Principles and Proofs

352 Pages·1992·72.83 MB·English

by  Richard D. McKirahan

PRINCIPLES AND PROOFS
{
Richard D. McKirahan, Jr.
PRINCIPLES
AND PROOFS
Aristotle's Theory of Demonstrative Science
Princeton University Press
Princeton, New Jersey
Copyright © 1992 by Princeton University Press
Published by Princeton University Press, 41 William Street,
Princeton, New Jersey 08540
In the United Kingdom: Princeton University Press, Oxford
ALL RIGHTS RESERVED
Library of Congress Cataloging-in-Publication Data
McKirahan, Richard D.
Principles and proofs: Aristotle's theory of demonstrative
science I Richard D. McKirahan, Jr.
p. cm.
Includes bibliographical references and index.
ISBN 0-691-{)7363-5
I. Aristotle. Posterior analytics. 2. Aristotle-Contributions
in concept of demonstrative science. 3. Science- Philosophy.
4. Knowledge, Theory of. 5. Logic. 6. Metaphysics. I. Title.
B44I.M525 1992
16o----dC20 91-36774
CIP
This book has been composed in Linotron Times Roman
Princeton University Press books are printed on acid-free paper,
and meet the guidelines for permanence and durability of the
Committee on Production Guidelines for Book Longevity of the
Council on Library Resources
Printed in the United States of America
10 9 8 7 6 5 4 3 2
TO MY PARENTS
CONTENTS
Acknowledgments Xl
Abbreviations xiii
Introduction 3
The Motivation for the Theory of Demonstration 7
tl The Approach to the Principles 21
Scientific Knowledge and Scientific Demonstrations 23
The Premises of Scientific Demonstrations 24
Six Requirements for Scientific Principles 24
PRINCIPLES ARE PRIMARY AND IMMEDIATE 24
PRINCIPLES ARE TRUE 29
PRINCIPLES ARE BETTER KNOWN, PRIOR, AND GROUNDS 29
III The Kinds of Principles
Summary 49
vii
viii CONTENTS
IV The Subject Genus 50
The Composition of the Subject Genus 57
Interpretations of the Subject Genus 60
V The Subordinate Sciences 64
VI Axioms or Common Principles 68
The Analogical Nature of Axioms 71
The Alleged Regulative Role of Axioms 74
Summary 75
Axioms and Subordinate Sciences 75
Appendix: I. I I 77al0-21 and the Law of Noncontradiction 76
Vll Definitions, I: The Per Se 80
In Every Case 84
Per Se 85
Per Se I 85
Per Se 2 87
Per Se I and Per Se 2: Summary and Comparison 90
Per Se 2 and Definitions of Attributes 91
Per Se 2 and Compound Subjects 92
Per Se 3 93
Per Se 4 94
Universal 95
Are Conclusions of Demonstrations Per Se? 98
In Every Case. Per Se, Universal. and Necessary 101
V III Scientific Essences !O3
Scientific Facts !O4
Individuals, Intelligibility. and Per Se Facts 105
Subjects and Attributes 106
Essence and Necessity 107
IX Definitions, U: Form and Content III
Contents ix
x Existence Claims 122
The Role of Existence Claims 123
Existence Claims and the Requirements for Principles 125
Existence and Necessity 125
XI Aristotle's Principles and Greek Mathematics 133
Pre-Euclidean Principles 136
Differences between Aristotle and Euclid 137
XII Aristotle's Demonstrations and Euclid's Elements 144
Geometrical Diagrams 146
Existence vs. Constructibility 147
Proofs and Syllogisms 149
XIII The Varieties of Demonstration, J:
Universal Subject-Attribute Demonstrations 164
The Nature of Demonstrations 164
Subjects and Attributes 165
An Aristotelian Demonstration 167
Per Se I and Per Se 2 169
Commensurate Universals 171
XIV The Varieties of Demonstration, II: Application Arguments 177
Applications to Species 177
Applications to Individuals 181
Applications to Natural Phenomena 184
Applications in the Preliminary Stages of Science 186
Application Arguments and Syllogisms 186
xv The Varieties of Demonstration, 1IJ: Demonstrations of Existence 188
XVI Demonstration of Essence: Another Form of Scientific Proof? 198
