Crescas’ Critique of Aristotle: Problems of Aristotle’s Physics in Jewish and Arabic Philosophy [2nd printing 1971. Reprint 2014 ed.] 9780674864214, 9780674864221

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HARVARD SEMITIC SERIES VOLUME VI

CRESCAS' CRITIQUE OF ARISTOTLE

CRESCAS' CRITIQUE OF ARISTOTLE PROBLEMS OF ARISTOTLE'S

PHYSICS

IN JEWISH AND ARABIC PHILOSOPHY

BY

HARRY AUSTRYN WOLFSON NATHAN LITTAUER PROFESSOR OF HEBREW LITERATURE AND PHILOSOPHY, EMERITUS, HARVARD UNIVERSITY

CAMBRIDGE

HARVARD UNIVERSITY PRESS

COPYRIGHT 1 9 2 9 BY THE PRESIDENT AND FELLOWS OF HARVARD COLLEGE

© Copyright 19S7 by HARRY AUSTRYN WOLFSON

Second Printing, 1971 Distributed in Great Britain by Oxford University Press, London SBN 674-1757S-1

PRINTED IN THE UNITED STATES OF AMERICA

TO

LUCIUS NATHAN LITTAUER LOVER OF LEARNING IN HIGH ESTEEM AND APPRECIATION

PREFACE philosophy is no longer considered as a barren interval between ancient and modern philosophy. Nor is it any longer identified with works written solely in Latin. Scholarship recognizes it more and more as a formative period in the history of philosophy the records of which are to be found in a threefold literature—Arabic, Hebrew and Latin. In certain respects, the delineation and treatment of the history of philosophy should follow the same lines as the delineation and treatment of the political and social history of Europe. The closing of the philosophic schools at Athens early in the sixth century is analogous in its effect to the fall of Rome toward the end of the fifth century. Like the latter, it brought a dying past to its end, and prepared the way for a shifting of scene in a phase of history. The successive translations of Greek treatises into Syriac, Arabic, Hebrew and Latin correspond, in philosophy, to the spread of the diverse elements of Roman civilization with the successions of tribal wanderings, of invasions, and of conversions. Both accomplished similar results, transforming something antiquated and moribund into something new, with life in it. By the same token, just as one cannot treat of the new life t h a t appeared in Europe during the Middle Ages as merely the result of the individual exploits of heroes, or of the eloquence of preachers, or of the inventive fancy of courtiers, so one cannot treat of the development of mediaeval philosophic thought as a mere interplay of abstract concepts. There is an earthly basis to the development of philosophic problems in the Middle Ages—and that is language and text. The present work is an a t t e m p t to trace the history of certain problems of philosophy by means of phi'ological and textual studies. MEDIAEVAL

VII

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PREFACE

In form this work is a study of certain portions of Hasdai Crescas' Or Adonai ("The Light of the Lord"). In substance it is a historical and critical investigation of the main problems of Aristotle's Physics and De Caelo. Its material, largely unpublished, is drawn from the general field of Jewish philosophy and from related works in Arabic philosophy, such as the writings of Avicenna and Algazali, and particularly the commentaries of Averroes on Aristotle. The scope of this work, confined as it is to a closely interdependent group of writings, did not call for citations from works outside the field of Greek, Arabic and Jewish philosophy. Yet the material is such that the discussion of the history of the various problems will furnish a background for corresponding discussions of the same problems in scholastic philosophy. The notes, which form the greater part of the work, are detachable from the text and can be used in connection with similar texts in other works. Many of the notes exceed the bounds of mere explanatory comments, being in fact extended investigations of the development of certain philosophic concepts by means of a study of the interpretation and criticism to which Aristotle's writings were subjected in two forms of mediaeval philosophic literature—the Arabic and the Hebrew. Hasdai Crescas, whose work is the subject of the special investigation, was a true representative of the interpénétration of the Arabic and Hebrew philosophic traditions. Born in Barcelona in 1340, he died in Saragossa in 1410. He flourished, it will be seen, two centuries after Maimonides (1135-1204), who was the last of that line of Jewish philosophers, beginning with Saadia (882-942), whose works were written in Arabic for Arabic speaking Jews. During these two intervening centuries the centre of Jewish philosophic activity had shifted to non-Arabic speaking countries—to Christian Spain, to Southern France and to Italy—where the sole literary language of the Jews was Hebrew. In these new centres, the entire philosophic literature written in Arabic by Jews as well as almost everything

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of general philosophic interest written by Moslems was translated into Hebrew, and thereby Hebrew literature became also the repository of the whole Aristotelian heritage of Greek philosophy. Acquaintance with the sources of philosophy acquired by means of these translations stimulated the production of an original philosophic literature in Hebrew, rich both in content and in volume. I t also gave rise to a new attitude toward philosophy, an attitude of independence, of research and of criticism, which, among those who continued to be opposed to philosophy, manifested itself in a change in the temper of their opposition, while among those who were aligned on the side of philosophy, it took the form of incisive, searching studies of older texts and problems. Of the vast learning so attained by fourteenth century Jewish scholars and also of the critical attitude which inspired their studies Crescas is the fruition. In his work are mirrored the achievements of five centuries of philosophic activity among Moslems and Jews, and in his method of inquiry is reflected the originality and the independence of mind which characterize the Jewish philosophic writings of his time—an originality and independence which is yet to be recognized. Crescas' method has been described elsewhere in this work (pp. 24-29) as the hypotheticodeductive method of Talmudic reasoning, usually called pilpul, which is in reality the application of the scientific procedure to the study of texts. Applied by Crescas to the study of the texts of others, this method is here applied to the text of his Or Adonai. T h e Or Adonai is divided into four Books (ma'amarim), the first three of which are subdivided into Parts (kelalim), or, as the Latin translators from the Hebrew would more accurately call them, summulae, and these are again subdivided into Chapters (perafyim). The first twenty-five chapters of Part I of Book I are written in the form of proofs of the twenty-five propositions in which Maimonides summed up the main prin-

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PREFACE

ciples of Aristotle's philosophy. The first twenty chapters of Part II of Book I are written in the form of a criticism of twenty out of the twenty-five propositions. The present work deals with these two sets of chapters, with the proofs and the criticisms. Together they compose about one sixth of the entire work. A separate study of Part III of Book I and of the remaining chapters of Parts I and II will be published shortly under the title Crescas on the Existence and Attributes of God. In reprinting the text I have changed somewhat its original order by placing the criticism of each proposition immediately after its respective proof. The text is edited on the basis of the first edition and of eleven manuscripts; it is accompanied by an English translation and is followed by a commentary in the form of notes on the translation. There is also an Introduction, which is divided into six chapters. Chapter I discusses literary and historical problems. Chapters II to V contain a systematic presentation of the main problems dealt with in the text and the notes. Chapter VI interprets some of the larger aspects of Crescas' philosophy and endeavors to appraise him as one of the first to forecast that which ever since the sixteenth century has been known as the new conception of the universe. Translation, commentary and introduction are interdependent and mutually complementary. The study of a text is always an adventure, the adventure of prying into the unknown recesses of the mind of another. There is sleuthing in scholarship as there is in crime, and it is as full of mystery, danger, intrigue, suspense and thrills—if only the story were told. In a work of this kind, however, the story is not the thing. What one is after is the information it uncovers. Accordingly, no attempt has been made to recount the processes of the search. Only the results arrived at are set down, and the corroborative data are so marshalled as to let them speak for themselves and convince the reader by the obviousness of the contention.

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A considerable part of this work—the study of the first proposition dealing with infinity, including text, translation, notes and introduction—was completed in 1915. Three years later, in 1918, the entire work was brought to a conclusion and the part on infinity thoroughly revised. When in the fall of 1927, through the liberality of Mr. Lucius N. Littauer, means were provided for the publication of the work, the manuscript was again gone over, to prepare it finally for the press. In addition, English translations were made of all the Hebrew passages quoted in the notes, and, wherever necessary, references to Aristotle were filled out with passages quoted from available English translations of his works. This, it is hoped, will open up the notes to a wider circle of readers. The work could not have been complete without good will and cooperation from many quarters. In the years 1912-14, while I was in Europe in search for manuscript material, I enjoyed the privileges of the libraries of Paris, Munich, Vienna, Parma, the Vatican, the British Museum, Jews' College, Oxford and Cambridge. The library resources and facilities of Harvard University have made it possible to correlate the special studies of Hebrew texts with the larger field of philosophic literature. In the collection of Hebrew manuscripts in Columbia University, through the kindness of Professor Richard Gottheil and the librarians, I was able to find several Hebrew manuscripts which, during the final stages of the printing of the book, it became necessary for me to consult. Mr. Adolph S. Oko, of the Hebrew Union College Library, generously supplied me with many books which I had to use constantly. Dr. Joshua Bloch, Chief of the Jewish Division of the New York Public Library, always responded to my distant requests for bibliographical data. Professor Alexander Marx, of the Jewish Theological Seminary, not only opened to me the great treasures of the library of which he is the head, but also directed my attention to rare books and manuscripts in its possession. Professor Julius

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PREFACE

Guttmann, of the Hochschule für die Wissenschaft des Judentums, Berlin, was kind enough to bring to my knowledge the existence of the Bloch manuscript of the Or Adonai, now in the possession of the Akademie für die Wissenschaft des Judentums, and to procure a photostatic copy of it for my use. For help in securing a greater degree of textual impeccability I am indebted to Professor Isaac Husik, of the University of Pennsylvania, Professor William Thomson, of Harvard, and Professor Ralph Marcus, of the Jewish Institute of Religion, who have read in proof considerable portions of the work. Dr. George Sarton, of Harvard, was kind enough to read Chapter VI of the Introduction and to reassure me when I entered on uncertain ground. Of inestimable aid in the final clarification of some of the views presented in this work was the opportunity I had for several successive years to ventilate them in the Seminar on Aristotle in which I was associated with Professor James H. Woods, and in the frequent discussions with Professor Horace M. Kallen, of the New School for Social Research, and Professor Henry M. Sheffer, of Harvard. To all these my grateful acknowledgments. And finally I wish to record my gratitude to two men under whose guidance I entered upon this work and whose encouragement has sustained me throughout its progress. In Professor David Gordon Lyon I have found an ideal exemplar of teacher and friend, through whose broad conception of the fields of Semitic learning opportunities were created for this undertaking. To the teaching and friendship of Professor George Foot Moore I shall always feel myself profoundly indebted. During my labors on this work, whenever I was confronted with a perplexing problem, I found in his wide learning and sage counsel the illumination I needed. H . A . WOLFSON

CONTENTS INTRODUCTION

CHAPTER I SOURCES, METHOD, INFLUENCE AND OPPOSITION

I. Maimonides' twenty-five propositions, 1.—Crescas' sources, 4.—Evidence of the existence of an oral interpretation of Aristotle's writings among Arabs and Jews, 7.—Examination of the alleged influence of Algazali's Tahafut al-Falasifah on the Or Adonai, 11.—The relative dates of the composition of the Or Adonai and the Bi((ul 'Inhere ha-No^erim, 16.— The Or Adonai probably not written in the order in which it now exists, 17.—The Hebrew translations of Altabrizi, 19.—Extent of Crescas' dependence on Altabrizi, 22. II. The logic of the Talmudic method of text study and its use in Jewish philosophic literature, 24.—The Or Adonai probably originated in classroom lectures, 30.—Echoes of Crescas' class-room discussions in Albo's 'Ikkarim, 30.—Opposition to Crescas on the part of the Jewish Aristotelians of the Ibn Shem-tob family, 31.—Influence on Giovanni Francesco Pico Delia Mirandola, on Spinoza, and possibly also on Bruno, 34. C H A P T E R II INFINITY, SPACE AND VACUUM

Crescas' restatement of Aristotle's arguments against infinity,38.—Main drift of Aristotle's discussion of infinity, 40.—The fallacy of arguing against an infinite from the analogy of a finite, 41.—The infinite may be either a simple or a composite body, 42.—The use of the definition of place as an argument against infinity, 43.—Aristotle's definition of place and its implications, 44.—Various views as to the place of the spheres and the universe, 45.—Crescas' criticism of Aristotle's definition of place, 46.— Crescas' definition of place, 48.—Aristotle's contention as to the incompatibility of infinity with rectilinear motion, 49.—Crescas' refutation: the possibility of an infinite number of proper places, 50.—Aristotle's contention that infinity is incompatible with circular motion on the ground that an infinite distance (1) cannot be traversed or (2) cannot be traversed in finite time; Crescas' refutation, 51.—Aristotle's denial of an incorporeal infinite magnitude on the ground of the impossibility of a vacuum, 53.— Different conceptions of a vacuum, 54.—Crescas' explanation of the sense in which a vacuum is said to be the cause of motion, 54.—Crescas' explanaXIII

XIV

CONTENTS

tion as to how motion in a vacuum would be possible, 55.—Aristotle's laws of motion, 56.—Avempaces' theory of an original time of motion, 57.— Averroes' rejection of the original time of motion, 57.—Crescas' reinstatement of the original time of motion and his denial of absolute lightness, 57.—The cause of the impenetrability of bodies, 59.—Crescas' concluding argument as to the existence of a vacuum, 60.—His conclusion as to the existence of an infinite incorporeal extension, 62.—The infinite and the indefinite: the sense in which one infinite is not greater than another and the sense in which it is, 63.—The problem of infinite number, 64.—The impossibility of an infinite number of corporeal magnitudes, 65.—Arguments for the impossibility of an infinite series of causes and effects; Crescas' refutation, 65.—The problem of the possibility of an infinite number of incorporeal beings, 67.—Crescas' conclusion as to the possibility of an infinite series of causes and effects in the downward direction if it is finite in the upward direction, 67.

C H A P T E R III MOTION

The enumeration of the categories of change and motion by Aristotle and by Arabic and Jewish philosophers, 70.—Change in time and change in no-time, 71.—The two subjects of change, the sustaining subject and the material subject, 72.—Change and motion, 74.—The three formulations of the Aristotelian definition of motion, 75.—The various classifications of motion in Aristotle and in Arabic and Jewish philosophy, 76.—Maimonides' definition of essential motion, 77.—Problem as to whether the circular motion of the spheres is voluntary or natural, 77.—Crescas' denial of proper places, of natural motion upward and of absolute lightness, 78.— Crescas' revision of the distinction between natural and violent motion, 79.—Meaning of accidental motion, 80.—-Exceptions to the principle that everything changeable is divisible, 80.—Two meanings of the expression "essential motion", 81.—No accidental and violent motion can be eternal, 81.—Crescas' qualification of the statement as to accidental motion, 82.— The accidental as the possible, 82.—The different senses in which motion may be called "one", 82.—Two meanings of the expression "continuous motion", 83.—Arguments that there is no continuity between opposite rectilinear motions; Crescas' refutation, 83.—Continuity and eternity of circular motion, 86.—The order of priority of the various categories of motion, 87.—The need of a cause for motion, 88.—The immediate cause of motion must be distinct from the object moved but not necessarily external to it, 88.—Avicenna, Averroes and Maimonides as to the cause of the natural motions of the elements, 88.—The ultimate cause of any transition from potentiality to actuality is always external, 89.—How a change in the object does not always imply a change in the agent, 90.— An efficient cause of motion is moved while producing motion, 90.—Different theories as to the cause of magnetic attraction, 90.

CONTENTS CHAPTER

XV

IV

TIME

T h e p h r a s i n g of C r e s c a s ' definition of t i m e c o m p a r e d w i t h t h a t of Aristotle's definition, 93.—-Analysis of t h e r e a s o n i n g l e a d i n g u p t o A r i s t o t l e ' s definit i o n of t i m e , 9 4 . — T h e i m p l i c a t i o n s of A r i s t o t l e ' s definition, 95.—Analysis of a n u n - A r i s t o t e l i a n definition of t i m e : d u r a t i o n , 9 6 . — C r e s c a s ' definition of t i m e a n d its implications, 97. CHAPTER

V

M A T T E R AND F O R M

T h e use of t h e t e r m " f o r c e " b y M a i m o n i d e s , 9 9 . — A r i s t o t l e ' s m e t h o d of d e d u c i n g t h e opposition of m a t t e r a n d f o r m , 9 9 . — T h e i n t r o d u c t i o n of " c o r p o r e a l f o r m " a n d its m e a n i n g a c c o r d i n g t o A v i c e n n a , Algazali a n d Averroes, 1 0 0 . — T h e n e w m e t h o d of d e d u c i n g t h e opposition of m a t t e r a n d f o r m , 1 0 1 . — T h e definition of s u b s t a n c e a n d t h e e n u m e r a t i o n of subs t a n c e s , 1 0 2 . — T h e definition of a c c i d e n t a n d t h e classification of a c c i d e n t s , 1 0 3 . — T h e o p p o s i n g views of A v i c e n n a a n d A v e r r o e s a s t o t h e composition of t h e s u b s t a n c e of t h e spheres, 103.—Crescas' elimination of t h e p u r e l y p o t e n t i a l i n e x t e n d e d p r i m e m a t t e r a n d his revision of t h e definition of form, 1 0 4 . — T h e divisibility a n d t h e indivisibility of t h e " f o r c e s " residing in a b o d y , 1 0 4 . — T h e finiteness of t h e m o t i v e force residing in a finite b o d y , 105.—Crescas' r e f u t a t i o n : distinction b e t w e e n a force infinite in i n t e n s i t y a n d a force infinite in t i m e , 106.—Crescas' n e w e x p l a n a t i o n for t h e e t e r n i t y of t h e motion of t h e spheres, 1 0 6 . — H o w universals a r e n u m b e r e d , 107.— T h e o p p o s i n g views of A v i c e n n a a n d Averroes as t o how t h e i m m a t e r i a l Intelligences a r e n u m b e r e d , 1 0 8 . — H o w t h e d i s e m b o d i e d souls a r e n u m bered, 109.—Aristotle's definition of " n e c e s s a r y " a n d "possible", 109.— A v i c e n n a ' s i n t r o d u c t i o n of t h a t which is possible per se b u t n e c e s s a r y b y its cause, 1 1 0 . — A v i c e n n a ' s idenitfication of necessity per se with causelessness, 111.—Averroes' r e t e n t i o n of Aristotle's m e a n i n g of t h e t e r m necessary, 111.—Avicenna's necessary per se as precluding a n y f o r m of composition, 111.—Difference between " p o s s i b i l i t y " a n d " p o t e n t i a l i t y " , 1 1 1 . — M a t t e r a s t h e p o t e n t i a l a n d f o r m as t h e a c t u a l , 112.—Crescas' denial of t h e p u r e p o t e n t i a l i t y of m a t t e r , 113.—A k i n d of possibility which is n o t in m a t t e r , 113.

CHAPTER

VI

F O R E S H A D O W I N G A N E W C O N C E P T I O N OF T H E U N I V E R S E .

S o m e positive t e n d e n c i e s in Crescas' criticism of Aristotle, 114.—Aristotle's failure t o explain w h a t is outside his finite universe, 115.—Crescas' infinite universe, 116.—Crescas a n d Aristotle on t h e distinction b e t w e e n place a n d space, 116.—Logical a n a l o g y between Crescas' infinite v a c u u m a n d t h e p o s t u l a t e of a universal e t h e r , 117.—Infinite n u m b e r of worlds, 117.— C r e s c a s a n d B r u n o , 1 1 8 . — H e t e r o g e n e i t y a n d d i s c o n t i n u i t y in Aristotle's

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universe, 118.—Crescas' establishment of a complete homogeneity and continuity of nature, 119.—The characteristic feature of atomism in Arabic and Jewish philosophy, 120.—Crescas as tending toward a revival of atomism, 121.—Crescas' unification of the forces of nature by bringing magnetic attraction under the general laws of natural motion, 121.— The contrast between Aristotle's and Spinoza's conceptions as to the relation of God to the universe, 122.—Crescas' stopping short of Spinoza's conception, 123.—Implications of the expression "God is the place of the world", 123.—The three stages in the history of the opposition to Aristotle as reflected in Crescas, 124.—Crescas, Newton and Galileo, 126.

EXPLANATION OF SYMBOLS

128

TEXT AND TRANSLATION OF THE TWENTY-FIVE PROPOSITIONS OF BOOK I OF THE Or Adonai

130-315

NOTES TO THE TWENTY-FIVE PROPOSITIONS OF BOOK I OF THE Or Adonai

319-700

BIBLIOGRAPHY: I. II. III.

Manuscripts and editions of the Or Adonai 703 Manuscripts and editions of works cited 706 Selected list of works, articles and other items about Crescas.. 712

INDEXES: I. II.

INDEX OF SUBJECTS AND N A M E S INDEX OF PASSAGES

A. Greek Authors B. Arabic Authors C. Jewish Authors D. European Authors III.

715

735 740 743 749

INDEX OF T E R M S :

A. Hebrew B. Arabic C. Greek D. Latin

751 756 757 759

INTRODUCTION

CHAPTER I S O U R C E S , M E T H O D , O P P O S I T I O N AND I N F L U E N C E

I THE power of generalization which is so remarkably displayed by Maimonides in all his writings, whether philosophic or Talmudic, is nowhere employed by him to greater advantage than in his introduction to the second part of the Guide of the Perplexed. Within the limited range of twenty-five propositions he contrived to summarize in compact and pithy form the main doctrines of Aristotle, which, supplemented by some from Avicenna, form the premises upon which are built his proofs for the existence, unity and incorporeality of God. Of these propositions Maimonides says t h a t "some may be verified by means of a little reflection," while "others require many arguments and propositions, all of which, however, have been established by conclusive proofs in the Physics and its commentaries and partly in the Metaphysics and its commentaries." 1 But Maimonides himself did not consider it as part of his task to reproduce those proofs, for, as he again and again declares, "in this work it is not my intention to copy the books of the philosophers." 1 T o the students of the Guide, however, the explanation and proofs of these propositions offered a wide field of research, and among the numerous commentaries which in the course of time have clustered around the Guide quite a few dealt exclusively with the propositions Four commentaries of this latter kind were written during the thirteenth and fourteenth centuries, by Altabrizi, Hillel of Verona, 1 Moreh Nebukim II, Introduction, Prop. XXV: Bjma inud Ninp no ono 1'« noma oVia n«ann naa& NVN ,nm moipni o-nBiD1? hd onoi . . . nunann "fiTBi yaun irmp no isoa onxpi vwivsi yD»n nsDa anxp ,ia pso-

• Ibid. ia O'siD ^"RN HDD p'nyn1? nrn -IDNDH rma J W .

