Order and Organism: Steps Toward a Whiteheadian Philosophy of Mathematics and the Natural Sciences

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SUNY Press, Jan 1, 1985 - Mathematics - 265 pages
What is now needed is a way of thinking about the physical that is realistic in outlook but which departs radically from the mechanistic post-Galilean tradition. Since it seems clear that we can no longer take for granted the certainty and absolute objectivity of scientific knowledge, any alternative view must be able to do full justice to subjective modes of knowing.

Order and Organism shows how Alfred North Whitehead's thought can reconcile some of the most insistent demands of common sense with the esoteric results of modern physics and mathematics. Whitehead shows a way to resolve the perennial puzzle of why mathematics works. Under his view, it is possible to account for the necessity and uniqueness of mathematical theories without denying the fact that such theories often arise from the mathematician's essentially aesthetic interest in various kinds of pattern.
 

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Contents

Chapter One Introduction
1
2 Mathematics and Knowledge
7
3 On the Relation Between Epistemology and Ontology
10
4 On Conceptual Complementarity
16
Chapter Two Whitehead on Mathematics and Philosophy
24
2 The Method of Retroduction
29
3 Pure Mathematics and Applied Mathematics
33
4 Some Problems in the Philosophy of Mathematics
37
2 The NoModel Argument
115
3 The Concept of Reality in Modern Physics
120
4 Summary
124
Chapter Six The Model of Organism in Physical Science
126
2 Substantiality and Matter
130
3 Whiteheads Theory of Primates
137
4 The Hierarchy of Organisms
141
5 The Extensive Continuum
146

5 On Mathematics and Metaphysics
40
Mathematical and Metaphysical Responses
48
2 The Exactcorrespondence Hypothesis
52
3 The Metrical Paradox of Extension
54
4 Zeno Mathematics and Reality
61
5 Number and the Continuum
62
6 Whitehead and Zeno
67
7 Real and Artificial Zenonian Problems
71
8 Conclusion
78
Chapter Four On Philosophizing Adequately About Science Mathematics and Reality
80
2 Realism and Monistic Materialism
83
3 On Modes of Philosophizing
89
4 Philosophy and Evolutionary Materialism
94
5 Philosophy and the Story
98
6 Scientific and Metaphysical Explanation
103
Chapter five The Model in Physical Science
112
6 The Laws of Nature
150
Chapter Seven Mathematics and Necessity
158
2 The Theory of Eternal Objects
163
3 The Nature of Mathematics and Logic
169
4 Mathematical Knowledge
174
Chapter Eight Aspects of a Whiteheadian Philosophy of Mathematics
181
2 Ontological Commitment
187
3 On Platonism
190
4 Whitehead on the Nature and Scope of Mathematics
192
5 The Formal Limitations of Mathematics
196
6 Perspective and the Philosophy of Mathematics
199
7 Conclusion
203
NOTES
208
BIBLIOGRAPHY
248
INDEX
254
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About the author (1985)

Murray Code is Assistant Professor in the Department of Mathematics and Statistics, University of Guelph, Ontario, Canada.

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