X CONTENTS
XVII Scientific Explanation 209
Middle Tenns and Immediate Premises 209
Grounds of Truth or Grounds of Knowledge? 2 I 2
Knowledge of the Fact and Knowledge of the Reason Why 213
Two Kinds of Unsatisfactory Demonstrations 2] 3
CASE I: NONRECIPROCATIQN 2]4
CASE 2: RECIPROCATION IS NOT ENOUGH 216
Criteria for Grounds 2 I 7
8
PRIORITY OF THE ACCOUNT 2]
PRIORITY OF WHAT IS BETTER KNOWN 219
Priority, Primacy, and Ungrounded Grounds 222
CASE 2A: ANOTHER CASE OF NON~EXPERT KNOWLEIXiE? 224
I. 13 Summary 225
Scientific Explanations and the Four Causes 226
Aristotelian Grounds and Humean Causes 230
Aristotelian Explanations and the Deductive·Nomo!ogical Theory 230
Demonstration. Teaching, and Ideal Explanations 231
x V III Our Knowledge of the Principles 235
Perception and Science 237
The Path to the Principles 240
Grasping the Universals 244
Induction 250
Nous 257
Dialectic, Expertise, and the Principles 259
The Kinds of Principles 267
Assembling a Science 268
Research and the Good Life 269
Notes 273
Bibliography 309
Index Locorum 321
General Index 335
ACKNOWLEDGMENTS
THE PRESENT BOOK has had a lengthy gestation. It grew out of my 1973 doctoral
dissertation, entitled Aristotle's Theory of Demonstrative Science, which I wrote
under the supervision of the late Professor G. E. L. Owen. The research and
writing of the dissertation were supported by graduate fellowships at Harvard
University and a position as tutor at Kirkland House. Revision for publication
began in summer 1975 when I was awarded a Summer Stipend by the National
Endowment for the Humanities. The next lengthy stretch of work was carried out
at Cambridge University in spring and summer 1979. On this occasion I was
supported by the generous sabbatical policy of Pomona College and had the honor
of being associated with St. John's College, Cambridge. Spring 1983, the occa
sion of my next sabbatical leave, I spent at the American School of Classical
Studies at Athens, and during that spring and summer I was able to complete a
draft of the entire book. During summer 1985 at a National Endowment for the
Humanities Summer Seminar at Yale University, I was able to spend much of my
time revising the manuscript. Professor G. E. R. Lloyd, then of King's College,
Cambridge, and Professor Ian Mueller, of the University of Chicago, had the
kindness to read and make extensive comments on this draft; their criticisms were
the basis of further revisions. The manuscript was submitted to Princeton Uni
versity Press in 1988 and accepted in early 1989. On the basis of anonymous
readers' reports I spent the year 1990, especially the summer, again at the Amer
ican School of Classical Studies, supported by a second N.E.H. Summer Sti
pend, making extensive final revisions.
The people for whose assistance I am grateful are too many to recount here.
My deepest debt is to Professor G. E. L. Owen, who was the model thesis-su
pervisor both in the advice he offered and in the scholarly ideal he embodied.
The book has benefited from the careful discussions of the Posterior Analytics by
xi
xii ACKNOWLEDGMENTS
the West Coast Aristotelian Society in which I participated, and from the oppor
tunity afforded by the Department of Classics at the University of California at
Berkeley to teach a graduate seminar on my work. I also wish to thank Stanford
University, the Society for Ancient Greek Philosophy, the "B" Club, the Uni
versity of California at Berkeley, and Pomona College for inviting me to read
papers on this subject. Finally I want to express my gratitude to my wife, Voula,
whose support as well as scholarly advice has enabled me to bring the project to
completion.