2

CRESCAS' CRITIQUE OF ARISTOTLE

Zerahia Gracian, and Jedaiah Bedersi.3 It is to this class of literature that Crescas' treatment of the twenty-five propositions in his Or Adotiai, completed in the early years of the fifteenth century, should be assigned. There is, however, a difference between Crescas and his predecessors. None of his predecessors has acted upon Maimonides' suggestion of going directly to the works of Aristotle and his commentators for the proofs of the propositions. What the nature of Bedersi's commentary was there is no way of determining, as the work is no longer extant. Zerahiah Gracian admits that for a complete explanation of the propositions one would have to resort to the sources out of which they sprang, but evidently awed by the enormity of the labor that such a task would involve he decided to restrict himself to brief explanatory notes in which, he says, he would especially endeavor to explain the order and sequence of the propositions.' Hillel of Verona, too, realized the need of a complete and comprehensive commentary upon the propositions and expressed the hope that some day either he himself or some one else would undertake to write it, but for the present, he said, he would give only a brief discussion of certain general topics.5 Nor does the commentary of Altabrizi do more justice to the subject. Though J Friedländer, The Guide of the Perplexed, Vol. I l l , Preface, pp. xix-xxiii; Steinschneider, "Die hebräischen Commentare zum 'Führer' des Maimonides" in Festschrift zum siebzigsten Geburtstage A. Berliner's, pp. 345-363. < MS. Paris, Bibliothèque Nationale, Cod. Heb. 985: ,'JiN )a 'n« .uneon -ion niaiw nun nwan jrvnBiö niy-ra n u n s )n '3 .nimpnn i^n 'Ji'jn by nibya lrip1? ib« .rnmpon njnb VaV -pis» 'b^ .niobyxm a m i"j>D bs *i'ya vn .man .rnmpnn i^k -nro •:« p by . . . nwwn jn nwann p ibd nt'Nai ,ono p nn« ,nmanb n m p it nnV yninS -iai ona »in« 'bim . . . m s p a i » ma'-ma «b nnn« nnbiib niDipnn. » Introduction to Hillel of Verona's commentary on the Twenty-five Propositions: bs b i t e ,-innn .B'j'jy 'J® mmpnn iSn n w a a j'ao babi -|nx '3 ,»™ j n i n'ban ni'« by b'ï ,nmpn ba nsia ,'jwm ,nmpnn nneu p i t s Vn ,noxya nmpnn pbi . . . m i p s r i ß « i w a n pbni .raoo naun rpuDn ivy m b't a-in na jiva lyix -ny o'o'b 'Vimi . . . mxpai viVa'B hd npn'oa -y1"* 'nanai "|bipa 'nyat TKD -]»bj "?mi anno« ri'Van by -p'Dyr ,'jbb Vru in« oan ih *jh ik.

CH. I — S O U R C E S , METHOD, OPPOSITION & INFLUENCE

3

his discussions of the propositions are full and elaborate, they reflect only faintly the original works of Aristotle; his material is drawn mainly from the works of Arabic authors. In the first proposition, for instance, Altabrizi cites none of the arguments given by Aristotle; the three arguments he advances are taken from later sources. The statement made by Narboni in connection with the propositions may be quoted here as expressing the general attitude of all those who undertook to comment upon them. "My object has been to discuss the meaning of the Master's propositions and not to give you the proofs by which they may be demonstrated. Their proofs are to be found in the works from which the propositions are taken, and were I to reproduce them the result of my effort would be a book instead of a commentary." 6 It was left for Crescas to undertake the task from which his predecessors had steered clear and to compile a commentary on the propositions, or rather a book, as Narboni would call it, along the lines indicated by Maimonides himself. Crescas, however, did not start out to write a mere commentary. He was primarily a critic of philosophy. His main object was to show that the Aristotelian explanation of the universe as outlined by Maimonides in his propositions was false and that the proofs of the existence of God which they were supposed to establish were groundless. But not wishing to appear as if he were arguing in the absence of his opponent, he felt it was necessary for him to present Aristotle's case before trying to demolish it. He therefore divides his treatment of the propositions into two parts, the proofs and his criticism of the proofs. In the proofs, as he himself avers, he intended to do nothing but to collect the arguments he had found in various sources and to present them in orderly and logical form according to a scheme of his own design. No such statement is made by him 4

Narboni on Prop. X X V : .»VniDa onnDft1? «V ann hdnd -p'anV 'ran ojbn 'jni nun dk '3 riTB ru dtp h^i .onioipDa dvidikb nom.

4

CRESCAS* CRITIQUE OF ARISTOTLE

with regard to his criticism. But we shall see that his criticism is likewise made up of material drawn from other sources, its originality—and there is a considerable amount of originality in it—consisting merely in the use made of this material and in the particular purpose it was made to serve, for Crescas uses his sources as the poet uses his words and the artist his paints. In fact, the history of the criticism of Aristotle is inseparable from the history of the interpretation of his works. His commentators were not mere expositors. They were investigators, constantly looking for new problems, discovering difficulties, raising objections, setting up alternative hypotheses and solutions, testing them; and pitting them against each other. What was therefore meant by them primarily to be an interpretation inevitably became a criticism, albeit a friendly criticism, carried on by indulgent disciples in the spirit of a search for the true understanding of the Master who had to be justified at all costs. It was only necessary for one like Crescas to free himself from the bondage of discipleship in order to convert these special pleadings into hostile criticisms. Nowhere, however, does Crescas give a complete account of his sources. In his prefatory statement to the first book, to be sure, he speaks of "Aristotle in his works the Physics and the Metaphysics; then his commentators, such as Themistius and Alexander, and the later commentators, such as Alfarabi and Averroes; then the authors after Aristotle, such as Avicenna, Algazali and Abraham ibn Daud." 7 But this list was not intended by Crescas as a catalogue of his own sources. It is rather a statement of the main authorities who prior to Maimonides had applied philosophical reasoning to the problem of the existence of God. Within the body of the commentary itself Crescas mentions the "Ancients"* (i. e., the pre-Aristotelian philoso' See below p. 131. » O'JlDipn Prop. X , P a r t I; Prop. X V , P a r t I.

CH. I — S O U R C E S , METHOD, OPPOSITION & I N F L U E N C E

5

phers), Aristotle,' Alexander, 10 Themistius, 11 Avicenna," Algazali,13 Avempace, 14 Averroes,15 Altabrizi, 16 and Narboni. 17 Vague references are also made by him to "authors other than Aristotle," 18 "commentators of [Aristotle],"1» "the multitude of philosophises," 20 "they," 21 "one of the later,"" "one of the commentators [of the Guide],"13 and "followers [of Avicenna and Algazali]."24 He names also several books by their titles: Physics,25 Metaphysics,'6 on the Physics,21

De Caelo et Mundo,27 Averroes' commentary and the Conic Sections [of Apollonius].2»

All

these names and titles, however, give us neither a complete nor an accurate idea as to the sources actually used by Crescas in the composition of his study of the twenty-five propositions. On the one hand, the extent of Crescas' indebtedness to other authors, named or unnamed by him, is much larger than one »lBD-iN n'^y npn rmrn nDnpnn rum Prop. I, Part I (p. 134) et passim. Prop. VII, Part I.

10 11

Ibid.

" Prop. II, Part II; Prop. Ill, Part I; Prop. X, Part II. " 14

Ibid.

"ID313N, i. e., Abu Bekr Mohammed ibn Yahya ibn al-Saig ibn Badja: Prop. I, Part II, (p. 184); Prop. VII, Parts I and II. 's Prop. I, Parts I (p. 144) and II (p. 184); Prop. II, Part II; Prop. Ill, Part I; Prop. VII, Part II; Prop. X, Part II; Prop. XII, Part II. 16 Prop. I, Parts I (p. 148) and II (p. 188); Prop. Ill, Part II; Prop. IV; Prop. VII, Part II; Prop. VIII, Part II. Prop. XXIII. 17 Prop. VIII, Part II; Prop. XXIII. '» Bnannno m^in Prop. I, Part I (p. 176). " vise 'tSHBBi ibid.-, Prop. X, Part I; D'anson Prop. VII, Part I. »o D«sol7BnDn lion Prop. V. " U'wn . . . wpn Prop. IX, Part I; n s t Prop. IX, Part II. " D'n-iriNnD Prop. I, Part I (p. 170) and Part II (p. 184). " D'iiison nxp Prop. Ill, Part II. " onnnK D>:>i>Djn Prop. X, Part II. •s Prop. I, Part I (p. 134); Prop. Ill, Part II; Prop. VIII, Part I; Prop. XII, Part I. " Prop. I, Part I (p. 134); Prop. Ill, Part II. " Prop. I, Part I (p. 134); Prop. XII, Part II. 18 jminn noD^ niioa ivn jsn Prop. II, Part II. J » D'Blinn 1BD Prop. I, Part II (p. 206).

6

CRESCAS' CRITIQUE OF ARISTOTLE

would be led to believe from his own acknowledgments and, on the other hand, many of the names and titles he mentions do not at all indicate sources which he had directly consulted; they are rather names quoted by him from other works. The failure on the part of Crescas to mention his sources, which is to be observed also in other places of his work, has been noted by one of his critics.30 Still there is no question of bad faith involved in it, for in omitting to give more specific information as to his immediate sources, Crescas was simply following the accepted literary practice of his time—a practice especially in vogue in philosophic writings. The scope and contents of philosophic writings at the time of Crescas, especially those which revolved around the works of Aristotle, were limited to certain sets of problems which by constant repetition became philosophic commonplaces and a sort of stock-in-trade. The existence of a large number of philosophic treatises of compendious and encyclopedic nature in which each author tried to present a complete catalogue of opinions on any given question and all the pros and cons of any given argument resulted in stripping philosophic discussions of their individual authorship and to invest them with a kind of anonymity. Crescas no more felt the need of mentioning authorities than do we when we deal with generally accepted views found in school text-books. The information which we fail to find in Crescas himself we have been able to obtain by a close comparison of his work with the entire field of philosophic literature which was available to Crescas and with which we have reason to believe he was acquainted. By means of such a comparison we have been able to identify the immediate sources used by Crescas and to trace the history of almost every argument employed by him. His sources, on the whole, fall within his own classification of the philosophic literature prior to Maimonides, namely, Aristotle, 10

Neveh Shalom

VIII, 9, p. 144b: chdin dío ona-rn -pain ¡ó Dsnn rw om.

CH. I — S O U R C E S , METHOD, OPPOSITION & INFLUENCE

7

his various commentators, and those who expounded Aristotle in independent works. Aristotle was unknown to Crescas in the original Greek. He was also unknown to him in the Arabic translations. He was known to him only through the Hebrew translations which were made from the Arabic. It would be, however, rash to conclude on the basis of this fact that his knowledge of Aristotle was hazy and vague and inaccurate, for, contrary to the prevalent opinion among students of the history of philosophy, the translations of Aristotle both in Arabic and in Hebrew have preserved to a remarkable degree not only clear-cut analyses of the text of Aristotle's works but also the exact meaning of his terminology and forms of expression. The literalness and faithfulness with which the successive translators from one language into another performed their task, coupled with a living tradition of Aristotelian scholarship, which can be shown to have continued uninterruptedly from the days of the Lyceum through the Syriac, Arabic and Hebrew schools of philosophy, enabled Crescas to obtain a pretty accurate knowledge of Aristotle's writings. That knowledge, to be sure, was traditional and one-sided, but the tradition upon which it was based, like the various traditional interpretations of the Bible text before the rise of independent critical scholarship, was clear and definite and suffered comparatively little corruption. In the present work we have shown how often terms and expressions used even in indirect paraphrases of Aristotle reflect the original Greek.31 We have also shown how commentators, who knew no Greek, speculated as to what was the original statement in Aristotle—and often guessed right. 31 In one place we have shown, how the Hebrew word for "limit" has preserved the different shades of meaning it had acquired through its being indirectly a translation of several 3' Cf. n. 16 (p. 337) on Prop. I, Part I; n. 3 (p. 398) on Prop. I, Part II; n. 8 (p. 700) on Prop. X X V . »' Gf. n. 54 (p. 410) on Prop. I, Part II.

8

C R E S C A S ' C R I T I Q U E OF A R I S T O T L E

different Greek words.33 Crescas' knowledge of Aristotle, furthermore, was extensive. He seems to have had the works of Aristotle on the tip of his tongue, and was always ready to use them at a moment's notice. He knew his Aristotle as he knew his Bible and Talmud. With an apparent ease and freedom he draws upon him whenever he is in need of some apt expression or statement for the purpose of illustrating a point or clinching an argument. 34 He never had to hunt Diogenes-like after a needed quotation nor had he ever to pray for a windfall. The immediate source of Crescas' knowledge of Aristotle was the series of works by Averroes known as the Intermediate Commentaries as distinguished from his Long Commentaries and Epitomes. In these commentaries, the text of Aristotle, sometimes translated and sometimes paraphrased, was interspersed with Averroes' own comments and discussion. To a reader unacquainted with the text of Aristotle's own works it would often be difficult to distinguish within those Intermediate Commentaries between Aristotle's original statements and Averroes' elaborations. Crescas, however, seems to have been able to distinguish between them. In one place, for instance, he reproduces what is supposed to be Aristotle's argument against the existence of an infinite number. The argument, however, though given in the Intermediate Commentary on the Physics, is not to be found in Aristotle's Physics. Subsequently, when Crescas takes up that argument for criticism, he significantly remarks that the argument "has indeed been advanced by Averroes in his commentary on the Physics."3S This is the only time that he directly refers to the "commentary" of Averroes as the source from which he has reproduced Aristotle's arguments and it would have been entirely uncalled for unless he meant to indicate thereby that Cf. n. 84 (p. 358) on Prop. I, Part I. " Cf. notes 3 (p. 398), 79 (p. 456), 96, (p. 462) 104 (p. 464) and 126 (p. 472) on Prop. I, Part II. is Prop. II, Part II, and n. 5 (p. 477).

CH. I—SOURCES, METHOD, OPPOSITION & INFLUENCE

9

the particular argument under discussion was not found in the original work of Aristotle. We have therefore reason to conclude that Crescas had another source of knowledge of Aristotle's writings. As there were no independent Hebrew translations of Aristotle's Physics, it must have been Averroes' Long Commentary which furnished him with a direct knowledge of the genuine text of Aristotle, for in that commentary the text of Aristotle was reproduced in such a way as to be distinguishable from the commentator's explanatory remarks. The same conclusion is to be drawn also from other instances where Crescas makes use of certain phrases and expressions which are to be found only in the Long Commentary. 3 ' In a few instances direct borrowing from the Long Commentary on the Physics can be discovered, though it is possible that the borrowing was made through some intermediary source.57 As for the Epitome, which is a free and independent paraphrase of the problems dealt with in Aristotle's works, there is no positive evidence that Crescas has made use of it. jS Two Hebrew translations of the Intermediate Physics are known, one made by Zeraljiah Gracian and the other by Kalonymus ben Kalonymus. Of these, Crescas seems to have used the latter. Though Crescas frequently refers to Alexander, Themistius and Avempace in connection with the interpretation of certain passages in the Physics,** there is no evidence that he had a direct knowledge of their commentaries on the Physics which, as far as known, were never translated into Hebrew. His references to them are all taken from Averroes. On the other hand, extensive use was made by him of Gersonides' supercommentary on Averroes' Intermediate Commentary on the Physics, and Cf. notes 5, 7 and 8 (p. 541) on Prop. VII. " Cf. n. 54 (p. 437) on Prop. I, Part II. 3 * Cf. list of quotations from the Epitome of the Physics Passages". " Cf. above p. 5, notes 10, 11, 14.

in the "Index of

10

CRESCAS' CRITIQUE OF ARISTOTLE

perhaps also of his supercommentary on De Caelo, though no reference is ever made to either of them. In many places, in fact, both Aristotle and Averroes are reproduced through Gersonides, For this there is abundant evidence of a literary nature.40 On the basis of many similarities, though not on direct literary evidence, it may also be inferred that Crescas has made use of Narboni's supercommentary on the Intermediate Physics.*1 This work, too, is never mentioned by Crescas. As for the original works of Arabic authors he mentions, there is no evidence that he made use of Avicenna's writings. All the references to Avicenna can be traced to intermediary sources. Of Averroes' original works, Crescas may have used the Hebrew text of the Sermo De Substantia Orbis, for an important point in his criticism of Aristotle is based upon a distinction made by Averroes in that work.42 However, the same distinction occurs also in the Intermediate De Caelo which we know to have been used by him.43 It is certain, however, that he has made use of Algazali's Makafid al-Falasifah (Kawwanot ha-Pilosofim), though the work is never mentioned by title and no direct quotation from it can be discerned. This work, translated into Hebrew many times44 and commented upon by Narboni and Albalag, was a popular source book of philosophic information and was used as a text book in the instruction of philosophy to the young until late in the sixteenth century.45 It must have Cf. notes 91,97,99, 100 and 103 (p. 365 f.) on Prop. I, Part I; notes 13, 16, 17 (p. 403) and 40 (p. 424) on Prop. I, Part II; n. 8 (p. 556) on Prop. VIII. M n r | TJ>n0 iD3i nnDy lnuyni «inn nsiDn na»i «nipn jwVV iDKon iniN. 60 Ibid. pp. 27-28: 1« nm n^p 'b^ 'iODn 'in1? mp nrn myon ^DV -)1? jn nnw isco lnpi^no ]3 urn p« '13131 o ' s d i ^ ' d h n b n ibd3 iDni3N '1313 )"y 13N11DITI3N '13T run iiBD '«iDn 'in rwyv 'inN® 'jn 3ii>nt on1? v D'ts®^ 0JJH1 miiD1?. Cf. Graetz, Geschichte der Juden, Vol. VIII, Note 2. Or Adonai III, viii, 2: n'3n |3ini> nji3»i a'tt>bv ni«o vbtn i1?« ruti» N'ne> nny. This is the correct reading according to the Munich, Paris, Vienna and New 42

18

CRESCAS' CRITIQUE OF A R I S T O T L E

ters in Book IV bear the unmistakable internal evidence of having been written originally as a sort of preliminary studies to problems dealt with in earlier parts of the work. Thus the discussion as to "whether there is only one world or whether there are many worlds at the same time" in IV, 2, seems to have been written as precursory to the same problem dealt with at the end of Prop. I, Part II, and similarly the discussion as to "whether the celestial spheres are animate and intelligent beings" in IV, 3, seems to have been written as precursory to the same problem discussed in Prop. VI. In both these instances, the problems are treated in greater detail and in a spirit of greater impartiality in Book IV than in the earlier parts of the work. It is thus not impossible that the problem of creation was among the first to have been taken up by Crescas and to have been written by him long before 1398. But whatever value one may attach to the conclusions of Joseph ben Shem-tob and Abravanel, there is no positive evidence of Crescas' acquaintance with the Tahafut al-Falasifah. Even if we assume his acquaintance with that work and recognize it as the source of all those arguments for which we find parallels in it, it is far from being the predominant influence upon the Or Adonai. The most that can be said is that it is one of the many works from which Crescas has borrowed certain arguments which he has incorporated in his own work. It is not impossible that his knowledge of the Tahafut, assuming that he had any knowledge of it, he obtained not from a study of the book itself but from his pupil Zerahiah Saladin who was versed in Arabic and later translated the Tahafut into Hebrew/ 4 Another class of sources of the Or Adonai are the commentaries on the Moreh. Of these the most widely used by Crescas is Altabrizi's commentary on the twenty-five propositions. York manuscripts. The editions and here corrupt readings. •« See above p. 11, n. 48.

some of the other manuscripts have

CH. I — S O U R C E S , M E T H O D , O P P O S I T I O N & I N F L U E N C E

19

The commentary of Altabrizi was originally written in Arabic. Its author was a Persian Mohammedan, who flourished probably in the thirteenth century. From a remark in his introduction it may be inferred that the author had intended to interpret the entire work of the Moreh,6s but whether he really did so or not there is no way of determining. Two Hebrew translations of this commentary are extant, one of which, done by Isaac ben Nathan of Cordova or Xativa, was published in Venice, 1574, and the other, anonymous, is found only in manuscript form. 66 The fact that this anonymous commentary is a translation of Altabrizi was first noticed by Steinschneider.' 7 There is, however, this to be added to the description of this work. While indeed it is nothing but a translation of Altabrizi, there is sufficient evidence to show that the translator, whoever he was, wished to have that fact unknown and to have his work passed off as an original composition or, at least, as a compilation made by himself out of different Arabic sources. The deliberate purpose of the translator to mislead his readers is evident at the very outset of the work. In Isaac ben Nathan's translation, Altabrizi begins with that inevitable jingle of glorifications, exaltations and elevation to the Creator, Causator, and Originator of this our universe, from which he passes to a second topic wherein he gives an account of himself and of his genealogy and concludes with a eulogy of Maimonides and his works. All these are omitted by the anonymous translator in the three out of the 6s

Cf. Altabrizi's Introduction in the Vienna manuscript of Isaac ben Nathans translation: db"tj3] una -i»n p^nn nt .'tnan^K nDnD ]a -oau« iDriD lay ion: :dbi33] iBDno 'aanpn '^tnirn o'n^Nn l a y hpd [pmn :«]du db-ij3] l a a n [in -hd D'aujn intoin1? :dbu3] ninina oienn i d on mm .lnib'jSi nuaS awra if« [O'ibdhd. My inference as to the author's intention of writing a commentary on the entire Moreh is based upon the expression una 1 ? awrn "wk ibdho. It is quite possible, however, that the clause awm 1®« refers to pbnn. 66 Six MSS. are recorded by Steinschneider in Die hebraeischen Uebersetzungen, p. 362. ' ' See Catalogus Librorum

Hebraeorum

in Bibliotheca

Bodeliana,

p. 1143.

20

CRESCAS' CRITIQUE OF ARISTOTLE

six extant manuscripts which I have examined in Paris, Vienna, and London.

But beginning with the third topic of Altabrizi's

Introduction which contains a brief description of the twentyfive propositions, the translator adds a long statement of his own, the evident purpose of which is to create the impression that his work is a compilation of various Arabic commentaries supplemented by numerous remarks of his own, which, however, he modestly says, are not differentiated by him from the unoriginal portions of the work, as his main object, he concludes, is to impart information. 68

Upon examination, however, his claim

seems to be rather exaggerated.

The commentary faithfully

follows the single work of Altabrizi with a few exceptions where the translator either omits some passage found in the original, or, acting upon a suggestion of Altabrizi himself, expands certain brief statements of the author.

