AND REASON
7
DESERTING EUCLIDEAN STANDARDS
10
THE RETURN TO EUCLIDEAN STANDARDS
25
FREGE ARITHMETIC AS LOGIC
33
NUMBERS AND THE NATURE OF ARITHMETICAL TRUTHS
38
NUMBERS AS OBJECTS
42
THE NATURAL NUMBERS
49
FORGING THE FORMAL CHAINS OF REASON
103
SUCCESSES AND FAILURES
110
LOGIC AND ITS LIMITATIONS
123
APPENDIX RECURSIVE FUNCTIONS
128
IDEAL ELEMENTS AND RATIONAL IDEALS
129
FORMULAE SYMBOLS AND FORMS
130
IDEAL ELEMENTS AND IDEALS
138
DIAGRAMS AND RIGOUR
142

WORD GAMES?
54
RUSSELL MATHEMATICS AS LOGIC
59
GEOMETRY AND RELATIONAL STRUCTURES
60
PARADOXES AND LOGICAL TYPES
70
EMPIRICISM LOGICAL POSITIVISM AND THE STERILITY OF REASON
78
HILBERT MATHEMATICS AS A FORMULAGAME?
89
FORMALISM AND HILBERTS PROGRAMME
90
GEOMETRICAL RIGOUR
92
PRAGMATISM AXIOMATIZATION AND IDEALS
147
LOGIC AND THE OBJECTS OF MATHEMATICAL KNOWLEDGE
154
LACK OF CLOSURE AND THE POWER OF REASON
166
GLOSSARY OF SYMBOLS
175
FURTHER READING
176
BIBLIOGRAPHY
178
INDEX
184
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