The Idea of Principle in Leibnitz and the Evolution of Deductive Theory

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The Idea of Principle in Leibnitz and The Evolution of Deductive Theory

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by JOSE ORTEGA Y GASSET SOME LESSONS IN METAPHYSICS THE ORIGIN OF PHILOSOPHY THE REVOLT OF THE MASSES MAN AND PEOPLE MAN AND CRISIS WHAT IS PHILOSOPHY? MEDITArlONS ON QUIXOTE HISTORY AS A SYSTEM CONCORD AND LIBERTY MISSION OF THE UNIVERSITY THE IDEA OF PRINCIPLE IN LEIBNITZ AND THE EVOLUTION OF DEDUCTIVE THEORY

JOSE ORTEGA Y GASSET

THE IDEA OF PRINCIPLE IN LEIBNITZ AND THE EVOLUTION OF DEDUCTIVE THEORY TRANSLATED BY MILDRED ADAMS

W·W·NORTON & COMPANY- INC· New York

COPYRIGHT @ 1971 BY W. W. NORTON & COMPANY, INC.

First Edition

Originally published under the title La Idea de Principio en Leibniz y la Evoluci6n de la Teorfa Deductiva

All rights reserved. Published simultaneously in Canada by George J. McLeod Limited, Toronto. Library of Congress Catalog Card No. 66-18068 SBN

393 01086 4

PRINTED IN THE UNITED STATES OF AMERICA 1 2 3 4 S 6 7 8 9 0

Contents

PRELIMINARY NOTE

1 2 3 4

7

THE IDEA OF PRINCIPLE IN LEIBNITZ

11

WHAT A PRINCIPLE IS

15

THINKING AND BEING, OR THE HEAVENLY TWINS

20

THREE POSITIONS OF PHILOSOPHY \VITH RESPECT TO SCIENCE

22

5

THE REIGN OF PHYSICS BEGINS ABOUT 1750

39

6

BACK OVER THE ROAD

44

7

ALGEBRA AS A "WAY OF THINKING"

46

8

ANALYTICAL GEOMETRY

9

54

CONCEPT AS A "TERM"

57

10

TRUTH A�D LOGICALITY

62

11

THE CONCEPT IN PRE-CARTESIAN DEDUCTIVE THEORY

65

12

PROOF IN THE DEDUCTIVE THEORY ACCORDING TO ARISTOTLE

13

LOGICAL STRUCTURE IN THE SCIENCE OF EUCLID

87

14

DEFINITIONS IN EUCLID

93

15

"EVIDENCE" IN EUCLID'S AXIOMS

16

ARISTOTLE AND THE "TRANSCENDENTAL DEDUCTION" OF PRINCIPLES

17

107

THE "IMPLICIT AXIOMS" IN EUCLID--COMMON AXIOMS AND "PROPER" AXIOMS

18

100

113

SENSUALISM IN THE ARISTOTELIAN "WAY OF THINKING"

128

6

19

CONTENTS ESSAY ON WHAT HAPPENED TO ARISTOTLE WITH PRINCIPLES

144

20

PARENTHETICAL NOTE ON SCHOLASTICISMS

21

NEW REVISION OF THE ITINERARY

201 2I3

22

INCOMMUNICABILITY OF THE GENERA

2I8

23

MODERNITY AND PRIMITIVISM IN ARISTOTLE

232

24

THE NEW "WAY OF THINKING" AND ARISTOTELIAN DEMAGOGUERY

237

25

THE CATALEPTIC IMAGINATION OF THE STOICS

246

26

IDEOMA-DRAOMA

257

27

DOUBT, THE BEGINNING OF PHILOSOPHY

2 62

28

THE HISTORICAL ORIGIN OF PHILOSOPHY

27 I

29

THE LEVEL OF OUR ROOTS

30

276

BELIEF AND TRUTH

29 5

31

THE DRAMATIC SIDE OF PHILOSOPHY

305

32

THE JOVIAL SIDE OF PHILOSOPHY

J20

33

THE CARTESIAN "WAY OF THINKING"

3 34

APPENDIX

1:

CONCERNING OPTIMISM IN LEIBNITZ

APPENDIX

2:

RENAISSANCE, HUMANISM, AND COUNTER

REFORMATION

34 3

376

Preliminary Note Tms BOOK was written by Ortega, almost all of it in Lisbon, in the spring and early summer of 1947. He planned to finish it in the autumn and then give it to the printer. Its first title was El principialismo de Leibnitz y algunos problemas anejos (Principalism in Leibnitz and Some Related Problems); but later, after using some of its paragraphs in the "Prologue" to the Castilian version of El Collar de la Paloma by lbn Hazm (Madrid, 1952), Ortega gave it the title La idea de principio en Leibnitz y la evoluci6n de la teorfa deductiva (The Idea of Principle in Leibnitz and the Evolution of De­ ductive Theory) with the announcement that it was going to be published by the Hemeroteca Municipal of Madrid. They had agreed to celebrate the tercentenary of the birth of Leib­ nitz with the first Spanish edition of the "Essays," which ap­ peared in the Acta Eruditoreum, Leipzig 1688-1716, presented with a preliminary study by Jose Ortega y Gasset. Some sheets to this end were printed in 1948. Ortega then revised the first draft in part, and added some pages and notes. Nevertheless, various obligations took him from this work, and delayed its finishing. On his account, the homage to Leibnitz was not per­ formed. Among the author's unpublished papers there appeared the originals of the study as it is now published. Its editing was not finished, for in the text he announces a second and a third chapter ( pages 157 and 159) which were never written. We added as Appendices the discourse "Concerning Opti­ mism in Leibnitz," written for the opening of The XIX Con­ gress of the Spanish Association for the Progress of the Sci­ ences, celebrated in San Sebastian in 1947, and some pages on the Renaissance, which Ortega had interrupted and set apart from the study. 7

8

PRELIMINARY NOTE

The exceptional significance of this book-because of its length, its subjects and the manner of treating them-and what it has of novelty in Ortega's intellectual trajectory gives it a preeminent place in his philosophic production. The Compilers

The Idea of Principle in Leibnitz and The Evolution of Deductive Theory

1

The Idea of Principle

in Leibnitz

KNOWLEDGE, whether formal .9r informal.., j�_ a�ways_ based on the c; o_ _�teIJ:1plat1.9n of __some��J_�g �_!�_i!)g -�9-�- p_rinciple. 1 In the sciences, this process becomes formalized and ·converted into a method or a calculated procedure whereby the data on a problem are related to a principle which "explains" them. In philosophy this is �d to an extreme, which tries not only to ex lain thin s on the bas1S of their rinciples, but also re­ qu· es those rinci les to be "ultimate" in t e g root principles. The fact that we customarily call these root principles, these "most principle" of all principles, "ultimate" shows that in our intellectual life we move habitually within an intermediate zone which is not pure empiricism or an absence of principle, nor is it in the area of root principles; these seem to us remote, far out at the limit of the mind's horizon, representing a goal still to be achieved, a point not yet reached. Inversely, at other times, we call these "first" principles. Note that when we say this, or think it, we tend to move the head slightly upward. This is because, even when we call these principles "first" rather than "ultimate" we still do not bring them close to us but regard them as distant, although now in a vertical direc­ tion. As a matter of fact, we set those principles as high as possi-

1. To avoid possible confusion it must be remembered that in both English and Spanish the primary meaning of "principle" (Sp. principio) is "origin, source, beginning." A secondary meaning is "fun�amental truth law or motive force." Either set, or both, of these meanmgs can be r�ad into the text of these chapters at various points [Translator's note]. II

I2

THE IDEA OF PRINCIPLE IN LEIBNITZ

hie: in the sky, and at the zenith. This is a relic of our Indo­ European and Semitic (i.e., Hebraic) tradition, the tradition of peoples whose religion is shot through with the brilliant and the starry, for whom the gods are made manifest in the planets and the meteors. Always the same, we see them at the greatest possible distance. They appear, then, as both necessity and aspiration. The other forms of knowledge range across the intermediate zone which extends, from the place where we normally and spontaneously are, a place made up of vaguely generalized facts, to that last line of the horizon where the root principles lie hidden. E.hilP�Qphy, which is intellectual radical­ ism or _ ex;tremisl!!,.!� __determin-ed-to-reach by'-the mosf direct pa�h that_last line of the- horiz-on-�vhere- -the ultimate principles abide; thereTore-:;-)tis not- merely a form of k_nowledge that, like --�!Q.��sJ _ is_ __ _d�a":7_r_-i _ from principles, but philosophy is a _ to -the- di�covery of those principles. form_al__�)fp _ lqratl