The following examples

will illustrate the nature of what the translator has claimed as his own original contributions. (1) In Proposition I, after the third argument against the existence of an infinite magnitude, the translator remarks that his restatement of the arguments is the fine flour of the lengthy discussions of the numerous commentators.6®

As a matter of

fact, his text is a faithful translation of Altabrizi except for the omission of a few digressions found in the original. (2) In Proposition IV, Altabrizi has a brief illustration of the phenomenon of expansion, which is included among the subdivisions of quantitative change.

That illustration is more

sa pyen .nionpnn dhtibidi mina vpkti ,nDann '¡¡>jnd nxp nnya »non Vy now N'sn lBD'-iw ici« mn '3 .yns inara n^n mar «V a"D ainsn ,pioy iruan dj 'mo« ,anyn jw^a rvn moipnn nuaoD l'Vy 'rnoy nsm pyni ,|hd nrm Va yie^a -pi onV j onxp oj? crisp D'pbnn n1?« dvid h ' t s n1?!)' mm,

1'Vy D.i'Woi Dn'pbn -j^ no«

72 Tata in fiYsn n^iDi ,o'jn®D D'pitb3 D'SI *a l^a^an: loxyo yyunDn PITS OJDKI. " Cf. above p. 5, n. 17. ™ Cf, n. 16 (p. 492) on Prop. I l l ; notes 8 (p. 507), 9, 11 and 16 on Prop. IV; n. 8 (p. 534) on Prop. VI; notes 4 and 10 (p. 551) on Prop. VIII; n. 5 (p. 605) on Prop. X I ; n. 2 (p. 682) on Prop. X I X ; n. 5 (p. 697) on Prop. X X I V ; n. 6 (p. 700) on Prop. X X V .

22

CRESCAS' C R I T I Q U E OF ARISTOTLE

follows Altabrizi's method in expounding the proposition, it is sometimes not clear as to which of these sources he directly follows.75 Besides Altabrizi and Narboni, no other commentary on the Moreh is mentioned by Crescas, but it is not impossible that he made use of the Moreh ha-Moreh and also of Hillel of Verona's commentary on the twenty-five propositions.76 It is certain, however, that Crescas had no knowledge of Maimonides' own comments on Propositions IV, X X I I I and X X I V , contained in his letter to Samuel ibn Tibbon, for Crescas gives entirely different interpretations of those propositions.77 In addition to these works there is the entire body of philosophic Hebrew literature extant at the time of Crescas. Whether any of these Hebrew works is mentioned by him or not and whether it is directly used by him in the Or Adonai or not, we have reason to assume that he was acquainted with it and we are therefore justified in drawing upon it for the reconstruction of the historical background of his ideas. One can speak, however, with greater certainty as to Crescas' direct indebtedness to the Emunah Ramah. Not only is its author Abraham ibn Daud mentioned by him in the general list of Maimonides' philosophic predecessors,78 but one can discover in several places not merely parallels to some of Crescas' arguments but concrete literary relationships.7» Close observation of Crescas' proofs of the propositions reveals the fact that with the exception of propositions I, V I I I , X I I , X I V , X X I V , X X V , all of them start out with an opening based on Altabrizi and that even of those which do not start with such an opening all, with the exception of X X I V and X X V , contain » Cf. n. 8 (p. 534) on Prop. V I ; n. 3 (p. 540) on Prop. V I I ; n. 4 (p. 551) on Prop. VIII. ' 6 See "Index of Passages" under these names. " Cf. n. 3 (p. 502) on Prop. IV; n. 2 (p. 690) on Prop. X X I I I . " Cf. above p. 4, n. 7. " Cf. n. 73 (p. 354) on Prop. I, Part I; notes 7, 8, 9, 13, 16 (pp. 5 7 1 - 5 7 9 ) , 26 and 27 (p. 598) on Prop. X ; notes 6 and 7 (p. 670) on Prop. X V I I .

CH. I—SOURCES, METHOD, OPPOSITION & INFLUENCE

23

some elements which can be traced to Altabrizi. Then also the Hebrew text of seventeen propositions (II, III, IV, VI, VII, VIII, X I I , X I I I , XIV, X V I I , X V I I I , X I X , X X , X X I , X X I I , X X I I I , X X V ) is taken from Isaac ben Nathan's translation of Altabrizi, the text of five propositions (I, IX, X I , XV, XVI) is taken from Ibn Tibbon's translation of the Moreh, two of these (XI, XV), however, containing some phrases from Altabrizi. Propositions V and X I V read alike in both translations, and Proposition X is composed of parts taken from both translations. T h e inference to be drawn from this is t h a t Crescas has taken Isaac ben N a t h a n ' s translation of Altabrizi as the basis of his own commentary on the propositions, departing from it only when he finds it unsatisfactory or insufficient for his purpose. In most cases his departure from Altabrizi consists merely in amplifying the former's discussion by the introduction of material drawn from other sources. But sometimes he departs from Altabrizi completely and follows entirely new sources. An example of this is the first proposition, where the entire structure of the proof is independent of t h a t of Altabrizi, though within it are incorporated also the arguments of Altabrizi.

It is not im-

possible t h a t the collection of material and especially the abstracts of literature used in the composition of the work were prepared by students, for Crescas informs us t h a t in preparing the work he is to avail himself of the assistance of a selected group of associates 80 —"associates" being a polite Talmudic term applied by teachers to their advanced students.

This may explain the

inadequacy of some of these abstracts, the unevenness of their style and their occasional misplacement in the text.' 1 ,0

Cf. Or Adonai, Hakdamah, p. 2a: omryai o n a n n nDjonai, and p. 2b: ay onartn 'awn. See, for instance, notes 104 (p. 374) and 107 on Prop. I, P a r t I; n. 6 (p. 611) on Prop. X I ; n. 6 (p. 699) on Prop. X X V .

24

CRESCAS* CRITIQUE OF ARISTOTLE

II The research into the literary sources of Crescas undertaken in the present study was not a matter of mere idle play or even of intellectual curiosity. understanding of the text.

It was essentially necessary for the Crescas like all mediaeval philoso-

phers operates on the whole with conventional concepts of his time which to a large extent are foreign to our way of thinking and to understand which we must acquaint ourselves with their origin and background. But there is even something more than this in Crescas' method of literary composition.

He not only

re-echoes the ideas of his predecessors but he collocates torn bits of their texts.

The expository part of his work is a varie-

gated texture into which are woven many different strands. Mosaic in its structure, it is studded with garbled phrases and expressions torn out of their context and strung together in what would seem to be a haphazard fashion.

A t times the text is

entirely unintelligible and at times it is still worse—misleading. We read it, and think we understand it.

If we do happen to

come across some ambiguity, some abrupt transition, some change of point of view, or some unevenness of style, we are apt to attribute it to an inadequacy of expression on the part of the author and try our best, by whatever general information we may happen to possess or may be able to gather, to force some meaning upon it—and trying, we think we succeed. B u t sometimes by a stroke of good luck we may happen to stumble upon the immediate source of Crescas' utterances and at once our eyes are opened wide with surprize and astonishment, ambiguities are cleared up, certainties call for revision and what has previously seemed to us meaningless or insignificant assumes an importance undreamed of. The critical part of Crescal' works offers still greater difficulties to the modern reader on account of its adherence to what may be called the Talmudic method of text study. In this

CH. I — S O U R C E S , METHOD, OPPOSITION & I N F L U E N C E

25

method the starting point is the principle that any text that is deemed worthy of serious study must be assumed to have been written with such care and precision that every term, expression, generalization or exception is significant not so much for what it states as for what it implies. T h e contents of ideas as well as the diction and phraseology in which they are clothed are to enter into the reasoning.

This method is characteristic

of the Tannaitic interpretation of the Bible from the earliest times; the belief in the divine origin of the Bible was sufficient justification for attaching importance to its external forms of expression. The same method was followed later by the Amoraim in their interpretation of the Mishnah and by their successors in the interpretation of the Talmud, and it continued to be applied to the later forms of rabbinic literature. Serious students themselves, accustomed to a rigid form of logical reasoning and to the usage of precise forms of expression, the Talmudic trained scholars attributed the same quality of precision and exactness to any authoritative work, be it of divine origin or the product of the human mind.

Their attitude toward the written word

of any kind is like that of the jurist toward the external phrasing of statutes and laws, and perhaps also, in some respect, like that of the latest kind of historical and literary criticism which applies the method of psycho-analysis to the study of texts. This attitude toward texts had its necessary concomitant in what may again be called the Talmudic hypothetico-deductive method of text interpretation.

Confronted with a statement

on any subject, the Talmudic student will proceed to raise a series of questions before he satisfies himself of having understood its full meaning. If the statement is not clear enough, he will ask, 'What does the author intend to say here?'

If it is

too obvious, he will again ask, ' I t is too plain, why then expressly say it?' If it is a statement of fact or of a concrete instance, he will then ask, 'What underlying principle does it involve?'

If

26

CRESCAS' CRITIQUE OF ARISTOTLE

it is a broad generalization, he will want to know exactly how much it is to include; and if it is an exception to a general rule, he will want to know how much it is to exclude. He will furthermore want to know all the circumstances under which a certain statement is true, and what qualifications are permissible. Statements apparently contradictory to each other will be reconciled by the discovery of some subtle distinction, and statements apparently irrelevant to each other will be subtly analyzed into their ultimate elements and shown to contain some common underlying principle. The harmonization of apparent contradictions and the inter-linking of apparent irrelevancies are two characteristic features of the Talmudic method of text study. And similarly every other phenomenon about the text becomes a matter of investigation. Why does the author use one word rather than another? What need was there for the mentioning of a specific instance as an illustration? Do certain authorities differ or not? If they do, why do they differ? All these are legitimate questions for the Talmudic student of texts. And any attempt to answer these questions calls for ingenuity and skill, the power of analysis and association, and the ability to set up hypotheses—and all these must be bolstered up by a wealth of accurate information and the use of good judgment. No limitation is set upon any subject; problems run into one another; they become intricate and interwoven, one throwing light upon the other. And there is a logic underlying this method of reasoning. It is the very same kind of logic which underlies any sort of scientific research, and by which one is enabled to form hypotheses, to test them and to formulate general laws. The Talmudic student approaches the study of texts in the same manner as the scientist approaches the study of nature. Just as the scientist proceeds on the assumption that there is a uniformity and continuity in nature so the Talmudic student proceeds on the assumption that there is a uniformity and

CH. I — S O U R C E S , METHOD, OPPOSITION & I N F L U E N C E

27

continuity in human reasoning. Now, this method of text interpretation is sometimes derogatorily referred to as Talmudic quibbling or pilpul. In truth it is nothing but the application of the scientific method to the study of texts. A similar attitude toward texts and a similar method of interpretation was introduced by Jewish thinkers into the study of philosophy. One need only look into some of the commentaries upon Averroes, or upon Maimonides, especially the commentary of Abravanel upon the Moreh, to become convinced of the truth of this observation. It is well-nigh impossible to understand their writings and to appreciate the mode of their reasoning unless we view them from this particular angle. It is still less possible to give an accurate account of their philosophy without applying to them the same method that they applied to their predecessors. The mere paraphrasing of the obscurities of their texts is not sufficient. Still less sufficient is the impressionistic modernization of their thought. We must think out their philosophy for them in all its implications and rewrite it for them in their own terms. We must constantly ask ourselves, concerning every statement they make, what is the reason? What does it intend to let us hear? What is the authority for this statement? Does it reproduce its authority correctly or not? If not, why does it depart from its authority? What is the difference between certain statements, and can such differences be reduced to other differences, so as to discover in them a common underlying principle? We must assume that their reasoning was sound, their method of expression precise and well-chosen, and we must present them as they would have presented them had they not reasoned in symbols after the manner of their schools. In the case of Maimonides we have his own statement as to the care he exercised in the choice of terms, and in the arrangement of his problems, declaring that what he has written in his work "was not the suggestion of the

28

CRESCAS' CRITIQUE OF ARISTOTLE

moment; it is the result of deep study and great application."' 1 Similarly Crescas declares that everything in his work, though briefly stated, was carefully thought out and is based upon long research.' 5 Now this Talmudic method of reasoning is intelligible enough when it is fully expressed, when its underlying assumptions are clearly stated and every step in the argument distinctly marked out. But in the literature in which this method is followed, owing to the intimacy of the circle to which it was addressed, the arguments are often given in an abbreviated form in which the essential assumptions are entirely omitted or only alluded to, the intermediary steps suppressed or only hinted at, and what we get is merely a resultant conclusion. This abbreviated form of argumentation is characteristic of the recorded minutes of the school-room discussions which make up the text of the Talmud. It was continued in the rabbinic novellae upon the Talmud, reaching its highest point of development in the French school of the Tosafists which began to flourish in the twelfth century. Shortly after, it was introduced into the philosophic literature in the form of novellae upon standard texts, resembling the Talmudic novellae in their external literary form even to the extent of using the same conventional phrases by which questions and answers are introduced.' 4 Crescas' work belongs to that type of novellae literature, conforming to the Talmudic novellae literature in all its main characteristics, its attitude toward texts, its method of text interpretation, its abbreviated form of argumentation. Again and again Crescas declares in his Or Adonai as well as in his Bi\\ul 'Ikkere haNozerim that whatever he has to say will be expressed by him >' Moreh Nebukim,

Introduction: ]Dira

D'-iain u iVsj N1? nin lONDn '3,

n i t rn'pnoi ^ni pnpia

'' Or Adonai, Hakdamah, p. 2b: rm m'pin ^n: p'ya djdk nn. E. g., such expressions as

oni, nwpn^ ®m, etc.

CH. I — S O U R C E S , METHOD, OPPOSITION & I N F L U E N C E

29

with the utmost brevity," 5 and to this declaration of his he has lived up faithfully. But it seems that Crescas' vaunted brevity was too much even for those who had been used to that form of expression. It often bordered upon obscurity.

Joseph ben Shem-tob, the

Hebrew translator of his Bi((ul 'Ikkere ha-No^erim was in one place

compelled

to

give

a

free paraphrase

of

a

certain

passage in order to make it intelligible, justifying himself for so doing in the following declaration: "This is how the words of the Master, of blessed memory, are to be understood here. In translating them I have expanded their meaning, for his original words in this passage are all too brief and all too abstruse, so that I have not met anybody who was able to understand them. Hence, in this passage, more than in any of the other passages of his book, I have allowed myself to overstep the bounds of what is proper in a translation." 86 A student of Crescas, in a marginal note on his copy of the Or Adonai preserved at the Biblioteca Palatina at Parma, has the following characterization of his master as lecturer and writer: "When I studied under my Master I could not fathom the full meaning of his view on this subject . . . The Master, of blessed memory, was accustomed to express himself with the utmost brevity both in speaking and in writing." 87

This statement would also lead us

to believe that the Or Adonai had its origin in class-room lectures and discussions.

We know of other instances where Hebrew

philosophic works were the result of class-room lectures. It was while thus addressing himself to a group of initiated students, expecting to be interrupted with questions whenever he failed *» Cf. Prop. I, Part I, p. 178: j^bid mpa; Bitjul'Ikkere airyi o n m man« *7D, nxpm i r ^ a n n^ana rrn< rrn.

ha-Nozerim, p. 11:

u Bi((ui 'I^ere ha-Nozerim, Ch. Ill, pp. 27-28: 'im uav® >un |Einn nr by Dipoa piayi nxp uirV 'a ,DniM *npnyna - w a n 'namn .nin oipDa ^'t ain i'iond ih»o m r nta npnynn pn »may .inj'a'c See

Introduction to Book I (p. 135).

CH. V I — N E W CONCEPTION OF THE UNIVERSE

125

legal portions of the Bible, it was rather in utter disregard of such logical consistency. In one place, in fact, he argues quite to the contrary that the philosophers cannot derive any support for one of their views from certain literal expressions of the Bible, for those expressions, he says, are to be understood in a figurative sense.30 Tradition, according to him, is a guide only in matters theological; he does not employ it in deciding problems concerning the nature of things. Only once, in connection with the nature of space, does he quote Biblical and rabbinic passages in support of his view,31 and then, too, he does it rather hesitatingly and uses them only as corroborative evidence and not as a basis for his knowledge. The method employed by Crescas in his opposition to Aristotle is of a more subtle and more effective kind. He carries the battle to the enemy's own ground. Like one Bible hero of old, he tries to slay his Egyptian with a spear plucked out of his adversary's own hand. He employs reason to show up the errors of reason. And yet for himself he is not convinced of the unlimited power of reason. Reason was well enough as a tool to be used in his attempt to upset Aristotle's scientific dogmas, but he does not consider it sufficiently reliable as a means of setting up new dogmas of his own. He is thus quite willing to employ reason in order to prove, in opposition to Aristotle, that the existence of many worlds is not impossible, but he doubts the power of reason to help us in attaining any knowledge of what is beyond this world of our experience and therefore counsels us, by suggestion, to suspend judgment and keep our mind open.32 With reason thus limited in its function, Crescas sometimes calls upon empirical observation for aid. He does so toward the 30 Or Adonai IV, 3, in connection with the verse "The heavens declare the glory of God" (Ps. 19, 2) commonly taken by mediaeval Jewish philosophers as implying that the celestial spheres are animate and rational beings. J1 Prop. I, Part II (p. 199). Prop. I, Part II (p. 217).

126

C R E S C A S ' C R I T I Q U E OF A R I S T O T L E

end of his discussion of infinity.33 Again, in the discussion of magnetic attraction, in a passage the reading of which is doubtful but of which the meaning is quite clear, he says something to the effect that any rational explanation of that phenomenon is at best only hypothetical; what is certain about it is only that which is vouchsafed by observation and experience.34 But experience as a guide to knowledge was to him still a new and untried venture. While forced to turn to its aid occasionally by his own skepticism as to the validity of speculative reasoning, he knew not what use to make of it and what its far-reaching possibilities were, and unlike the two Bacons, he did not attempt to build upon it a new method of science. Every experience to him was a single experience and was to prove only a single fact. It was never to give rise to a universal law. Again, an experience to him was something given, not something that was to be produced. It never became with him an experiment. Crescas, for instance, doubted the truth of Aristotle's theory as to the existence of naturally light objects and of a natural motion upward, and thus when he observed that air goes down into a ditch without the application of any external force, he concluded that air was not naturally light and had no natural motion upward. 35 But when Newton began to doubt these Aristotelian laws of motion, while he may not have received his original inspiration from the falling of the celebrated apple, he certainly did observe and study the falling of other bodies and after long and painstaking research established the universal law of gravitation. Again, when Crescas wanted to prove that something was wrong with a certain conclusion which was supposed to follow from Aristotle's theory that heavier bodies fall faster than lighter 33

Prop. I, Part II (p. 213). « Prop. IX, Part II (p. 257). Another reading of the same passage would imply that Crescas did not consider his explanation of magnetic attraction as conclusive until it had been verified by experience. See n. 11 (p. 568). « Prop. VI (p. 239).

CH. V I — N E W CONCEPTION OF THE UNIVERSE

127

bodies, he resorted to a hypothesis of an original time of motion. 3 '

It was subtle, but it led nowhere.

But when Galileo

wanted to prove that Aristotle's theory was totally wrong, he climbed up to the top of the tower of Pisa, and let two unequal weights fall down at the same time and watched their landing. It was simple, but it led to an epoch-making discovery in the history of science. In a larger sense, we may see in Crescas' critique of Aristotle the fluctuation of the human mind at the point when it began to realize that reason, which had once helped man to understand nature, to free himself from superstition and to raise his desultory observations to some kind of unity and wholeness, had itself in the system of Aristotle gone off into the wilds of speculation and built up an artificial structure entirely divorced from nature.

A new way of returning to nature was sought, but none

was as yet to be found.

Crescas had passed the stage when man

condemned reason; he had reached the stage when man began to doubt reason, but he had not yet entered upon that stage when man learned to control reason by facts.

J« Prop. X I I , Part II (p. 271).

Cf. n. 13 (p. 403) on Prop. I, Part II.

EXPLANATION OF SYMBOLS

s—Ferrara edition, 1555. X—MS. Sulzberger, Jewish Theological Seminary. a—MS. Munich. b—MS. Jews' College. ?—MS. Paris, Bibliothèque Nationale. 1—MS. Vienna. -I—MS. Rome, Vatican. l—MS. De-Rossi, Parma. p—MS. Oxford, Bodleian. a—MS. Bloch, Berlin. N—MS. Adler, Jewish Theological Seminary. l—MS. Bamberger, Jewish Theological Seminary. ( ) = omission. [ ] = addition. ] = different reading.

