## Order and Organism: Steps Toward a Whiteheadian Philosophy of Mathematics and the Natural SciencesWhat 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 |

254 | |

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### Common terms and phrases

abstract act of becoming actual entities application aspects assumption characteristics classical cognitive common sense complementary complete conceived concept of matter concrete continuity Copenhagen Interpretation definite described discussion elementary particles empirical epistemological essentially eternal objects existence experience explanation expression fact finite formal fundamental Gruenbaum hierarchy of organisms Ihid important individual infinite interpretation intuitionism involved Kant’s knowledge logical mathematical continuum mathematical theory means metaphysical mode modern physics nature notion observation ontological ontological commitment paradox particular pattern philosophy of mathematics philosophy of science physical organism physical reality physical world possible postulate presupposes primate principle principle of relativity problem quantum mechanics quantum physics quantum theory question rational realm of eternal reason reference regarded relatedness relational essence relationships retroductive scientific seems significance spatio-temporal structure systematic theory of organism things truth ultimately Whitehead Whitehead’s theory Whitehead’s view Whiteheadian Zeno Zeno’s Zeno’s arguments Zenonian