T E X T AND T R A N S L A T I O N of the

Twenty-five Propositions of

Book I of the Or Adonai

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INTRODUCTION TO BOOK I OF THE first of those principles of belief designated by us as Roots, which is the source of all the other principles designated by us as Scriptural Beliefs,1 namely, the belief in the existence of God. The purport of any proposition can be made clear and the proof thereof established by the explanation of two things: 2 first, the meaning of the terms which constitute the proposition, and, second, the relation of the terms to each other, that is to say, whether the predicate is to be affirmed of the subject or whether it is to be denied. In the proposition under consideration, i. e., 'God is existent,' it need hardly be said that the subject is 'God' and the predicate is 'existent.' Furthermore, it is generally admitted, as will be shown later, 3 God willing, that God is absolutely inscrutable. It follows, therefore, that the proposition is nothing but an affirmation that the Cause or Principle of all beings is existent. The study of this principle of belief must thus be confined to the second kind of inquiry, namely, to show how we know that the predicate is to be affirmed of the subject. 4 The task before us then is to inquire whether our knowledge of the truth of this principle of belief rests upon tradition 5 alone, that is to say, upon the authority of the Scripture, or whether we may also attain to it by way of reason and speculation. Of those who discoursed in detail upon the question of God's existence from the point of view of speculative reason, the first was Aristotle in his works the Physics6 and the Metaphysics; then his commentators, such as Themistius and Alexander, and the later 7 commentators, such as Alfarabi and Averroes; then the authors after Aristotle, such as Avicenna, Algazali and Abraham ibn Daud. 8 Finally Maimonides, in his work called The Guide of the Perplexed, has made use of the main teachings of 131

132

C R E S C A S ' C R I T I Q U E OF A R I S T O T L E

oy

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INTRODUCTION TO BOOK I

133

these men,' restating them briefly in the form of propositions, out of which he constructed various proofs to establish this principle of God's existence. Furthermore, the Master has deemed it fit to add thereunto two other precious principles, namely, that God is one and that He is not a body nor a force inherent in a body.10 By reason of all this, we have selected the proofs advanced by Maimonides as the subject of our investigation, with a view to determining whether they establish the truth of these three principles in every respect11 or not, for his proofs alone are derived from the generality of the teachings of the first philosophers, and therefore nothing that has been said by others on this subject deserves consideration." Inasmuch as Maimonides' proofs are all based upon twentysix propositions which he has placed at the beginning of the second part of his work, our investigation of the subject will have to deal with the following two questions: First, whether the propositions which he has made use of in proving the principles are themselves established by demonstrative reasoning,13 for if the propositions necessary for the proof of the principles have not been established by demonstrative reasoning, the principles, too, will not have been conclusively established. Second, granting those propositions to be true and to have been established by demonstrative reasoning, whether the principles can be shown conclusively to follow therefrom. In this twofold kind of investigation we shall reason from the opinion of the affirmer.14 In accordance with this plan it seems to us proper to divide Book I into three parts. Part I. A commentary wherein the propositions are proved in accordance with the arguments employed by the philosophers in their own writings, and also a restatement of the Master's proofs [for the existence, unity and incorporeality of God], for intending as we do to subject both the propositions and the proofs to a

134

CRESCAS* CRITIQUE OF ARISTOTLE

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^ a n

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P R O P O S I T I O N I, P A R T I

135

critical examination we must first endeavor to understand them in a manner clear and thorough and free from any ambiguity, even as the Master himself would have wished them to be understood. Part II. Wherein we shall inquire into some of the propositions and also into the Master's proofs with a view to determining whether they have been conclusively demonstrated. Part III. An exposition of the same principles in accordance with the strict teachings of the Scripture and also a statement of the method by which we arrive at them. Therein the main contention of Book I will be made clear, namely, that it is impossible15 to arrive at a perfect understanding of these principles except by way of prophecy, in so far as the teachings of prophecy are directly testified of in the Scripture and indirectly corroborated in tradition, though it will also be shown that reason is not necessarily at variance wth the teachings thus arrived at.

PROPOSITION

I

PART I .

the first proposition, which reads: 1 'The existence of any infinite 2 magnitude whatsoever is impossible.' P R O O F OF

An inquiry into this proposition has been made by Aristotle in several places of his works, in the Physics, De Caelo et Mundo, and the Metaphysics,3 and in support of it he has advanced arguments to show the impossibility of an incorporeal4 infinite magnitude, or the impossibility of a corporeal infinite magnitude, or the impossibility of an infinite body having either circular or rectilinear motion, or again to show, by means of a general proof, 5 the impossibility of any actually infinite body. In correspondence to these four classes of arguments, we have divided this chapter into four sections.6

136

CRESCAS' CRITIQUE OF ARISTOTLE

jitwnn p a n .rv^jn "?ya 'n^a ^ - q j ^-ria niN'xo m y » n HN'aa n'n'» dn .npiVno ]"3yn a^o' t ò idn . p nsinn n m d n i .npi"?nn V a p o ' n ^ a i n npibnn "?3po "?na3n nrn V m n n'^sn "?ya 'n"?3 Nin»a -inw' nV mn .npiVnn Vnpn n'n Nin» nNioai n ^ a n 'n1?^ N'n» m i p u no«'» nVn p d « ca^D' «Vi .npibnn ^ripo n'n'» p d n i n » 3 .yo»3 'n1?^ . • ? 3 » m » 3 3 3 .O'bnnsn D'osyn p oxy 1« "?n33 noD n'n'»o VapD i3'N «in» non Vnasn» no"? ,"?-i33 oxy n'n'» "71331 .npi^nn "?3po min nasi .npi^nn .p^nno ir«» i n p^nno Nin» n o N 3 » d n taVo' nV» myi n'n'» 3"in .o'p^nn nonna t yjD'tB^D' 11 .»nxjJin'n'»] ""^»•syin'n']-""n'n'ifa .»"i J):D' n'aa [pi]i6 .mapiiu^D ^gm pVnm3 a'Ti-1»381 nonnoi-1«3?'-1'1"1* .» D'Nin: [DHEHJ22 .» • iTn'0 DM [OH ìTrPf - « 0 » JJJD' [Q^D' 18

PROPOSITION I, PART I

137

T H E FIRST CLASS OF ARGUMENTS

Proof for the impossibility of an incorporeal infinite magnitude. Aristotle has framed the argument in the following manner:' There is no escape from the disjunctive proposition 8 t h a t this incorporeal magnitude is either divisible or indivisible. Now, if it were indivisible, it could not be described as infinite, except in the sense in which a point is said to be infinite or color inaudible. It must, therefore, be divisible. If so, however, it must inevitably be either an incorporeal quantity or one of the incorporeal substances, as, for instance, soul and intellect. But to say that it is an incorporeal substance is impossible, for the incorporeal qua incorporeal is not subject to division, whereas the infinite is now assumed to be capable of division.® Again, that incorporeal substance would inevitably have to be either divisible or indivisible. If it be divisible, since it is also incorporeal, simple and homoeomerous, it would follow that the definition of any of its parts would be identical with t h a t of the whole, and since the whole is now assumed to be infinite, any part thereof would likewise have to be infinite. But it is of the utmost absurdity t h a t the whole and a part of the whole should be alike [in infinity]. And if it is indivisible, which, indeed, as an incorporeal, it must be, we can no longer call it infinite except as a point is said to be infinite. 10 Hence, by the process of elimination, the infinite must be a quantity. But then, it must inevitably be either a quantity subsisting in a subject or an incorporeal quantity. 1 1 It cannot be an incorporeal quantity, for number and magnitude, of which two infinity is predicated, are never themselves separable from sensible objects. And if the infinite were a quantity subsisting in a subject, it would have to be inseparable from corporeal objects, for since quantity itself is inseparable and finitude and infinity are accidents whose subject is quantity, like all other accidents, finitude and infinity could not exist apart from their subject."

138

CRESCAS' CRITIQUE

OF

ARISTOTLE

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.nyiann n a D n i p m n ' n dm . p « i n ' l a i n n n p » n i x a nam T V V . r r ^ a n IN ^ y i s

"73« . n ^ a n 1« ^ y i s n ' n ' » a " i i v

no 1 ? , - m i a a D-np 1 ? - p a a n n i p a n n n a v n nam . o n i p n - i n i D "pyism n m x m n a i n n o m , n y a - i N D n a m niaDt? n«anntî> . n n m t ó i nyiann n a i n n i p m rW no Na1 xb UDDIP no yao ib n'n' NV» IN VVNE» no yna IN UDDW no JIDD lV IN 8

.P (DD) D rro» [nD- 121 " 11 '^ 0 uran [raimo

.DYATI II^N IXD N"?N niyi:nn «ji^n

.1 N'NF [RRRRO -» IN

.1 nob> « i n nan , n a

m p i a i k d d « i n ® n o 1 ? ! / y a t a n l o i p o 1 ? "?isup n y p n n

nmm nnm

- n a n a y y u n o n m r t p n " i m n a n , n y u n n ^ u p "?y n j i n vnb> . » m a n a m ® n o i s n torn . n n a o n nnDtf Kim , n i » n p n w ,"?npDn ^ n on

"?y

v m

' jt? n n s i a n

ik . y i o n ^l^n Kin . o ' y y u n o a m m ^ m

, - v n D m v m m prn -inv y ' J D n

T i t o - ^ u p n

prn n n v , n y u n n n

-|l'n:n'*3pTHD3'H™n(pDK4 .»• TIB' [jiyurv 9 q»i3

' tt>'

[i3i2

,nr n i o i

-ib>n y r i D o n m m

.in:m[n'm3

p

.i'3")[p2

nimnDn .omit? in .^apon -]WDjn)i

.» trao: [NXDII 7

nfN^i p®« - T m-ona) - •> yyuno [yyun's

.'"'nrn'iu

V a p 1 ? [ ' j n p 6 $ » - » D (Kin) - p runourm) 10

.p raw» 14

.«nn 1 ? - *•> * nan trio - 1 vhsdhd «yasn i m s o n - •>

PROPOSITION I, PART I

143

the consequent can be established by sense perception; and as for the cogency of the connection between the consequent and the antecedent, it may be shown in this way. Motion is either natural or violent. Natural motion must differ in direction, and this is possible only through a difference in the nature of the places from which and toward which it tends.16 Since the vacuum admits of no difference in the nature of its parts, there can of course be no natural motion in it. And as violent motion is so called only with reference to natural motion, which is prior to it in nature,' 7 for an object set in motion by some external force is said to be moving by violence only because it moves away from the place toward which it has a natural tendency,' 8 it follows that by proving natural motion to be impossible in a vacuum violent motion becomes likewise impossible. Furthermore, if there existed violent motion in a vacuum, the motum would have to come to rest as soon as the motor which had set it in motion was removed. In the case of a shooting arrow," for instance, it is only because the air on account of its lightness is endowed with the capacity of retaining this impelling force [imparted by the motor] that the arrow, having once been set in motion by its impellent, namely, the string, [will continue in its motion], even though the string has come to rest, for the air will continue to propel it until it comes to its natural locality.30 But as it is clear that the vacuum has no capacity of retaining the impelling force of motion, an object moving in it would necessarily have to come to rest as soon as it has parted from the motor. But this is contrary to sense perception. The second and third arguments31 are based upon two propositions. 3 '

First, the swiftness and slowness of moving objects

are due to the difference in the motive force33 or in the receptacle34 or in both, that is to say,35 the stronger the motive force the greater the velocity; likewise, the stronger the receptacle, i. e., the medium in which the motion takes place—as, for instance,

144

CRESCAS* CRITIQUE OF ARISTOTLE

. T n o i n i ' i d DJ n ' n ' - D ' D H D h a p n p r n m v « i n » h w o - ] - n "?y .yaon nan

y j n n nan Diva n y u n n

yaaneo ^ u p n na

n y i a n n Dn'ty ,'3Pni

^ a p n n a D n o i n n n t * yxiDDntpa

"?upn n a m ya»n na

y^aon n a o - i a i n o D m a i n n n «

-IBD3 i K a n n - i a a i . D ' s ^ n n n D ' y n o o n i D ' y ^ o n t t o , " ? n p n n a inaine -into . - l a m o n Dn'n n n ' p V

-|-n DT^pixV

nmD'n

^apon -ixd -man n s i o n v i d . p x y n n n N u o a mo-ipnn .yaon i x d

nn«m

a " m v ,n:£D3 m p n n n ' n d n . p n n D b a p o n - i x d -ibw o x ,-ipty « i n ]or n " ? m n y i a n m ,]or n V u a y y u i v n •man'

D-np"?

-jpoan

nipa-rnn

nam . o n p n

yyianont?

idid

a"nrr

nan . n i p - m T i t o , y i T ^ - m , n n « y s o o m « y y i a n n ìan'ana « i n n ? a n n « m n n ' n o n n a D P 'D1?

-iNanntp i o a ^ a p o n

T i t t n o n ' a « i n nra n n ' N n i n i T n n n Dn'i .naitptnn n o n p n a D ^ a p o n 'arca i « u a p

on a"in

T'iJin

N i n i . r r a a a -iNanntt» i o a

,nipnn

"?ya v i V a n b n n ^ a n ^ y a n o r n a n o n ' » n o V ,-ipG> « i n i

. p r n"?ira r n p n a n y u n n n ' n n t ?

p^nn'ty n " n n ' i . p ^ n n o ^ - m n n v n 1 ? , p r n h r a ' m a a

nyian

. u nyiann p^nna p r n ,i3dd i ^ v i t » « n e i o n n a i n a n t n n s i o n t y ,-ittn p « njrann nam 10

> nn«UDn 7 0

(«ini) 15

.3 man) 2

p m t h d -inv - »

."[5?iT] y'3DDi2

Kinunmn

-id«i - = òy> 1 .»pi-"^»

145

PROPOSITION I, PART I

air which has a stronger receptive power 36 than w a t e r — t h e more rapid the motion. Second, the ratio of two motions is equal to the ratio of the powers of their respective motive forces, when the medium is the same, or to the ratio of the receptive powers [of their respective media], when the motive force is the same; or to the compound ratio of the powers of their respective motive forces and receptivities, when both motive force and medium are different—the rule for manipulating compound ratios having already been explained in Euclid's Elements.31

W i t h these two

propositions assumed as self-evident, he has framed one argument with respect to the receptacle and another with respect to the motive force. A s to the one with respect to the receptacle, it runs as follows. 38 If a v a c u u m exists, an object moving in it will have to move in no-time. B u t motion in no-time is inconceivable. Hence it leads to a conclusion which denies the antecedent.

T h e connection of

the consequent with the antecedent m a y be explained b y assuming an object moved b y the same m o t o r — a certain m a g n i t u d e — both in air and in a v a c u u m . Since according to the first proposition a difference in the velocity would have to arise in consequence of the difference in its respective receptacles, and according to the second proposition the ratio between its respective velocities would be equal to the ratio between the air and the vacuum, and as it is furthermore clear that the ratio between

these

two receptacles would be equal to the ratio between a

finite

and an infinite, 39 it would thus follow that motion in a vacuum would take place in no-time. 40

B u t that is impossible, for

no magnitude can be conceived as being moved in no-time, since every magnitude must be divisible, and the time of its motion must consequently be divisible along with its motion. 41 Averroes has remarked here that the force of this argument is like that of the argument b y which it is sought to prove

146

CRESCAS* CRITIQUE OF ARISTOTLE

yyian'tp 3"in'tí> .'a^vn n'^sn ^3 'n^a yao n3 n'n dnb> .pr n'jm iaoo yyianon mpm n'n on .p nno yaon nso

nsion oaoNi

niKUD nnvn ay ,namon nonpnn nnp® 3"nn' ,K2£oa hin D'B^nno .D'yao 'atpo .o'yyiano 'atp ían'ans nn .noxys -vno-ini' nnxntc nacían nonpnno 3"nn' nam ;nipi3 ,yrr ,mpB> no 'bí? ,mp-i3 yyiano "733 inuo «intf 'sh patyno .nyiann ^nnn

yaon ^l^nnty 3"nn' run ,nny3 yyian't?

unoNo 3"nn' nrn nptpm .nacían nonpnn 'b1? nptt> Kim .Nxoa mpnne> 3 " n n o n'n .«xoa m p n n n'n dn

d«b> ,yaoa Kirr

. p n n o ' y ' 3 -1 n n s i o n

a t f ) 3 o c a Dasn "?3Ni

x j t f 5 3 o p a D33n n n t y s N

nipnnts» tVv .^mn i'nn obnyn D33t'p ntPBK n'n 'B"? .p nian' amp"? -|it>oan mpsnnn 3vn nam .«soa .D'^nsa o'pm ntf"?ti>n niK'xo pi -i3i ir« mpnn nwsD® DHpo ün3

D'otyj oaw no1? ,p dk nan ;Dct>an p o'tDPBio

D33'tí>3

ooipo lTO'tP

Dn3

ICBN ' N nan , 1 3 1 3

D'KltM

dm nan .pn n 3 i n 3 i^veo npitP3 -wn o'on wyw 103 ,Dtt>an nan ,'nts>BN Kin oto .mpnn 'pm3 otfan 'pm 1D333133 p Dtpj D33n3 n«T ntpt* niyaonn '3 nn .ntfB« 01033 dim Dasn "?y3 tói ,ntoo "?y3 mvn -txd n^i ,Dxy invn nxo laa'N diwq W>7

ntonn i'nKan'[3"nn'6 ,

,

,

-.i'rrn [n n-P[piTni«'7'aT(i 7 0[p]

.«»iNVrn-«p,'5HDn-"'¡T¡V[n'm .í^aau

[Kin] DW3320 .'n'n »»«in »Dm[n:ni6

.-''»run [n'n 11

djd'p a^iy - d w

PROPOSITION I, PART I

147

t h a t if there existed a corporeal infinite moving force, the object set in motion by it would have to move in no-time. 42 T h e argument with respect to the motive force runs as follows: 43 If a vacuum existed, it would lead to the falsity of the first proposition, despite its being self-evident. For suppose two objects in a vacuum were moved by two unequal motors, differing from each other by a given magnitude. According to the first proposition the velocity of one of those moving objects would have to be greater than that of the other. But an object moving in a vacuum, as has been shown before, would have to perform its motion in an instant. It would thus follow t h a t though the motors differed, the velocity of the motion would not differ. This, however, is impossible according to the first proposition. And this impossibility will of necessity arise once we admit the existence of a vacuum. T h e fourth argument runs as follows: 44 If a vacuum existed, it would follow t h a t one body could enter into another. But the interpénétration of bodies is impossible, for, were it not so, the world could enter into a grain of mustard seed.4S Hence it follows t h a t a vacuum does not exist. The cogency of the connection between the consequent and the antecedent may be explained as follows: The existence of a vacuum means nothing but the existence of three abstract dimensions, divested of body. Since those dimensions are not bodies, nor accidents inherent in a subject, 4 4 they could not leave their place if another body were entered into them, as would happen, for instance, in the case of a trough full of water, if a stone were thrown into it. Hence the dimensions of the body would have to be considered as penetrating the dimensions of the vacuum. But if t h a t were possible, the penetration of one body into another would likewise have to be possible, for the interpénétration of bodies is considered impossible not because of their being substances or of their being endowed with color and other qualities, but rather

148

CRESCAS' CRITIQUE OF ARISTOTLE

otpj oaan dk , p dx mn .nwbwn v p r n -T^D K1?« mn .Vían nptf Nim .ntPBN d»j3 Dt^a .i1? n n n

D^iyn -pn

djdh nxoj

.'-iipsn D ' p m a mpm

fN

p a»

na -rsa oipo

a w n -icpnd my nynn nr prn mm

D ' p n m p m îa-iDX' p

dni

,na mi' n t ^ p o ' p m b'ya

Ninp

nv^an a'pninty myi .rr^ori viba"? nn , D ' p m no»

^-nvp

u

-ie>sn

.p^nn»

vi^a Nine? noa «rr^anm

."7-133 p n n niK'so m y w n p

a"nrr .ir^an Nintp

'nVa Vmj m ^ s o niyjon - i w a a v"?y -]dd

mD'n Nim

.|itî>tnn )'Dn Nim ,nrn nsion poa |na -ipn Nim .n'^an Vya 'n'ja

niN'so niywn n w a a nsio nnan 1 ?« n o my

"?ya Ti^a ip umn -lawa» nn . n i p a i n nsio Kim .rvVan "?ya u"?nnm . n ^ a n Vya 'n^a ip r ^ y upam ,-rn« "txd rrbon ip mmp a"nrv .rvban "?ya «in ntt>N ipn nspa nn« nmpjo Hint? ,"iptf Nim .n ,( 7an *7ya 'n^a ipo

rr^an "?ya 'n^a

. n ^ a n "?ya Ti^ao "7m n ,( ?an "?ya 'n^a i w yimn id a"in [a'Tirr m l^nnm n'bon Vj?ai3 * wan Vn < nan d .•> n"a in"aa (i'«w yi-rn id)->=pi'yrr [yiTn qD)i6 .-> Vnin'aip 14-15 .» tor®

149

PROPOSITION I, PART I

because of the three dimensions which they possess.

If it be,

therefore, maintained, t h a t these dimensions, [i. e., a vacuum], can be penetrated by a corporeal object, all other corporeal objects would likewise have to be penetrable by one another. But this is an impossible falsehood. 47 Hence a vacuum does not exist either within the world or outside thereof. 48 He has further strengthened his view [by two additional arguments]. 49

(1) If a body requires a place for its existence, it

is only because of the three dimensions in which it is posited. [Now, if incorporeal dimensions or a vacuum existed], these dimensions, too, would require dimensions, and so on to infinity. 50 (2) Then, again, dimensions are the limits of bodies, and a limit, in so far as it [is a limit], is indivisible. It is therefore inseparable from the object of which it is a limit. Hence the existence of an incorporeal extension is impossible. 51 This is the premise upon which he depended in trying to prove the impossibility of an infinite magnitude, and this is what he intended to prove by this class of arguments, namely, the first class. Another argument to prove the impossibility of an infinite magnitude has been advanced by Altabrizi, namely, the argument of application. Si

Suppose we have a line infinite only in one

direction. To this line we apply an infinite line [which is likewise infinite only in one direction], having the finite end of the second line fall on some point near the finite end of the first line.13

It

would then follow t h a t one infinite, [i. e., the first line], would be greater than another, 5 4 [i. e., the second line]. But this is impossible, for it is well known that one infinite cannot be greater than another.

150

CRESCAS' CRITIQUE OF ARISTOTLE

. n ' ^ a n ^>ya ' n b o ' » » a "7-na d i k ' x d m y a o n V y a ' n ^ a "7113 n i N ' x o n v n ^ l a "73

. p nsion -hdi nto» n

n'^an p

i w a a

nN'aa

n"?'nn ^ n n n nam

.yaoa .'-no 1 ? i n n ' n ' » » a , " ? y i B a n ' " ? a n

* i ' p ' » h d V a i ,o'nt3ti> 1 « n n N n t a » l a * i ' p '

"7ya otya "?a p

d n nan ¡ n ' ^ a n

^ya

«in

n 3 n

nm

d n nan . n ' b o n "?ya o » a "?a n v n i b - i N a n n n » « a i

]ai

.D»an p

^ya wn® ^ y s a

o'ntatp .nnana

i"?~rav n1? o n » 'B 1 ? . n ' ^ a n "?ya 'ip ^ a i

• ? a » 'b 1 ? , r n a n a n ' b o n

D t w

no»

n s D o a 11? - i N a n n

, - n s a o n i air o n " ? y s a t i b d "?ai . ^ y s a t i b d « i n " ? y s a - i b d d . n ^ a n "?ya i b d d ^ a p •?-na n i N ' x o y a o n n t o a

c y a o

o n nan

o ' n s i D n y a -1 n v t d

my

. n ^ a n "?ya ' n ^ a ' D » a "?ya ' n ^ a » » i d d

o»a n'n on

.p

n n D

j i p r t h

nsion

m a n a n ' n , n ' n ' » -|'Ni . a a m o i n d i » b m a n a » i n nan . n ' ^ a n yaon

-iNann»

m «

,"?niaa n ' " ? a n ^ y a

'n"?a

vnniD'o

-mN n'n dni

. y D » n o p » N n a n ' b o n "?ya ' n ^ a n m D '

^yai

Nin»

»»idd

m N

,"?-naa

n'"?an

no"? . n n i D ' n

-in» t d b d i

,n'inn

n"?i . o n ' n i a ' N n v y x n t o

Tonn

"?ya 'n"?a n n « n

n'n o n »

[no — ^ (run) ° nin [run 5 wr\

. p n n o

' 3

p

p'Vya

n'n

. p

n n o

nsion

' w

"?ya

b w n

no1?

,-inuo

nr

• n a n (V«oti>ni I ' O ' m n n « m

.poa

n'Van

'Vya

nsion moipon ,n'Van

moipontp

o ' i s m ntanm n V y o n Dm

.o'Vano

. n ' V a n ' V y a v n nV onip no1? , a " i n o « i n ,my'E>a n ' V a n .^poxna

«Vn

^ V m o

nao

nVi

.a'Vano ,oipoa Vya

tt>mo D t f j V a

ooipnon

own

n'n

aVmo

nVyo

o"yaon

on

. p

mn'ti> a " n n '

fNaa

a n a m

n n o

mn

' y a m

n a m

*i'p' o i p o n p ,nnNn

,n'B"Vti>m ,n'ya-im nra

imr

Dsy

Vy

. u o o p V n U ' n i V n a 3 Nintp , n ' J B > m .oipon

VyaV

D'otiuntp , n ' t i > ' o n m irn'oy

naw

«in

.nuo p

[anen-DB

nn«in

.» (L^TTID HDD ^ 1 ) 1 3 ."(Min)2o

.n'Van

Nini

Vya n o

. o i p o iV

Nm-WN

,ptPN-in

oiponty

13001 n V y o iVn

oipom

m o n p n tpon

.ipny

DB: ». c r a i "731 ' DBJ 'JS [Qiwn 8

p i l l a i vn'CT

. m a p - i n i ^ o DDipDni6

,-mvon

monpnn

mnipon vrrw [mDipnrro 10 vni2

mtf

umto

.nnana n'Van

.oosya n m i a o

nV

nsion

« i p m n t » n o V , i o x y a n N i a o -]tt>03n m p a n n n a v n n a m n r a , * i ' p o n « i n D i p a n a i N a r i ' -]'N o V i n i

'Vya

nN-n

,*i'pon n'Vann

dni

vi^aa

.attua * i ' p o n n ' V a n n Nin m p o n t p -iNanne> - i n «

omVnani»

nam

, n V 7 p i"? n ' n

" ? y a Dtpjn m m t p a " i m n a n , - n y n p a i p o a n ' V a n ' " ? y a •Vini

noa

n'n on

.n'?an I ' m , D i p o a t p m o d p s "?a n ' n o n

onti>

n

oipoa n'n , n n a a

.ri'Van

. - " noa

uoo vVni

mponp Dipon

.-"»win [nan 1 pi •>">•>*

.» n"3 [l^J I'D >=P"» ttl'^Ml

.i^nipainnn-i'mn

»avn)-p°nini7

153

PROPOSITION I, PART I

of the elements were infinite, it would be infinite in all its dimensions, for, being a simple substance, all its dimensions would have to be equal, and so there would be no room left for the other elements. The second argument runs as follows: 65

Every tangible body

must have either weight or lightness. Consequently, if the infinite had weight, it would have to be in the lower region and separated from the upper, 66 and if it had lightness it would have to be in the upper region and separated from the lower. impossible in an

But all this is

infinite. 67

The third argument runs as follows: Since 68 every sensible body is in a place,6® and since places are finite in both kind and magnitude, 70 it follows that every body must be finite, for place has been shown to be the limit that surrounds a body. 71 T h a t places are finite in kind is evident, for their differences are limited in number, namely, above and below, before and behind, right and left.

T h a t they must also be finite in magnitude follows as a

logical conclusion, for if they were not finite, there would be no absolute up and no absolute down, but only relative.

B u t we

observe that the natural places are limited. 73 The fourth

argument runs as follows:73 Since every sensible

body is in place, and place is the surrounding limit, it follows that the body which occupies place must 74 be finite. The cogency of the connection of the consequent is self-evident, for that which is surrounded must of necessity be

finite.

But how can it be

proved that place is that which surrounds? laid down five self-evident

propositions: 75

T o do this he has

First, that place sur-

rounds the object of which it is the place. Second, that place is separated [from its occupant] and is not a part thereof. that first

place, 76

Third,

i. e., proper place, is equal to its occupant.

Fourth, that place has the distinction of up and down.

Fifth,

that the elements are at rest in their respective places and toward those places they tend to return. These are the propositions which

154

CRESCAS* C R I T I Q U E OF A R I S T O T L E

m a n a

DipDn

n^ann

. p

n n o

, p ? n n » '«an œpn nwy n y

d«i . ' ^ v n n dni , n n x n

N-ip'

ami

,Tpnn n s n

-ma

rv'jann

irai

-iNair

.«l'pon

"]'« oVini

,-inud

«in

n ^ a n n

ton

n'n'P

mixn

.n'^an

«in

.ir^on

ne«

pnnn

. n t p ^ n n n n « n'n* m a n a p

pki

.ni^Vn .ni^nni .nœWno

~rn«

D r » i ,-ia-in n i o x y n

nnxntp

u w

.«l'pon

n n

trvtbvno

umn

no«ni

dm

.rvj^n

.«vpDn i r b o n

.D'-ipts» ,(

ibd-ini

'jtt> i : d d

îa^nri'

.ni^nn ,DD^ya

u w

dh»

'd1?

nonpnn «b»

. î n ^ a j r n ^ r n 1 ? n , ( ? a n «intf no1? noNDntf ,nra

n«T

dni

a"in'

dn «in

djdn

,ud» D^naa

ION'

j'a

.«rpon n ^ a n n

'^rnm

d n a riD«nn

on .nya-mo -m« wn®

nv'jan

^ v n m nmxn m b

.mpon

*)pion n'1?an

- i K a w -mtpj n r r onoiy

œprn

n n

? y a ' n ^ a - i r r D ' a n n i o i p o m x y a - m a n na-r1? n ' n ' P ,iitp&an

.mpoa

o i p o n r r r v t i n D ' y y u n o n i o i p o n v n ' t p ,'3ti>m

l'a t v «

pnnn

,o^ya mpoa n n

n ' n nfcw n n o ^ n

. - i d i n p n a ' s a ?nr a " v r t «

iu'kis

.« min 1 inDKnns

,-ikud] -iDKan» » iDKDn [iDKDn»i2 i n t » - ' n ' n ® m ' n ' » 14

otwntp i o a o

nn

.i 1 ? n i ® p n n a i n v n 1 ? . m p n a v p ^ n o n n » "?a

n n w - » (K1?) - » n v m [mSVn4

» {tòis i3®"nn® na»,,n,f - » 19 . > = [ e m - p ° mpnniMs .» nn .n'^aio ,yxo«n in y x o « n p « ' n m e n nyunni , n ' a i 3 D n o "?y3 ' n ^ s "?-m i « 3 3 n ' n d « i , y x o « n 3 ' 3 D « ' n

n'auoni

. y x o « ] « 3 3 n ' n ' «"? o w n ' p ^ n ] ' 3

«"? •?« nn ,n?o n'ryo1? nr m .ta^nioa ntaoi n"?yo

]«33

«

bo mpott> no«'tt>

n'n'

«"? , p

m n n

n'^an

-ioi«1? v « i

n'n

o«tp

¡n'bon

n"?yon •?« ono ,D'yyiino nyan«n nniD'n n « u unm> 'b1?] ntaon

n^yon "?« onoi .amnios neon i?« anoi ,amnion

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PROPOSITION I, PART I

159

If an infinite body existed, it would inevitably have to be either of similar" or of dissimilar parts. [In the first case], if it were of similar parts, it could not have [rectilinear] motion; for according to the second self-evident proposition, the place of the part and the whole is [generically] one, and furthermore the proper place must be equal to its occupant; consequently in whatever part of the [infinite] place of the whole any part of the body finds itself, it will always be in its proper place, and no object can have [rectilinear] motion while in its proper place.' 6 [In the second case], if it were of dissimilar parts, those parts would have to be either finite or infinite in number.' 7 If they were finite in number, one of them would have to be infinite in magnitude, and, as in the preceding case, would be incapable of motion.' 8 If they were infinite in number, the kinds of places would have to be infinite in number," in accordance with the first self-evident proposition. But 100 the kinds of places must be limited, for the existence of natural places is derived from the existence of rectilinear and circular motion, and rectilinear motion is from or toward the centre and circular motion is around the centre"'; but there would be no centre if the sum of the parts of the body formed an infinite magnitude. 102 It cannot be said that the places of the elements are one above the other and so on to infinity; for if that were the case, there would be no absolute up and down." 3 [But104 we observe that the four elements are moved, one absolutely upward, another absolutely downward, and of the remaining two, one relatively upward and the other relatively downward. We also observe that absolute lowness is limited; consequently its contrary, absolute height, must likewise be limited, inasmuch as contraries are those things which are most distant from each other.105] Thus it has been shown that in either case the existence of an infinite bodv would exclude the possibility of rectilinear motion.

160

CRESCAS' CRITIQUE OF ARISTOTLE

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P R O P O S I T I O N I, P A R T I

But rectilinear motion is a matter of sense perception.

161 Hence

an infinite body does not exist. T h e second argument runs as follows: 106 If an infinite body existed, infinite weight or lightness would likewise exist. But infinite weight and infinite lightness are impossible. Hence an infinite body does not exist. The connection of the consequent with the antecedent in this syllogism may be made clear as follows: (For 107 we observe t h a t the four elements are moved, one absolutely upward, another absolutely downward, and of the remaining two, one relatively upward and the other relatively downward. We also observe t h a t absolute lowness is limited, consequently its contrary, absolute height, must likewise be limited, inasmuch as contraries are those things which are most distant from each other. 10 ') We say it must follow t h a t if an infinite body existed, infinite weight would also exist, for if the infinite body could not have infinite weight, then its weight would have to be finite. Let us then assume a finite part taken from t h a t infinite body."" T h e weight of this finite part would of course be less than t h a t of the infinite. Let us then increase the magnitude of the finite part until its weight equals t h a t of the infinite, since the weight of that infinite is now assumed to be finite. It is also evident t h a t the finite part could be continually increased until its weight became even greater than the first finite weight of the infinite body. But all this is absolutely impossible, namely, that the weight of only a finite part of the body should be as great as that of the infinite whole of the same body, nay, even greater than it. Hence the connection of the consequent with the antecedent in this syllogism, namely, t h a t if an infinite body existed, infinite weight and lightness would likewise have to exist. As for the proposition which denies the consequent, namely, t h a t infinite weight or infinite lightness cannot exist, it will become evident after we have laid down three propositions. First, an object of greater weight, in the course of its natural motion,

162

CUESCAS' CRITIQUE OF ARISTOTLE

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PROPOSITION I, PART I

163

will traverse a given distance in shorter time than would be required by an object of lesser weight moving over the very same distance. Second, that the ratio between the [shorter] time and the [longer] time is equal to the ratio between the [smaller] weight and the [greater] weight. Third, every motion is in time.110 Having laid down the propositions, let us now suppose two weights, one infinite and the other finite, to be moving over the same given distance. It would follow that the ratio of the time required by the infinite to that required by the finite would be equal to the ratio of the weight of the finite to that of the infinite. But infinity has no ratio to finitude except as a point to a line and as an instant to time. It would consequently follow that the infinite weight would traverse a long and a short distance without any difference in time, that is to say, in an instant. 111 Even if we were to allow in the case of the infinite weight a certain fraction of time, some finite weight might still be assumed whose ratio to the former finite weight would be equal to the ratio between the time of the infinite weight and that of the former finite weight. The time of this new finite weight would then be equal to the time of the infinite weight. Furthermore, by increasing the new finite weight it would follow that that finite weight would perform its motion in shorter time than the infinite weight. But all this is most absurd. And these absurdities have arisen from our assumption that an infinite weight existed. Having thus shown the impossibility of an infinite weight, we have thereby also shown that there can be no infinite body among the simple bodies. In the case of composite bodies,112 however, the impossibility of an infinite body can be demonstrated by a disjunctive syllogism. An infinite compound body would inevitably have to be composed of elements which were infinite in one of these three respects: magnitude, number, or form. They could not be infinite in magnitude, for it has already been shown that the magnitude of simple bodies cannot be infinite. Nor could they be infinite in

164

CRESCAS* CRITIQUE OF ARISTOTLE

itiWDnns» n x o ' a , n s D o a r v ^ a n ' V y a ' n ^ a onvn 1 ?

- w b « p i

on® n n « ,iyaon n a a n n p . r r ^ a n "?ya ' n ^ a m y p oVia i v r . m i x a n ' V a n ^ y a ' n ^ a vn'tf ntps« n«na iana«it> m y i

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.p n n e

nsion

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nan

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P R O P O S I T I O N I, P A R T I

165

number, for being contiguous" 3 to each other and one in form, their aggregate would make [a continuous, simple], infinite magnitude, which has been shown to be impossible. Finally, they could not be infinite in form, for were they to be so, they would require an infinite number of places. Moreover, we observe t h a t the motions are finite."4 I t is thus clear t h a t an infinite body, whether simple or compound, has no existence, and all these are indeed arguments from motion [proper]." 5 T h e third argument runs as follows:" 6 If an infinite body existed, it could neither act nor suffer action. But every sensible body must either act or suffer action. Hence a conclusion which denies the antecedent, that is to say, an infinite body does not exist. By acting and suffering action we mean here an action or passion that is [completely realized] in time." 7 T h a t every sensible body must either act or suffer action may be made clear by induction. Every sensible body either only acts, as, e. g., the celestial bodies, or both acts and suffers action, as, e. g., the elements and the composite bodies. T h a t unlike these, an infinite body could neither act nor suffer action will be shown after we have laid down three self-evident propositions. First, two equal objects are affected by the action of one and the same agent in equal time, and a smaller object will be affected by the same agent in shorter time. Second, when two unequal agents affect two objects [in equal time], the ratio between the two objects is equal to the ratio between their respective agents." 8 Third, every agent must complete its action in finite t i m e . " ' These propositions having been laid down, it becomes clear t h a t an infinite could neither act nor suffer action, for it can be shown t h a t a finite could not impart action to an infinite, nor an infinite to a finite, nor, finally, one infinite to another. T h a t no finite could impart action to an infinite is evident, for were t h a t possible, let a finite act upon the infinite in some given

166

CRESCAS* C R I T I Q U E O F A R I S T O T L E

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PROPOSITION I, PART I

167

time, and let again another finite act upon a finite object in some other given time. The time in the latter case would, of course, be shorter than that in the former. Let us now increase the finite object so that its time would be equal to the given time of the infinite object. This, according to the second proposition, could be done. It will hence follow that an infinite body would be affected by a finite agent in the same time as would be required by a finite body to be affected by a finite agent. This is contrary to truth. Furthermore," 0 if the finite object were still further increased, the result would be that an infinite would be affected by a finite in less time than a finite by a finite. But this is very absurd. It can likewise be proved that an infinite agent could not impart action to a finite object, for if it could, let the infinite act upon a finite in a certain given time and let again a finite act upon another finite in some greater time than the former. Let us now increase the finite agent so that it would complete its action in a time equal to that of the infinite agent. This, according to the second proposition, could be done. The result would be that a finite would impart action to another finite in the same time as would be required by an infinite acting upon a finite—contrary to what has been assumed. Furthermore," 1 if the finite [agent] were still further increased, the result would be that it would perform its action in less time than the infinite agent. This is very absurd. Finally, it can similarly be proved that an infinite could not impart action to another infinite, for if it could, let an infinite act upon another infinite in some given time, and let again a finite part of the infinite object be acted upon by the infinite agent in some other given time. The second given time would, of course, be less than the former. Let us now increase the finite object until it would receive the action in the same time as the infinite object. This, on the strength of the second proposition, could be done. The result would be that an infinite and a finite would be

1 6 8

C R E S C A S '

C R I T I Q U E

OF

A R I S T O T L E

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PROPOSITION I, PART I

169

affected by the same agent in equal time. This is contrary to what has been assumed.

Furthermore, if the [finite] object were still

further increased, the result would be that an infinite object would be affected by an infinite agent in less time than a finite object by the same infinite agent. 1 " This is very absurd. Having thus demonstrated that an infinite could neither act nor suffer action, we must consequently conclude that an infinite has no existence, and this indeed has been proved from the impossibility of [rectilinear] motion [in an infinite], for change is a species of motion, and, furthermore, it is analogous to rectilinear motion, inasmuch as they both take place between opposites." 3 It is in view of this consideration that we have included this argument among those derived from the incompatibility of rectilinear motion with the existence of an infinite." 4 As to circular motion, he has framed six arguments to show that it would be impossible in an infinite body." s The first argument runs as follows:" 6 If an infinite, spherical body moving in a circle existed, it would follow that one of its radii" 7 , assumed to revolve on the centre, on reaching the position of another radius, assumed to be at rest, would have to coincide with the latter." 8 But this is impossible. Hence an infinite spherical body could not have circular motion. The connection of the consequent with the antecedent is self-evident, for the lines extending from the centre of a sphere to its circumference are all equal. As for the proposition which denies the consequent, its validity can be demonstrated as follows: It is well-known that the distance between any two lines emerging from the centre to the circumference increases in proportion to the elongation of those lines." 9 Since in the case under consideration the lines would be infinite,130 the distance between them would likewise have to be infinite. As it is obvious, however, that no moving object can traverse an infinite distance' 31 , it must follow that the revolving radius could never coincide with the fixed radius. But we have

170

CRESCAS' CRITIQUE OF ARISTOTLE

u r v n o « s ' n r n n p o n v - m i a o K i m . i a p a n l n u m n n a a i .nan .yyuno im« '¡sna p a n ' - p m :-IDKBO , n r n n s i o n ptritp m i l e n m .ranonD D'nxv o'ip

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t a i o n o •ip k ' x i j k o , i a - i t t > s K n ' n , a i a D a

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Ti'ra

CRITIQUE OF

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,3'an

PROPOSITION I, PART I

177

body around a centre, and if it had a centre it would also have extremities. But an infinite has no extremities. Hence it could not have circular motion. It must, therefore, have rectilinear motion. But if so, it would need two places, both of infinite magnitude, one to account for natural motion and to serve as a terminus ad quern and the other to account for violent motion and to serve as a terminus a quo. Now, since these places are to be two in number, they must be finite in size, for two infinites cannot exist together. But they were assumed to be infinite. Hence it must be concluded that an infinite body could not have rectilinear motion. Moreover, place cannot be infinite, since it must be bounded, for it has been shown concerning it that it is the surrounding limit. The second argument is as follows:1®0 If an infinite body existed, it would have either to move itself or to be moved by something not itself. If it were to move itself, it would then be an animate being endowed with sense perception. But a body endowed with sense perception must have perceptible objects outside itself to surround it,161 and anything of such a description must be finite. If it is moved by something external to itself, the motive agent would likewise have to be an infinite body. Thus there would be two infinites. This is impossible, for since the sum of the two will be greater than either one of them, it would follow that one infinite would be greater than another. Besides, if the infinite were moved by something external to itself, there would also follow the possibility of an infinite number of movers and things moved each infinite in magnitude.1'1 He has further strengthened this class of arguments by the application of the reasoning contained in the arguments already mentioned.163 Such then are the arguments with regard to this problem which are to be found in the works of Aristotle and of other authors as well as in the works of Aristotle's commentators, but lacking in

178

CRESCAS' CRITIQUE OF ARISTOTLE

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P R O P O S I T I O N I, PART II

179

orderly arrangement they tend merely to bewilder the reader in what is one of those topics164 that easily lend themselves to misunderstanding. 165 In view of this, we have recast these arguments in their logical form,' 66 restating them in exceeding brief language, strengthening some of them with points not mentioned by any of those authors, our main object being to have all their arguments well arranged and classified, in order to be able afterwards to distinguish truth from error and to detect the loci of the fallacy—and this without regard for anything but the truth. This is what we intended to accomplish in this chapter.

PART I I .

we shall inquire into the arguments which he has framed in support of the first proposition with a view to determining whether they establish the truth thereof in every respect. We shall divide this chapter into four Speculations, corresponding to the four classes of arguments which have been set forth in the corresponding chapter of Part I. WHEREIN

T H E F I R S T SPECULATION

Examination of the argument which he has framed to prove the impossibility of an incorporeal infinite magnitude. We say that the argument is fallacious and a begging of the question. For he who assumes the existence of an incorporeal infinite magnitude likewise affirms the existence of an incorporeal quantity. By the same token, it does not follow that the definition of the infinite would have to be applicable to all its parts, just as such reasoning does notfollow in the case of a mathematical line. Nor would there have to be any composition in it except of its own parts. 1 The argument, however, as has already been pointed out in Part I, is obviously based upon the negation of a vacuum, for if

180 Y W

CRESCAS' CRITIQUE OF IÓ

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nob .iniN'XD 3"in'

NN

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PROPOSITION I, PART II

183

as has been stated, it was never considered by them as a cause except in an accidental sense. It would not be impossible, therefore, for the [sublunar] elements, though interspersed with a vacuum, 7 still to possess an affinity 8 to their respective natural places, nor [would it be impossible for the vacuum to possess within itself] a distinction of parts, one having the nature of a terminus a quo and the other of a terminus ad quern, this distinction to be determined by the proximity of the vacuum® to the circumference or the centre, or by its remoteness therefrom. 10 Hence, with the assumption of a vacuum, neither natural nor violent motion would be impossible. Much less does this argument prove the impossibility of a vacuum outside the world,11 for even if there existed outside the world a vacuum in which there were no distinction of terminus a quo and terminus ad quem, it would not be impossible for a spherical body [existing in it] to have circular motion." This is self-evident. As for the second and third arguments, they are based upon two propositions, one of which is false, namely, the one which states that the ratio of one motion to another is equal to the ratio of their respective receptacles, when these latter are unlike. For since every motion by its very essence involves time in its process, it will follow that even by eliminating the receptacle there will still remain an original time of motion,13 required by the nature of motion itself,14 varying only according to the power of the motive force. It is only true, therefore, to say that the ratio of the retardation of one original motion to that of another is equal to the ratio between their respective receptacles, as, e. g., the ratio of the diminution of the natural speed of a person when he is fatigued to the diminution in the natural speed of the same person when he is more fatigued is equal to the ratio between the two states of fatigue, in which case, if the fatigue were to be eliminated, there would still remain an original speed. Averroes, to

184

C R E S C A S ' CRITIQUE OF ARISTOTLE

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n t o n n

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.o^iyn

'ton

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nan , n y i a n n n i t r a t o s

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nam

mniNn1? nn , n y u n n n i K ' s o s

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p N

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m y a o n - 1 N 3 1 ? 3tpntp ' a

. v ^ n p no1?

"ItPBtW

nan

myi yao'

tt 1 ?

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,3UD3

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.ioipo

n n s n

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1 3 3 13« * 1X313« P 3 3 1 3 N - » » ' J i a p n e p 1 1 3 « [ 7 1 1 3 ] pDDH 1

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P R O P O S I T I O N I, P A R T II

185

be sure, attempted to answer this objection, which in part 1 5 had already been anticipated by Avempace, but his answer rather answers to the description: 'Manv words t h a t increase vanity'. 1 6 Among the later thinkers there is one 17 who proposed to prove the impossibility of a vacuum by maintaining that the medium is a necessary condition in the existence of motion, 18 and this because the medium has in its nature something akin to a terminus ad quern.19 But this is an assertion which has never been demonstrated and never will be, for it may be claimed, on the contrary, t h a t the movable bodies have weight and lightness by nature, and have no need for media. 20 Or, it may also be said that all the movable bodies have a certain amount of weight, differing only secundum minus et majus." Accordingly, those bodies which move upward are so moved only by reason of the pressure exerted upon them by bodies of heavier weight," as, e. g., air, when compressed in water, will tend to rise on account of the pressure of the weight of the water, which, being heavier, will seek the below. T h a t this is so will appear from the fact that when we make a hollow in the earth, even as far as the centre, it will immediately fill up with water or air, though, [it must be admitted], whether this is due to the impossibility of a vacuum within the world or to the weight of the air has not so far been demonstrated and never will be.23 Furthermore, even if we were to admit that the medium is a necessary condition in the existence of motion, it is still not impossible for a vacuum to exist outside the world 24 , and in it for a spherical body to move with circular motion; for all these arguments show only the impossibility of rectilinear motion in a body assumed to be in a vacuum, whereas a spherical body may have motion in a vacuum without changing its place. 25 This is very evident. As for the fourth argument, it is based upon the assumption t h a t the impenetrability of bodies is due exclusively to their

186

CRESCAS* C R I T I Q U E O F A R I S T O T L E

"inud

nptp Nim

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myjnnn

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oni

,-ioin

k1? m i , o i p o n n t a '

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n'n

nxo

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nan , m p o

n W

v p m o

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.»[on] V a N - 1 ^ 1 ' k 1 ™ [^at«-'D'tiPDian

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P R O P O S I T I O N I, P A R T II

187

tridimensionality. But this, according to those who believe in a vacuum, is obviously not true, for according to them, the impenetrability of bodies is due not to dimensions existing apart from matter, but rather to dimensions in so far as they are possessed of matter. 26 Matter alone, to be sure, could not account for impenetrability, for were it not for its dimensionality, matter alone would not occupy place, but neither would the dimensions alone occupy a place were it not for their materiality. This being the case, one could not argue, [as does Aristotle], that the dimensions would require an infinite number of places. The fact of the matter is, while neither of the reasons mentioned is sufficient when taken separately, that is to say, neither of them by itself is sufficient to render the penetrability of bodies impossible, they are sufficient when taken together, 37 that is to say, in view of the fact that material dimensions occupy place, it is impossible for bodies to enter into one another. 38 Hence it does not follow that the dimensions even when they are immaterial, las in his argument], would require a place for their existence. This is very evident. As for the statement by which he reinforced his view, namely, that dimensions are the limits of bodies, this, too, will not be admitted by him who affirms the existence of an incorporeal interval.3» It is thus a begging of the question. It has thus been shown that in all he has said there is nothing which merits attention as an argument to disprove the existence of an incorporeal interval. This is what we intended to do to his proof. Furthermore, it would seem that the existence of an incorporeal interval is implied even in the view of those who deny the possibility of an infinite body. For according to their view there can be no body outside the world, and if there is no body, there is no plenum, and if there is no plenum, would that I knewJ° what should prevent that which is outside the world from being capable of receiving corporeal dimensions. But incorporeal dimensions

188

CRESCAS* CRITIQUE OF ARISTOTLE

Dipon m a x i .atw *pm b i p b 'nsn aipon ar'jy D'^ina ,otP3^ mtpn 'N3sn «in OÌM^? 'noan Dipani; nKTtp na1? .'usn .DB»n mrca iDipoa -ifcU3tt> IDD ,De>3n HT-IB' -IB>N .n"ino '^ik h i » ,iD2£jn jno3 ir« "?-n3 h i ® -i*ann nr^i - i j w o «ini , p p in b n i u m « ' naa losya '«ism iòoru i ò i ,-i'iKn p p n n n n y p 'bo nann ibw .udd p"?nn -lywn «ini , p p in

u -idn' Ninn ' w s n nan

p»3 t i «

«in njn ,pannDn noon m i v"?y pnx'tp nn«i .un» p b m . p r 133'«» i n « ,Wi3 n u n a onoiNn ,an-uD 's1? atw D^iy1? p n i n a i .'«3s ni3nn 1

's ?! Dtya

dni

,rigori ^yn 'n^a DB>3 niy3on:a

W 1

Vni3 ni« *» p DN n«ann ,irm NinB> n«nnnty n^s'if n"in» «ina* no"?

,'i3£3

in« p

rrbonn m«'SD y3»3 «ina;

n^o' p a« n3n ,otw Vk n^o'P -ipsk 'ki ,'i3B 1

1« 1

•7-1:13 "?ni3 niN'xo a r n a o 's ? p dn n t a n m .rv^on 'n^n ? idi .rrbon "pya 'n^a .n^sn

'n1?^ ^tw m t t ^ o m o n a n t a n n .n'n'i» -pai

.]itt>tan ]vyn u mnn1? u'tatp no inn 3 - n 3 1 « n'n db>3 «in .nipmnnn nsio i t n p new .unan 1 ?« nsion ^yn

DV»I«I

n r n niysontp nn .apri» no 3"nn' t ò » i « u o

aoxjn 'tuoni) 5 .»,i]sn[,Kisn-«nxT®nDl7)-»,u£)2 qap ito-'(«inn'iosnnn) 7 .> = myp'irTnyp-^pVna 6 .isp-i-m^o 1 'WB14 .inspiro (noDn) - » irfy;[l'Vy - « p i o pbrb a ny^ pyi»a 1 - P T-QÌÒ 19 oinnV P-ita ? irmi 'INI»] noinma .upu (run) -»['«] DM - » . » 'd ino 20 ^ mn [«in -1 ^ nipmn1 » ?1 ropa-inn 1

P R O P O S I T I O N I, P A R T II

189

mean nothing but empty place capable of receiving corporeal dimensions.31 We have advisedly used the words 'empty place' because it is evident that the true place of a body is the void, equal to the body and filled by the body, as we shall prove in its proper place,32 God willing. Thus it has been shown that an incorporeal magnitude is by its own nature not impossible; nay, its existence must inevitably be implied. Arid why should it not? when the void itself, [without any content], may be described as great and small" and may be measured by a part of itself,34 for when, for instance, you imagine a closed vessel from which the air has been cleared and into which no other air was admitted, the void within it will be described as great and small, and will be measured by a part of itself. Since the definition of a continuous quantity can thus be applied to the void, and since it is not time, it must of necessity be a magnitude. 35 We thus conclude: Since according to the view of those who maintain the impossibility of an infinite body, there is no body outside the world, there must necessarily be there a void.36 Since the void has been shown to be a magnitude, it has thus been shown that an incorporeal magnitude exists. But this incorporeal magnitude outside the world cannot have a limit, for if it had a limit it would have to terminate either at a body or at another void. That it should terminate at a body, however, is impossible. It must therefore terminate at another void, and so it will go on to infinity. It has thus been shown that on their own premises an infinite incorporeal magnitude must exist. However that may be, it has been conclusively shown that an infinite magnitude, be it a body or something incorporeal, must exist. With this we deem fit to conclude the first Speculation. As for Altabrizi's proof, which he terms the proof of application, it is obvious that his alleged conclusion does not follow. The impossibility of one infinite to be greater than another is true

190

CRESCAS' CRITIQUE OF ARISTOTLE

inn'33»3»

,-nynpn -rxo Kin r r ^ a n

K i n i1? r r ^ n

l'N» noi . n y n y n

"?3» 's1? , n n « n o

^na nnan

D«i , i n « n »

urn

.îoxys

nrVi

-i«uD nn

^yn

'n^ao

'rna

^ - n a 13 n 3 i i 3 n « i n ' x a

î p n n*n

nr^i

.lb'b'oa - n y » n

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.nyi»o

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nn«

. r r b a n ^ y s t o n » n x n o »^dij

- i d i k 1 ? ,|Dfn i " 3 j ? o n « u a « î n t f no^> , » i n n p

nr nDNrr

i r b o n "?y3 in K i n o n x n n ^ D i n o « i n p r n » ,i3"3y n r » myi

rr^an

n'n

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. i m o n p n n o i x 1 ? , n n « n n x n o r r ' j s n ^»y3 ' n b a i n v n

» n n a

nviDNn

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13 ^ n n n »

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, D ' n t o » i n n t a » 13 * p p ' o » a " ? 3 » m o w n .n^sn

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- 1

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P R O P O S I T I O N I, PART II

191

only with respect to measurability, that is to say, when we use the term greater in the sense of being greater by a certain measure, and that indeed is impossible because an infinite is immeasurable. In this sense, to be sure, the first one-side infinite line [in Altabrizi's proof] cannot be greater than the second one-side infinite line, inasmuch as neither of them is measurable in its totality. Thus indeed the former line is not greater than the latter, even though it extends beyond the latter on the side which is finite. 3 ' This is self-evident. That this is so may be demonstrated from observation, from the case of time, which according to those who believe in its eternity, must be conceived in a similar way, that is to say, it must be conceived as capable of increase on the side on which it is limited even though it is infinite on the other side.38 Furthermore, it will be shown subsequently, God willing, that this distinction will have to be accepted beyond any doubt even according to our own true belief in creation.39

T H E SECOND S P E C U L A T I O N

Examination of the arguments which he has framed to prove the impossibility of a corporeal infinite magnitude. As for the general argument with which he begins his proof, its unsoundness is obvious, for the minor premise, namely, that every body is contained by a surface or surfaces is contradicted by the opponent who affirms the existence of an infinite body.40 He is thus arguing in a circle. Furthermore, even if we agree with his conclusion as to the impossibility of a corporeal infinite magnitude, that conclusion of his must not necessarily be true with respect to magnitude in general, for dimensions, as we have already shown, are capable of existence apart from body. A s to number, we shall discuss it in a subsequent chapter,41 God willing.

192

C R E S C A S ' CRITIQUE OF ARISTOTLE

. n m m

n a i n n -TDBJ ] I1? « -I N N A N , O P A C A N O ' n s i a n D^INI

' n V a - | t y a n n i p a - m n t t n , n m a ' n V a n i a n p n a n a i n a «into n n ' n b o n n i D ' m N ' x a m j j a o n a m a i « n nanpnntt» n n .rmyta ' i w a I'K nam

yawn» ptPtna m « a n n

.nyv

u

*]'pn

.a"ina

t ò . n ' V a n '"?ya

n ' V a n "?ya ' n ^ a n ' a

,nn«n

- i k u b « í m . m y r r i n v n 1 ? n i ^ n n n onto n a a m ^ n n n n m a n o n'n n ^ a n

'"?ya v ò a

aa-iia u m n a ,(?ya

n n i D ' n v n dkb> , r i ' 3 t p m

nrVi . » m n

mm

.ìaxya

.n'bon Vya 'n^a

aana

' n ^ a n m D ' n w s a m y j o n - i « a n ' x b n ' V a n "?ya 'n"?3

i s a d ^ i « ! . n o n n x a n o s a tppnn n v n ]a a « - m a n n

.n'bon

n ^ a n V y a v i ^ a n n i D ' n o i n « u n ^ n a a " n n ' K1?^ no 1 ? n a a t y no 1 ? , n i 3 ' K V y a n ' n '

f

imix

-WBK n a a ' a , - i * w n T D S ' t p

t o n n x n n r a i .I1? m a ' « i ' « r i m a r i V y a ' n ^ a otoa nave» -MAN .TID' an 1 ? t o n i . a ^ a a W w a

i n v n n s a , n i ' 3 ' K n "73 V a p a

D ' D i a a p a y a , a r n a D 'B 1 ? , r n a ' N V y a v i ^ a am

«xaa naai

nratp p t p "731 . n i ' a ' N n Vap 1 ? n a a m n 3 iato ' n ^ a D^iyV pin n n a

,D"a'atpn

DIM n i N ' x a n i y a a n - m a n n

nsian

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n'an [n'nj 10 n'Van b>yan [n'Van

PROPOSITION I, PART II

193

As for the physical arguments, the first is both materially and formally defective: viz., it consists of propositions which are inadmissible 41 and the connection of the consequent with the antecedent is not necessary. The proposition denying the existence of an infinite number of elements has been demonstrated in the first book of the Physics43 only by two arguments.

The first

of them is that the infinite cannot be comprehended by knowledge. But it is not necessary that principles qua principles should be known.44 This is self-evident. The second argument is that if the elements were infinite, there would be an infinite composite body. But this is what was to be proved here. If we assume, therefore, the existence of an infinite composite body, there will be no argument for the impossibility of the existence of infinite elements. It has thus been shown that the syllogism is materially defective. As for the defectiveness of its form, it does not necessarily follow, if we assume one of the elements to be infinite, that it would cause the destruction of the other elements, for that element may be conceived as being devoid of any qualities, inasmuch as it is possible to assume an infinite element without any qualities, which, on account of its being devoid of any qualities, may be the recipient of all the qualities and act as their substratum. 45

Such a body, devoid of any qualities, is to be found,

according to their own admission, in the case of the celestial bodies, 46 —a body endowed only with a capacity and predisposition for the recipiency of qualities. Still less has this argument proved the impossibility of the existence of an infinite spherical body outside the world. 47 As for the statement by which he has reinforced his contention, namely, that if an infinite existed it would have to be infinite in all its dimensions, this, too, is inconclusive. If infinity were essential to dimensions as such, there would be some ground for his conclusion; but since infinity is to be only one of the properties of

194

CRESCAS' CRITIQUE OF ARISTOTLE

n n . D ' p m n "?33 nr 3 " n r v N1? .i1? ' o x y ' n ^ a i vrtpoo a'®» .~R«D " I N U O

w o m n Q mp 1 ? « i n . m ^ p m n a i s n H I D 1

,'JTPN DJBNI

*?y3 'n"?3n o t m n o i a n D"?ini .^¡tan n n n -IB>N a m n i o n D'om

- i » « ' » m a . n i ^ p N ^ i n a i s 11? T»® n o » '

jr^sn

.1UD-1N ny-r1? •"O'DB'n u m n d « nan ,Dipnn n x o i m nn .3B>nB> i d s n o « n urv

n1?

y ' a -1 n 1 '

'"? b> n ojdni

njn , n o «

oipon

n t w n x o ] « i n impotp n o x ' ri'^an V y a ' n ^ a n

-iDi«ntp

' n ^ a Kin l r n n a j I S D I . r a i o n f p o n ntatpn « i m ' » ' o w n Dtpam ?«*? -pro . « ' n n n « B 3 Dipo i1? *ppo m p a i1?

na

.inmyp

. n ^ a n 'rya

' i i x n , n « i n nr IDD-I« n y n ' s 1 ? "73a * p p » n .•qpio

nsn 1 ? ' n o « n mpone> , n « T t p no'£>"? , i o x y 3 nDNntp N1?« IEJD-IK 3 " N - I P N o n p t p m . * p p o n N V ^ S N p a NTY« p m n

«in

- p n a -IB>K D'pmnty "?y OHDVD onts> ^n 1 ? p o y p « n y n n nr1? Dnpe>n c r a ^ n n D v n r«i , ' ^ a n p n y n 3 D ' p n y j d'D

^an

v t a m p - i i ' u s a DHDI« 1 ? o'pn-ino ,DDN u'to , ' r r a « m i . o n n . o n n a ^ i t a a n u " n r r k1? nr1?! . D ' y y u n o .NVI3) i a " n n ' cnpoa IBD-IN nnao 1 ? NAM mpo

nn . m p o a i s ^ n / v D " o , D » n D'onntp , a n n

.»(njra-i'inDNtna« s .>=n"33i»n'an(ri'VonVya'rtarM-s ncj»n nn * ne&> «in -»imnyp 10 .^ann 'WTD ,my»n'D .•> D'IM 20

.»podi«™* 'nDDin nxo] 9

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ia"nrv [lE^nir - •»' D'oun 21

PROPOSITION I, PART II

195

the infinite and unessential to it, it would not follow that all the dimensions would have to be infinite.48 This is very evident. As for the second argument, based upon the consideration of weight and lightness, it is derived from an analogy of sublunar sensible bodies. But he who affirms the existence of an infinite body conceives it to be without either weight or lightness, as is said to be the case of the celestial bodies according to the view of Aristotle himself.4' As for the third and fourth arguments, based upon place, even if we accept his definition of place, they do not sustain his alleged conclusion. For he who affirms the existence of an infinite body would maintain that the infinite has place only with reference to50 the surface of its concavity, 51 that is, the surface which surrounds the centre,53 whereas with reference to its convexity53 it is infinite and therefore has no place on that side. Why should it not be so? when the all-encompassing celestial sphere answers exactly to this description, according to Aristotle's own theory, namely, that it has no place which surrounds, but one which is surrounded.54 The truth of the matter, as it seems, is that the true place of a thing is the interval between the limits of that which surrounds.55 The impossibilities which, according to Aristotle, would have to ensue from this view,56 are beside the mark, resting as they do upon the assumption that the dimensions within a vessel full of water will be moved together with the vessel, whence indeed, were this true, the alleged possibilities would have to follow. But the assumption is a figment of the imagination and is not true. The dimensions, according to those who believe in an empty space and a vacuum, are immovable, and so none of those supposed impossibilities would follow.57 Furthermore, Aristotle's definition of place will give rise to many absurdities: First, the celestial bodies will differ with regard to place. All the [internal] spheres will have essential place, that is, the sur-

196

CRESCAS' C R I T I Q U E OF ARISTOTLE

. o x y a m p o i1? n ' n ' k 1 ? " ? a a T p o m u'N nu'jaaa axya

,*i'pon n o o n ' n x n

- i p n ntatpn ' a ^ n a j m »

T p o

mp»

i1?

no"?

-ipn . u n »

"7133

n w

1

noi ? p n V j nr m a y a

,Dxya

.mpD3 m t f « i ' p o nm

urx

«mea

1

.D'p^n ? n n r o n aipontp n n

-IPN - n a n »

. m » ' n y u n o ' y y u n o ' ? an

n ' n ' t ? p i t u " 7 1 3 3 mtt> * i ' p o u r n . ^ a n n y u n a a x y a , - m n

Dipoty n n

,B>«n n n n y p a

,ûnai

D'yyunon

. n n n ntPNa a i p n n 'p"?n b s b i v o n «vpon

TiNn i» ' y s o a n

ntatpn « i n

p"?nn m o w

many

's1? , b v a

imaD

d o d o

i n

1

.p'Dm n m y

nn1?

ob> i ? w v

-îtfN , ' y a c a n i D i p a a u'Ntp o n , ' y a c a n i o i p » a «înty d n ca^ni xV impôt? 3"niv,'yacan î m p o a «in dki

.no«

'yacan Dipa1? ^ n n '

rr'rana w m .bih

nirmnn

b

p ^ n 1 ? -ib>n ' y a c a n .nujn

. n n p o a i « n ' n D x y a ,"D'Dtî>n D'ODipaa

n o «

.ncann

-\m

ommxn 1

many

i? w

p'om

mm«nn o"D'D¡2>n

n t o N m p o n dnb> , D n o i u

pri'

D'mia

,o~ion T'ix'

«i'po

nVsp n n

.^Vaa

n s n m » n t m ,n"?yDn a n n - r ty«n t i d ' o p p

many

n'n'

-|'N " o ' n t o n

«m

•nanB'i ,*i'p»a

^ai p'oni

.ncaon

."PtmwiiBixa?

.^Vians

,':>p->i''' = ^3Nn®N3

' V D a n - ^ a p n oyntan laipaa ron® a « t ^ o : k S h 1

- » niniKn - *=p •>» * 1V [W] 12 1

nao ? - 1 6 ^ 3 3 ) 17 [^N —

-

»

,'=mia!

.'(-i'i«n|D)io

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-kpk inob] -•> e y a u n impon i r « » n«) -

.» aaipan - » niniNn - » n ' n iron 16 m ' n ' - ' » ^ P " " ^ «a ' a

"?aa

. o i p o n

"?yi

n u a

a m p

invn

ay

'a

nx-p

^naa

invn

nvriD'ai»

ma'yn

-iid'

«in»

"jina

n o «

]"jyn

m a a

]VDnn

» n p

wbwa

dtyn

l a n y n

p

.nioboy

nan

lBnno

,«i?E>3 n r n

-parr

ae>n

« ^

e m

n'nw

nsnn

noi^a

,ott>n " ? «

d«i

a»

. m a n

'uan

n'n'i

- 0 U'nia« - 1 1133 [DlpD - 1 1 ' > t 1DSJ)3 2 ' n n ' * - " 1 ^ o k t t i » ' ^ ™ ™

dutids -

3 1

' c r m - D lrnmN 5 .lap-i-i1*

.l»=M-iniN)-i»=pnjnin[-|njn--'Nl?i8

.''•IDltO-'i'D-IOtOn-IDtOII .P invn1? 1 mm 1 ?« [invn

-i«ina>

loipoo

n r - i a p i n » nn'Bi l ^ a j a i l i n n o * l^naai linrwi n r r n 7 n"3] D i p n n - » ' D n y i [i:nyn9

ana

. « i ^ ni31D [J7131D - = lDipa® [lDipOO1

.» rrn [ K i n - ^ p n ' y n w 3

1' 1 ^ 0

rnix->" nwn

[lDipD nVlJJH I'Kl] oVlJJ - • .1 inn'® D nun'» u i d t ® .» n«in Vn -idww lVto [iKinif .»laipaas»-1»3"1'311

201

PROPOSITION I, P A R T II

tively to the form and essence of a thing, as, when they say: 'It is proved from its own place;' 83 'From the place from which you come,' 84 that is to say, from the very thing itself; 'He fills his ancestors' place.' 85 You may note how in the last-quoted expression they have indirectly testified that place is identical with the void which an object occupies, thus accounting for their use of the word 'fills,' for if by 'place' in this quotation were meant 'grade,' 8 6 they would have said, 'He was in his ancestors' place,' which would mean, 'in the exalted position of his ancestors.' Accordingly, since the Blessed One is the form of the entire universe, having created, individuated and determined it, He is figuratively

called Place, as in their oft-repeated expressions,

'Blessed be the Place;' 8 7 'We cause thee to swear not in thy sense, but in our sense and in the sense of the Place;' 8 8 ' He is the Place of

the

world.' 8 '

This

last

metaphor

is

remarkably

apt,

for as the dimensions of the void permeate through those of the body and its fullness, so His glory, blessed be He, is present in all the parts of the world and the fullness thereof, as it is said, '[Holy, holy, holy is the Lord of Hosts], the whole earth is full of his glory',» 0 the meaning of which may be stated as follows: Though God is holy and separated by a threefold holiness," alluding thereby to His separation from three worlds, still the whole earth is full of His glory, which is an allusion to the element of impregnation, which is one of the elements of Glory.»3 Of the same tenor is the conclusion of the verse, 'Blessed be the glory of the Lord from His place,' that is to say, the 'Blessedness' and 'Affluence,' ascribed to God is from His place, that is, to say, from God's own essence and not from something outside Himself, and so the pronominal suffix 'His' in 'from His place' will refer to 'glory.'»3 If, however, you prefer to consider 'Glory' as an emanation, the verse will be taken according to its more literal meaning, the pronominal suffix referring to God, the meaning of the verse thus being, the 'Glory of God' is 'blessed' and is

202

CUESCAS' CRITIQUE OF ARISTOTLE

.imoxy í o i p o

-iDi 1 ? n x n

,at?n

t i n ' s IB»« m n

oipoo

ystnoi

í p i t s 1 ? -jntflX'

.Dwn

n m o

'Br^pn

'n

n a a e »

,uoo ^ x w

wvn1?

orv^ ' í m i'n o

.'awn ] v y n nr u

rvban

*yna

, i n m o

mnn1? ía'totp n o

nn

]vyn

»n^a y y i a n o m y a o n a

^ d b

D'nDioa

nTpna

. i r a u D 1« m » '

nyian

" ? y a ' n ^ a n Dtpa1? n i t y n y i a n m y a o n a -nDB> o ' n t n o n nan ^ ' " r a n .'pbn

"?ya ' n ^ a arnn

dw

n'n'

n w s o

myaon nto a " r n

nr 1 ?! . ^ m o n

o p a n "?y

abo

.m'jan

o"iaa

. o r n o ' n ^ a m ^ a n ^ y a ' n ^ a dim n i K ' x o m y i o n y n y . d o b b s b y d d n h D'jrm 'n"?a DNxoa D n a

"mam

npnatsop .fmo

-ioitó n"?yon

-idiV

nbyab

nr o n

nro m p '

e>' , n a « n n m

"?y n o r o n

.j'oa

D'^aaiD

]itf«-in onvn

oy

neian» ,na«n

m o i p o n t ? n n .{»'«a o ^ a a i o ' n ^ a , t 3 ^ m » a n " ? y o dip

dni

Dn

.mbon

atpaa nn

moipotp

an

.nooni

'n^a^

nro

. » m a m & n a n * w n n y i a n n p n ' n d n i .bncj'a maatto n a n , m b p m n a i a n b y n o v a n , D'avnn ia"nm

->03)4

.mb'pi n a i a

t,n,i DB>n3

piaiv a » n ' » a"in'9 .maiVr^DaiS

'apn

oaoNi

"?ya m ' p a n "?ya ' n ^ a

. i i s p n i i » « iDipoo —

.>=' n'aas-s

nsion

pi nvn^2

D'nBwai6

."lIim'Dn HDl'DIl 14

catpan

.» yottno m m

n n ^ p i - m »

* D"H3 0^310

=

P R O P O S I T I O N I, PART II

203

poured forth in abundance 'from the place of God,' i.e., from His essence,94 inasmuch as it is an emanation. There is no need, therefore, for the Master's interpretation of 'His Place' to mean 'His grade,' 95 for it is an impropriety to ascribe to God any distinction of grade. This is wherewith we deem it fit to conclude this second Speculation. T H E T H I R D SPECULATION

Examination of the arguments which he has framed to prove the impossibility of an infinite body having either rectilinear or circular motion. As for the arguments which he has framed to prove the impossibility of rectilinear motion in an infinite body, whence he infers the impossibility of an infinite body, they are all based upon the analogy of a sensible body. His reasoning, therefore, proves only one particular case,96 but there still remains to be proved the impossibility of an infinite body which is imperceptible by the senses. Moreover, upon further inquiry we shall find that his arguments are not conclusive in any respect, even with regard to a sensible body. In the case of the first argument, based upon whereness, his opponent may contend that the places toward which the elements tend, though limited in kind, that is, the above and the below, are still unlimited individually, that is to say, those places exist one above the other ad infinitum,97 The fact that there would be no absolute above will give rise to no impossibility, even though rectilinear motion is perceptible by the senses.' 8 As for the second argument, based upon weight and lightness, even if we admit the infinite body to be endowed with weight and lightness, the consequences he saw in his imagination will not

204

C R E S C A S ' C R I T I Q U E OF A R I S T O T L E

-itPN ' y x a K n n K s a

dk . n n »

13 d k

.pra

3

. n ^ a n

, ,

nn'

"?ya

kVi 'n^a

n a i a 1 ? mti> p r a

nyunn

naiaa

p p

nKBai 'yxaKn

-ity«3 n n y a n ^ a n

nvn

p r a

yyuno n ^ a n

n K s a n i p n w no"? ^ í a a .nyunn

]ar ni^pi 1313 Va1?» nn nun

1

yyuna

?

oki

.nan»

.yyiarv

mVan

"?ya

naia

Vya dpi naia nvn a ^ n m

nra m p

nKsa

k"?i

1

. r n ^ a n "?ya

-i»k ,'mtpn

p m

,

ia

"?3«

n 1 7 3 Dt»a

n-ra»

m a n

Vya 'nVan naian yyurrtp a ^ m r

nr"?i .attn

avnn

,ni^ysm

by

"?ysn

i ^ tf'tf n a y r t y n ^ a n 'n^aa

in^iys

m a n n

p

mnnif

rvbwr]

iDvan

V y a v i ^ a n acu1? -ib>sk w 'iKn m m

. a m u

dki

.naia

,pr n^ira m » a i

nwa m m

p

d»

,"iaK'if

laiK^i

.nar» nuD1? 3UD3 o»:a

f]k Dna

na«n

.wk

nyun1?

,»man

,pr

m m »

nan

,"i'K3

«"71 . ^ l a a u a a

nip'

nyrnn n a s a

d j Kin nan , n u u D n

"i»k

.m'ran

n a *?aa ] ' k » i K i a a Kin

.3"ina n - w n 'n^a

a»n

nn

Vyis n,!7an 'jya 'n^an n v n a

'nbo dcj niyaan iKa1? i n n »

ww

nabw

n y u n n m a on ,^-itf p r

.»man

,3"ina

(

nam

Dm i ' t w no1?

K i n , p r a k ^ k n y u n 1 ? nttfSK w

n y u n n mi

nsian

nyunn

atwn ^y

p

ni^i

rn^an

nKsa

"?ya

ojbki

dj D"ua

Dnvn"?

yyuna

'nba

Kim ,n'Van

'pya ' n ^ a

obn

D^nu

'nba

DKsaj ,ona

n p i w a

nam .»ma

.» njron^ pi?] 12 ,ik=i KSB321

a v n n [hbb a'Tirv í ó ] 9 . ® n : ® B - i ' « i n [ran 14

.MJ-Dt I t » « 2 "IDr "TO 20

.'rnwie

.s^uns

. » ^ a p [W7P1

.¡»ap-ini? n w u runa [n:t3 o n

dni

/i*n»K7

v t a

pnion

nn

.yyuno

opjV

n'3i3Dn

o'nBiDntp

Vy3 'nVsn

."»n^snins

m"ITÍ> • i3"rw 1

. - " p i n n [»idi: - 1 d'i [ p

.» D'un' > » ne:' 9

.•> aVij?^ »jpiDi3-i4

.» nn'::i8

Vy3

> Him [Kim - * (13) -

.» n r a w » ) - * » vv - 1 ' rem 10 ."n"ji3--" l '(-n5;)i4

" t d ^ s v n n n * n dnb>

rr^on

-nDP

.n^on

.» T £ D - » p i i D'ip->=p (']»)2

n:m [«m 12

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«mi

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,-rrr i r b s n

Vitas

Vy3 'n^s

ni«'SD

HIH

^Din'»

"?y3 ' n ^ s p m o n t p ,-vtoîn n o « n

c h y ^ p n - i o n nvn"7

u

, m p i v

.13 -iidíp r r ^ s n n ¡ r r m . o ^ i y 1 ?

,0'ip

,nr

."ON13

-tobn ' k c .in"33n-t"1»

.« a'nBionwi - « (nn> ' m m [nn 17

.3 nn'

PROPOSITION I , PART II

207

In the first argument, he proves the proposition which denies the consequent [by contending] that the distance at the circumference between any two radii [of an infinite sphere] must be infinite on the ground that the distance between radii increases in proportion to the elongation of those radii, concluding from this that wherever there is an infinite elongation of the radii there must be an infinite distance between them. To this the opponent may answer that distance increases [infinitely] in the same way as number103 is said to increase [infinitely], namely, without ever ceasing to be limited. That the possibility of infinite increase is not incompatible with being actually limited may appear from the case of infinite decrease, for the examination into contraries is by one and the same science.104 It has been demonstrated in the book on Conic Sections,os that it is possible for a distance infinitely to decrease and still never completely to disappear. It is possible to assume, for instance, two lines, which, by how much farther they are extended, are brought by so much nearer to each other and still will never meet, even if they are produced'06 to infinity. If, in the case of decrease, there is 107 always a certain residual distance which does not disappear, a fortiori in the case of increase it should be possible for a distance, though infinitely increased, always to remain limited. What we have just said is wholly in accordance with the truth, for an infinite distance between lines has no existence even when the lines themselves are infinite, inasmuch as a distance must always be bounded, as will appear in the sequel, God willing. But first we shall endeavor to show that if the reasoning by which he established the minor premise which denies the consequent were true, it would follow that the distance in question would be both infinite and finite at the same time—and this even if we do not assume that the infinite is capable of motion. For, according to him, the arguments are only meant to show that an infinite body could not have circular motion, whereas were we to assume an

208

CRESCAS' CRITIQUE OF ARISTOTLE

-lKanat? -in« pe>

."jitaa u a a m p ' «"7 yyuna 'n"?a n ^ n n

^ y a ' n ^ a p m n'n't» -pro ,mp-i IN 'l^'a m a n a o^ny^ pin» u pano'ty nx ^y inn'Hts> U'^y . k s d ' 1'K

D^INT

n'^an

.Q'tntpna infirm ,D"naun D'ipn

B>ya ' n ^ a p m a n rprvtp a"nrvON

dk

NAN .~IOINB>

NO«

TTQ

iwytp a v n n n'n

DKSP

Dinan noNiv

no ' s a nan . i n ' n ' ^ a n "7yai n ' ^ a n

Dn'J'a p m a n n ' n ' » ranana o'NXi'n n'i?an '"?ya ' n ^ a D'ipa jpnnsDina

p m a n nvn1? .n'^an "?ya 'n"?a *)'pan n s a

. p i r n n'ir ir'Nai .ranana o'trcvn ü'ip 'ííp "702 nr a " n n ' nan .n'^an "?ya ' n ^ a on'3'a p m a n -IPN *]'pan nxa T ' x j newai uV -wsNtp pBD

, m i p j y n ' n y p a m a n ipn bxx mtnsi

|a Nintp na1? , r a í a n rmpa nmpj

naitinn n m p n a íp K'nn"?

a - w ip N'nn 1 ? -itpstw n u w N m r n y r n

*?ya p m a a *i'p»n nxa vn oxi , y r p m r p

a n m .mips

i t r m ' p i r n n'ir i r « a o'Nsvn D'ipn ^atp nam naai . n ^ a n n'Van "?ya n'n p a « ^ ' V a n "?ya ' n ^ a p m o *]'pan u r a ,'NA«

a v n n U'nmna a " n n ' nrn

NPTPM

.-TIT

n ' ^ a n "?ya 'n^ai

N1? ,rv^an "7ya ' n ^ a ipn nvn aytt> majn na«na> Nina» nn .D'ip 'jb> ]'a n ' ^ a n b»ya 'n"?a p m o niK'sa a " n n ' .»»Drain» - » (•«) - « i » is [«]Ni 3 3 p' prim ¡pm -»n'n® nn«i [n'n'» I'm 2 .>='D3(™n)6 .i1» n'n» [n'n'c — ^ roNnns .= ' > D'majn-» m a - " (D-nnDn>4 .o Q'ipa [D'ip -» boa nr> - •> [•«] nan 9 nvn1?! - P i'ponDs > n*aan7 ...rrnpano) 12-13 = .> ipn N'xin^ 12 .1 "> [iiron nn nxT] nn«n - * aitfmi [Di»n:i 11 - •> n'aani" n'aa 17 mn [n'n -.»(p> 16 íznnn' ni'Ka 15 .>= op .« •'ípn-H-'n^'an [':»19 lni'nis .^pi nown • 'no«n

PROPOSITION I, PART II

209

infinite body incapable of motion, he would find nothing impossible in the assumption of an infinite body. Moreover, according to what has been shown already, there must be outside the world either a plenum or a vacuum, in either of which cases there must exist an infinite distance. Or, if it does not actually exist, we may still assume its existence after the manner of the geometer who makes use of infinity in the definition of parallel lines,108 and in the other hypotheses.10® But how it could be shown, as we have suggested, that if his reasoning were correct it would result that the distance would have to be both infinite and finite at the same time, I will now explain by the following: If it were true that the distance between two infinite radii at their intersection with the circumference were infinite, on the ground that the distance between two emerging lines must increase in proportion to the elongation of those lines, that, of course, would have to be true in the case of any two radii emerging from the centre at any central angle whatsoever. Let us now imagine that, on the circumference between the radii which are infinitely distant from each other, we take a point at a certain distance from one of the radii. A line can undoubtedly be drawn from that point to the centre, for it is one of the postulates 110 that a straight line can be drawn between any two points. This line will make a certain central angle with the aforesaid radius, and at the same time the two lines will be at a finite distance from each other at the circumference. But the assumption is that any two radii, making any central angle whatsoever, would be infinitely distant from each other at the circumference. Hence the distance would be both finite and infinite at the same time. This absurdity will follow if we assume his reasoning to be true. The real truth of the matter is that even if the radius in an infinite sphere is assumed to be infinite, it need not necessarily follow that there would have to be an infinite distance between two such radii. For it is evident that whatever point we may take

210

CRESCAS' CRITIQUE OF ARISTOTLE

mttnatp - w e « irmi

, m » n jo N x v n n ' ^ s n V y 3 ' n ^ s n îpntf j u t

. n ' " ? 3 n ^ 3 D - i o m m i p a n i'3it> i p n n ' n ' n 1 ?^ , n m p a 13 *n!?3 n v n 1 ? n i p s « ' n c n p n |'3tp

n'^sn

pmontp

T « N ' n n n m p a m ,n'"?3n ' r y s 'n"?3 i p n n a ¡vrrtp n n i p a ]'3tt> n ' ^ D D ^ y n ' n " ? 3 n p m o 1 ? p i n s «irbon ^ys

d n n i N ' x o j ' N .n1? n i ^ s o

Nintt> i p 3 " i d w b o p ^ s s i

. D ' i p n 'aw

1

•?y3 ' n ^ 3 p m o tœoa n ' n i ^ n i , n ' " ? 3 n i n x p i ? ]'Ntt> 13 i n o « p m o nan . n s p n ^ i t p o « i n i , n x p 3 n ' n n ? ' i t o n ' n ,n'"?3n o w n » n ' n o t o .i1? n i N ' s o iaoo p"?n y y i a n '

o'ipn j'3 n ^ s n

"?y3 'n"?3

nan . n ^ s n "?y3 ' n ^ s K i m , y y i a n '

i^ss

"?3ti»n nan , - i v x n i d p i r n nr n ' n o n i . n ' b o n b y n i p b y «"7« .i3"na o ' i p n 'at? ]'3W p m o n n v n ,i33"ne> n r n 3vnne> y i n » ' i n t i n v n 3 " n ' , n ^ 3 n *?y3 r s n o n i d o ' K X v n n ' " ? 3 n ' ^ 3

'n"?3n

. m ^ p 3 n t o n ' n n . r r ^ s n V y 3 n r n y y i a n o s n x o ' p 3 U D n ^3 ni'ir u n n

- i p n n ' " ? 3 n " ? y 3 n n'irnty no 1 ?

u p í o ,D-ion

nvn1? , n i 3 n 3

- i s d o 3 n'"?3n ' ^ y s

nan .i 1 ?*« ò

vn

,n'"?3n b y n - i s D o n n ' m . n ' ^ s n "?y3 D i o n

nnti>

-ipn p m o n

. r n s n s n ' ^ n *7y3 p m o n n ' n ' » 3 " i n 1

- p o a n m i D u s ' ^ ? 3tt>ntt> 3i'nntt> n « 3 n n , p nr n ' n n w t o i . n o « ia'K n r n n s i 0 3 .[' b> ' o n n i n s i o n "7D3na n r 3 i - j i n n "?y o h d v o ]'35

.pop mi

' t y ^ m

> n"3an-i (lpn)-i f ' f 1

» Min»!! ?!'«»? - m D'ipn ['3»]9

mipjn [rmp34

.T '0NIP3 13 p 11 ^ .

ia5

pnmn8

'ae>n n s i o n n a m

- i

.» n"33

in«2

[V^ZI^l - P D'lp 6

j^p-mS n"33n7-a

P"n^2o nrn1?!->= (mam) 17 .>«3 d i d h d h V'JH mapi-mox» 'in ['gCDnn 22 .'»= lU'K [13'K 21 .'^«n ' í h t b

.pniD* 1

prnnn-< a ? ]'«») w n "i®«i3 .» dwh (U) - 1 U'TlV » 3TIT^ ,nij!»n 'B by ti'j»

P R O P O S I T I O N I, P A R T II

211

in the infinite radius, the line between that point and the centre will always be finite. Consequently, since the distance between two radii cannot be infinite unless it be between two points in those radii at which the radii themselves are infinite, and since there are no such points, it must, therefore, follow that there can be no infinite distance between those radii. Generally speaking, when we say of a line that it is infinite, we mean that the line has no extremity or limit, whereas an infinite distance [between infinite radii], if it existed, would have to mean the distance between the extremities of the infinite radii. But an infinite radius has no extremity. Hence there can be no infinite distance between the radii. And even though the sphere as a whole is capable of rotation, notwithstanding its being infinite, any given part of it performs its rotation on a finite axis.111 This, to be sure, is remote from the imagination, but reason compels us to assume it. 1 " You may further know that the conclusion we arrived at, namely, that the distance between two infinite radii must always be finite, leads also to the conclusion that any distance which these radii may traverse in their revolution must likewise be finite. This can be easily demonstrated. If [in the argument in question] we draw around the centre a certain number of angles, each of them being equal to the finite central angle [formed by the infinite radii], the number of these new angles will have to be finite, inasmuch as the distance around the centre is finite. Now, since the number of the angles is finite, the distance [traversed by the radii] must likewise be finite. This being the case, it is evident that the reasoning by which he tried to establish the minor premise in order to deny the consequent in this argument [i. e., the first] is unsound. This also disposes of the fifth113 argument. As for the second, third and sixth114 arguments, they are based upon the intersection of the infinite line by a revolving line,

212

CRESCAS' CRITIQUE OF ARISTOTLE

nam

. n ' b o n ' j y a ' n " ? a n l p 1 ? xb

"?a

no1?

nawm

nmpa

n ^ a n

*?ya

.nyiana

niN'so

pawn

a^mr

m y ^ a

1« m n ' n a a , a i a D a y y i a n o i p

lpn

p"?n

«V

oias'tp

myaon

naannty

nan

.yyiann

pinn

laa'N

naa

nr^i

no1?

yyiano .ncasno

.]or n ^ i t a n y i a n n n ^ n n n n x p m a n ? n n . n ^ a n "?ya

nyiana

ooantp m o w n

nam

1

nonpnn

*?y t d v d

a i m . n ' a i a o n a i o n "b ,nnxpn

p y ' 3 -1 n i n D i o n

aiaDa yyiannn n

n n y a Kin nan , n ^ a n

"?ya ' n ^ a

naion a i a o a nyiann n n a n o n'n a « o naion

"?aa

ntt>BN n a a

"?a«

,pso

,!

nn

. n a i n n ib yx

mpo

nr 1 ?

.rraiaD

.anDa

yyiannb» .naionn

n a n nnDtp D ' n s i o n " ? a a i ' « » n r o n x a n n

naa

l a n a n o n t o n n ^ a « . n ^ a n V y a ' n V a n Dtt>aa n ' a i a o n arn my n«an' naai

. n ^ a n V y a ' n ^ a n catpaa n y i a n n

a n D a y y i a r v ' x u r a n otpan n t n a u n a « » n n •?ya

'n"?a

yao'

'nx'an nan

,ia

ipn

nona

Dnanon

nyiann nines«

.tfinno nnntPBN

nt£>na n a m

tt>ont£>' n t p u a

nr^i

n'n

ON a " n n '

.n'bon ^ya w v n p

»n^an

otMntP - i n t w ,nptt>

l a o o i a p ^ D n a n , r i ? i a a Dtyann l a p ^ D n i s w a i

pi"?D a " m

? a n "?ya

.n,!?an 1a

b>ya

tt>»nts>ai

ion

.n'ban

n a a d n i , n ' ! ? a n "7ya p r a n , ! ? a n ^ y a ' n ^ a n m y i a n yyian'ts>n "?ya 'n^a1? n i K ' s a

m n dni

.n^an

'nVa1? p x ' a n

y i s ' a n y a o ' k"7b> m i a ' ^ a t p n n a n , a n n ^ y a n n a D ' d 1 ?

3"nnn»a"nn3

.•>'

-

'nn w a i n s

]i»tnn p^n . = 1 n x p - " > nr

.•>•>' n M a n s

nyion [ m i e n 7

u p V n [i:p"?D 11

d a s ) - = nt"? p s o m p a 10

- n

n"33-iapi'^|,s

17

ii&tnn p^nn - • n y w n s nrVis

.'Vann ' » i t s

['n^aVio

3UD3 -

.r^an

.»ipai .^tnitras)-»

,n-iy»n'd Vy w w

p niiona

(nro)-" 1 ^ 133113

Dunon 1 3 - " »Dn®: [WDn»' 18

.»ip4

"j»»'

^ «in

[ m u i ] njinn 9

.>•>' up^n [i3p^D-'pi">

.» m y ) - » " " » i t u n n - 1 3 1 * n"3316 .»n'aisonin'^n^vs'n^nis

.«i«3n'

PROPOSITION I, PART II

213

whether that line be assumed to be parallel115 to the infinite line at the start or not." 6 Since, however, it has been shown that there can be no first part of motion, because every object that is moved must have already been moved, it does not follow, as he claimed, that there would have to be a first point of meeting." 7 It is not inconceivable, therefore, that the infinite line [in question] should meet the other line in a finite distance" 8 with a finite motion,11'—• and this may be accounted for by the fact that the extreme beginning of motion must take place in no-time.120 As for the fourth111 argument, it is based upon the proposition which states that an infinite body moving in a circle must necessarily have a spherical figure. This, however, is untrue, for if a body is conceived to be infinite it has no extremities, and thus it has no figure."2 There would be some ground for his objection if circular motion required a spherical figure, but an object of any figure may have circular motion." 3 By conceiving, therefore, a body devoid of any boundaries, we conceive it also to be devoid of any figure, and so it does not follow that it would have to be finite. All this has shown that among all the arguments he has adduced there is nothing which proves conclusively the impossibility of circular motion in an infinite body. Quite the contrary, our discussion has made it clear that motion is possible in an infinite body. This possibility may be further demonstrated by an argument from observation. We observe that a luminous body may complete a revolution in finite time. If we assume a ray of that luminous body to be infinite, allowing ourselves to make use of such an assumption after the manner of the geometer, we may conclude that it would not be impossible for that ray, though infinitely extended, to complete its infinite motion in finite time. Though according to the view of our opponent an infinite has no

214

CRESCAS' CRITIQUE OF ARISTOTLE

"iNua nn

. r r ^ a n "?ya ' n ^ a i n v n 1 ? n n i » s « r r n dm ^ y u n n 1 ? » .ipsaa

nan . i r ^ a n "?ya ' n ^ a p x ' j n n o - u n 1 ?^ n ' n a « o "?ya ' n b a n

^nn

inyuna

-nyi

n-npj d i p t

d^o'

n o u " W t o nr"?i ( m p - n i n '"i'roa a , v i n D m v n u n a n o nsp n n ,mio y w b .'sis'jn . n o

ntonn»

' n a i ,iv^an 'jya 'n^a íp «inn

r r r o i ipa rnipj d i p t

.yynrveo

ntPN D ' n s i o a i n a " n t p n o i s n n i ^ p a n r o

h i u .pix'an

-mam

.'tp^tpn ] v y n n n

T a i n

jvyn

T t u -iNa 1 ? - h d p D ' n s i D a

otw n i N ' ^ D y a o n

m

ni'pna

.^ysa rv^an ^ya ^ l P t o n

nsion n n

^ w d Kintp no 1 ? o yyurvtp no n a n

nn

-ib>bn n a a

. o ' o n p n D'nsinn naa on

. y * » « i1? w v a i a D a n y m n n

.ntpn

nsiom

.yxo«

. D ' B ' p o y i n o D'tfrno i1? v t p

ib

i'n

a"nxv

v t a dm 3"nxv

,nnspn .iDsya

. n o w » n o a ~i«ud D i n n , u notop n « r n n o n p n n no« 1 ? atynty n o "?aa j w

,nr ^ a »

n n « t f m y t a n "7« « ' a n n i ^ n n n a w m y i a n f ' b ^ i - *TD3iriTiDJ- p i " jijiun' neto7 ' y » iy:Dnn .i^'ysoi> ntsD1? nDii3

,!

'n^a

.?

.«p•>> u n t ò n o i u .•mjj®3)20

^ (neoi

> a"in' i s p n u a"rv - 2 iwb«7 yin Kin®i2 .» nam

pina 1 ?

.'»p-"nn«)i9

nD

.i myion o'» 1 ?

na 13-n

>ejj'aTn>-»

217

PROPOSITION II

principles," 6 the implication of this proposition has led him to conclude that there are not any other worlds." 7 For having first proved to his own satisfaction that outside the world there is neither a plenum nor a vacuum, [he argued therefrom that there cannot be many worlds], and he [further] argued that if there were many worlds the elements would move from one world to another," 8 to which arguments he added many other fanciful speculations and 'words that increase vanity.'"' But since the error of his initial premise is manifest, for it has already been shown before that an infinite magnitude must exist and that outside the world there must exist an infinite plenum or vacuum, it clearly follows that the existence of many worlds is possible. Nor can it be contended that the elements would move from one world to another, for it is quite possible that each element would move within the periphery of its own sphere towards its own suitable place.130 Thus everything said in negation of the possibility of many worlds is 'vanity and a striving after wind.'131 Inasmuch as the existence of many worlds is a possibility true and unimpeachable, yet as we are unable by means of mere speculation to ascertain the true nature of what is outside this world, our sages, peace be upon them, have seen fit to warn against searching and inquiring into 'what is above and what is below, what is before and what is behind.'132 With this we deem fit to close the fourth Speculation of the first chapter. PROPOSITION

II

PART I. PROOF OF the second proposition, which reads: 'The existence of an infinite number of magnitudes is impossible, that is, if they exist together'. 1 Having shown in the first proposition that magnitudes cannot be infinite in measure, he now shows in this second proposition that they cannot be infinite in number.

218

CRESCAS' CRITIQUE OF ARISTOTLE

,naits>*nn n o n p n n

'riEnna

ya'

nonpnn

rmr m n n «

n ' n , - i r m H i a v ^ y i a s p i n - » c ^ t o i , n o m y ' t p 11? w n ' ^ n

^ y a

^ n a bsw

' r i b s o ' ^ m a *i'Di' - w t o i . b n a n n v o n y t f

. l y a o n - i t o n n ntt>N . n ' ^ n

'n^a

'atwi p t s n rrbon

d3»ni

, ' w n

i'« D'^nu niK'^ow m o w n

ny'tpn n'n'

nn

psipo ,-isdd3

b ^ n

rvatpn n o n p n s

m ' p n a

.-ipti> D 1 S D D 1 ?

,naii2>N-in n o - r p n n m o « N ' n n s r n n o n p n n - i i d ' p n m p n n noNnn

Vitoa

rn"?p3

-idik1?

n"7B>3

.rrVrm Vy3 ' n ^ i n «

-ifcon' .naitytnn

"73 - n s a m

D~rp

-isdo myaon aitm , " n s a

o n i air o n

nr j w

n1?«

i s d d

-wioi

. r m n

n'atpn n a « n n

n a m . n ' b s n "7y3 - i b d d ^ 3 p

n o n u N oa , 3 - i n n y i

"71133 i K n n n

tP't?

t s d

Kim

n«rn

.naitfton

"73 n D M t p a

dm . r v ^ n

bnna

"7y3i

V ^ s n o ' t p ' ^ t p n p n s 3 ub» .IDy D'O'SDO Kl'D

'itnis> n o i

.yoti>n - i s d 1 ? m N ' 3 3

nr3 -imyna n u n p N

, i b d d db>3 o m s D n m i 1 ? n x n , ^ 3 3 '"7y3

"?3N , m 3 n 3

rr^sn

03^)14

jcnp[mpi3

]Dr[iDDDi2

.i Y a

nn

^y3

noNnmo ,

nam

neDDntp «in n n

"73310 ^ s i

.D'^aio

idnup Dn

.»n'n[n'n'4 ,

pNI

.= D aDDlDJ!-»»D"3l=»=t« D]3l15

nan

«£>')2 .atV

219

P R O P O S I T I O N II

As for the truth of this proposition, it can be established by the arguments employed in the proof of the first proposition.

The

reasoning may be stated as follows: Every magnitude is of a certain size. Now, if to any given magnitude we add another magnitude, their combined size will be greater. Consequently, if an infinite number of magnitudes were added together, their total size would be infinite. But a magnitude of infinite size has already been shown to be impossible.2

PART II.

EXAMINATION OF the second proposition, which reads: 'The coexistence of an infinite number of magnitudes is impossible'. It is obvious that this proposition rests upon the proof of the first proposition. But inasmuch as the falsity of the first proposition has been demonstrated, this proposition, too, can be easily shown to be false. One may, however, argue that even if the first proposition cannot be conclusively established, the second may still be demonstrated independently on the ground of the impossibility of an infinite number. That number cannot be infinite may be shown by the following reasoning: Every number is either even or odd; even and odd are each limited and finite; hence every number must be finite.3 In answer to this we may refer to what has been shown above, in the third chapter of the first part, [Proposition III, Part I], namely, that this absolute negation of infinite number does not represent the view of the Master and that both Algazali and Avicenna are in agreement with him.4 The argument from odd and even has indeed been advanced by Averroes in his commentary on the Physics.s

But in refutation of

it, the following may be urged with telling effect: Actual number, i. e., things counted and numbered, is indeed limited, and every thing limited must needs be

finite.

But things which only

220

CRESCAS* C R I T I Q U E O F A R I S T O T L E

o m s D

oj'k

^>3«

nsD'tf

i« nr n ' n 1 » m m

i"7i , o n a

d h - i b j 1« n ^ j n

,!

•nsj

a s n a

y3»3 n , l ? 3 n

"1331

^ 3

n x n

'nban

,"IBDDn

f «

.tysn

1

? y 3 ' n ? ^ O ' s i r n o « ' » -itt>B« -i33tt> n n

"?«i a n "?« - I S D O 1 ? n p i ^ n n o

"?jn T i ^ n

i»!1?

n®«

ibdd3

"73«

«in

,"?a3ion

. T I B 3 1 31T3 " 1 « i n D T l V s

niosn no«ni»

rr'rsn

«in

^yan

,-ns3

«"7«

-ibdd3

,"?331D 13'»® U ü b

Kin

.IT^Sn

. - o w n p i B 3 n r 3 131-pyn

^ D ' ^ y i

rnby

n ' n ' ® , n r bwa

p

n

p i s n

ni«'*»» ,!

,"7113

V ? d t \

,jitwnn

mDi«n

n'tt^Bn

nonpnn

~n«33

7 y 3 v n ' «V d « i ,~ipp d i b d d " ? i v ^ a n

i'«

' n " 7 3 "7« p i r w b v '3t2>n n 3 D i ,'3® "73® 1 0 3 D b w n - p n ^ a w n n ? . " 7 1 D 3 n " l « 1 3 D 1 3 Q3 HT . X l ^ S n *7y3 ' n V 3 n i « ' * » my3on

niy3on

-i«3 .D'^-mn

mtpn

,3XD3

rtmpru

-TTD o n 1 ?

-i«3® i n «

n®«

nsn

o n m a

n ^ a n

n ^ y n ' 3 ^ ^ l V y i n i 7 y 3 , y 3 £ n - h d Dn"? n ® « D n 3 n 3

idin'sd

l

- i " ! ^ 1 «"7 n - n y n

T'ix'

d«i .Vi^yn

nsd'

n«xon3

-itt>«

.Vi^yn ^ y n t f

nn

.y303 n ' b o n ' n ^ s 1 ? h ^ y i n"?y n i W ^ n i p n

y-irn

"7«

i n x

• m £ U ) 3—4 [vim

«im

ri3'n33

. ' » o t o - « ( r v ^ o n ' b y n tiVs) - > > rmir,»' ?1^»n'Jir

k u r o r t [un'Sffii

!TTJD20

n w x n n

1

> TIE: 1 » - h b j I

l

Vl^y ? [ ?l 7j;i19

-110:2 IN 7

1DJ» n t O » 1 4

«'n

mK'XD nr^i

h p s «

«in

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.13110 ' » ' ^ 1 2

.»Vil

P R O P O S I T I O N III

221

possess number, that is to say, which have the capacity of being numbered but are not actually numbered, 6 even though assumed to have the distinction of even and odd, are not excluded from the possibility of being infinite, for infinity may be predicated of even numbers or of odd numbers. 7 The real truth of the matter, however, is that the division of number into even and odd applies only to a finite and hence limited number; but infinite number, inasmuch as it is unlimited, does not admit of the description of even and odd. 8 We have already discussed this distinction in the aforementioned chapter.

PROPOSITION

III

PART I.

PROOF OF the third proposition, which reads: 'The existence of an infinite number of causes and effects is impossible, even if they are not magnitudes.

T o assume, for instance, that the cause of a

given Intelligence be a second Intelligence, and the cause of the second a third, and so on to infinity,can be likewise demonstrated to be impossible'. 1 Having shown in the second proposition the impossibility of an infinite [number] with reference to objects which have order in position, namely, magnitudes, he now shows that it is likewise impossible with reference to objects which have order in nature, namely, causes and effects, 2 for by a cause is meant that the existence of which implies the existence of an effect and should the cause be conceived not to exist the effect could not be conceived to exist. 3 It is because of this relation between cause and effect that an infinite series of causes and effects is impossible.

The argument

may be stated as follows: An effect by its own nature has only possible existence, requiring therefore a determinant to bring about

222

CRESCAS* C R I T I Q U E OF ARISTOTLE

nr*?i . l n ^ y « i n « i n n y n a o n i m

, m y n by l m « 1 * » y n j '

o n v n n a b b ^ d 1 ? » ' «"? n ^ s n v i ^ s 1 ? o ' ^ y i rn"?y m ^ t ^ n o n n t p s « a n nan . a ' b b y

o ^ j v n o«i

"?y a m « ' * » y - D ' y n s o vn

«V d « i

.man:»

.«"7 d k a ^ i ^ y

vntp 'a 1 ?! . n i K ' x n n

•?« a o n s

nVi^y

o"?o

an 1 ? nan

' n ^ n nby

,o-nyn

D ' ^ s n « i n i t ? « . n ' j i V y ' n ^ n n ' j y o n o i n « nan 3 t a n npty nr . r v ^ D n 11? ¡ r n «"?» n a m n a a i

D ^ y .m^tyVncnn

.dibdd1? r v ^ s n r « a ^ y i m ^ y u r v r a 3"nnn nin -ippni «*?« r r b o n

"?ya

niVya

.yacaa

.yncan

«Vi 32iD3 - n D

.n^nn

1«

'n^a

"?ya T i b o

niyjDn a " n

.o'^-nin

nn1? ] ' «

o m « ^ »

m y j o n n n«-p -rtn p «

.axoa

y w

d"?i«i

«*?&> , - m y r u t p - r d

-w«

onm"?

n n m a

.D'^i^yi

.nonu«i «ro p «

i«

a ^ a c a

n y n «in

nn

, - n o on1? i ' « » o n m a

dj

- i i b d "731 ^ y s a " i i b d « i n " ? y s a i b d d bsv r v b o n byz

on1?

«"? n a n . n i t p s n

"?ya « i n " ? y s a -iBDantp - i d « « i n o

- p x i

nn

. n u n a

rr^an

« i n t i d j 1 « air « i n » n o i , - t i b j q « i n r • « « i n " ? y s n .nnana

. r r n o « « ' n - i b d d 1 ? n « r n n p i ^ n n t p , « i n n r a 13*7 n « T B > mrn

in«

>ya

Ti^an

«in®6

.rrVan

"?ya ' n ' r a n

] ' « nr"?i . n - n e m

.»I'n'-o'-»•»•nH3B4 3

> urvjnD - « m n " n n n , 3"nnD Kin - r D'aiHS-"1?» NJ'D p » WD '113 »imenmao

iBDan nvmra

noi

,n3DD t a ^ o n -i«uv

«•? ,"?a:n»

r « 'n^a

m^y 1 « i n a o n i n - « • " r v - o n n - « i n a ' 1 • " n n ' ,P -> a " n n o .'O'-m^ll

. ' » " • " i ' i m i s >» n e n ' ]

3"nn38

.»i fl'IT

.> ' r t m 7 3"riIV [3"n9

IDNP UKI ' -innrraNi

PROPOSITION III

223

the preponderance of existence over non-existence, which determinant constitutes its cause. Now, it must inevitably follow that in the aggregate of an infinite series of causes and effects either all the members of the series would be effects or some of them would not be effects. If they were all effects, they would all have possible existence. They would require some determinant to bring about the preponderance of existence over non-existence, and so they would necessarily presuppose the existence of a causeless cause [outside the series]. And if they were not all effects, one of them at least would then be a causeless cause, which one would thus mark the end of the series. But the series is assumed to be endless. Hence an impossible contradiction. And this contradiction ensues because we have assumed the existence of an infinite number of causes and effects.4 We must observe, however, that the possibility of infinite number is denied by the author only with reference to objects which have order either in position, as magnitudes, or in nature, as causes and effects; he does not deny its possibility with reference to objects which have no order either in position or in nature, as, for instance, intellects or souls.5 This is in accordance with the view of Avicenna and Algazali.6 Averroes, however, finds it to be impossible even with reference to objects which have no order whatsoever,7 for he maintains that actual number must necessarily be finite. He reasons as follows: Every actual number is something actually numbered, and that which is actually numbered must be either even or odd, and that which is even or odd must necessarily be finite.8 For our own part, we will say this with regard to Averroes' argument: While indeed the division of number into odd and even is true and unavoidable, still infinite number, not being limited, is not to be described by either evenness or oddness.' And so an infinite number is not impossible in the case of intellects and souls. It is for this reason that in his propositions about the im-

224

CRESCAS' CRITIQUE OF ARISTOTLE

'n^an nsDon niywna ,yacan m pi

a n n pnp-itt> n a nr"?i

.D'^-mn .aicoa - n o

w b w b

'wb

n'ry

.ia yjoa n,l?an

o n 1 ? t»'» D n a n a in«n

n'n'ca

n,!?an

. o ' ^ y i

ni"?ya

.n^an

w ^ p n

p i s n

, ^ ¡ 1

D ' h ' j y i ni^>y n i N ' x o t p m » w n

"?ya

'n^a1?

^ s n

n'tî>,l7tj>n n m p n a

nTpna

.npti> DnDDD 1 ? n , ( 7 a n ] ' « vVy

u i - p y n ity« ,nra

nBDD

'rown

~iD«Da

vnan1?« nomi

T I D -ib>K n s m n t p

,ptt>N-in

bbino

-ioini

'tt^œn

pisa

a " r r h 1 ? Ninty n n . a m n y n ' s 1 ? p ' b d o ' n ^ a ,nn«t¡> n o a i y o p n -no

o n 1 ? b>'b> o n a n 1 ?

n"?y

n'rrtp i n «

xtin'xo niyaon

boaa

k1?« n ' ^ o n -ipbk

nt"?i . y a c s a

axoa

n m m

n n « n'py'? i o s « n ' n d n , n n N n"?yD n ^ a n ' V y a ' n V a

o'^i^y

nvni?

ni1?'*«

a"n'

p

i'tw

in«i

n^an

myion

o^aty

niyaon

.iSDoa

in

nBDD

?ya 'n^a

cr^y"?

l'N ^ a a i

"7ya ' n ^ a

,!

.-m« ^ y o

m v

QH n i n . o ^ a 1 ? n " ? y d h 1 ? d m , n , ! 7 a n ^ y a

'n'ra

nr^i .D'biby^? n ' ^ a n " j y a ' n ^ a n m y j o n u b b d b n ^ y n n i R ' ^ o rwbwb 'wm

n"?y n n « n n ' n ^ a . o ' ^ y i m " ? y m u n t m a

a " n ' i 1 « , n n « n V y i 1 ? « ^a"? n ' a t t o , y i « i j n ' ' » . a b n y 1 ? nn

cs^)-«' 1 1

.D^i^yi m^y^ n ^ a n

v a e m n i C i f ,» "inurusio

.» ni^y IN [m'i'x« 15 .«'* rrrr - m w a

.» a " v r - ® »

^ya 'n^an n i y w n

-incas

nniN'XD

.'«- t'pya] 'nW?4

(«in»)-»pn 1 ?

- t r a m a nnt»n rvn'ïois

pi

-op"*

di7i733,i11 (o'îW?)™

.» myjDnn n w x D [myicn nniN'XDîo

PROPOSITION III

225

possibility of infinite number the Master has specifically confined himself to objects that have order either in position, as magnitudes, or in nature, as causes and effects, when these are so arranged that the first is the cause of the second, the second of the third, and so on to infinity. PART I I .

the third proposition, which reads: 'The existence of an infinite number of causes and effects is impossible.' EXAMINATION OF

I say that the argument framed here by Altabrizi, which has been discussed by us in the third chapter of the first part, and of which there is a suggestion in the eighth book of thePhysics 10 and in the Metaphysicsis not altogether sufficient, considering the particular view espoused by the Master. For the Master, as has been shown, does not preclude the possibility of an infinite number except in the case of things which have order and gradation either in position or in nature. According to this, it will be possible for one Intelligence to be the cause of an infinite number of other Intelligences. On general principles, it must be admitted that the emanation of an infinite number of effects from one single cause would not be impossible, if it were only possible for a single cause to be the source of emanation of more than one effect." And so, inasmuch as it is evident that there can be an infinite number of effects, despite their all being dependent upon a common cause, it must follow that the assumption of a common cause for more than one effect would not make it impossible for those effects to be infinite in number. This being the case, assuming now a series of causes and effects wherein the first is the cause of the second and the second of the third and so on for ever, would that I knew why, by the mere assumption of a common cause for the series as a whole, the number of causes and effects within that series could not be infinite? That their infinity is impossible on

226

CRESCAS* C R I T I Q U E O F A R I S T O T L E

o ' ^ y

l a n m n a « i n c . d ^ s 1 ? naitPN-i n*?y n v n n x o n t

- i K i a o Mini . o b s b naia>M-i n " ? y a m i ) - i a a r r b o n "?ya ' n ^ a y a o n mm

nnM

7ya

'n^a

' ^ y a ' n ^ a o n v n y a o ' m"?b>

. y a o a im a s o a n o

Dn"7 i w

n"?y n n M "73 r r ^ a n ^ y a y-D' im1? o o n s

,(

a"in'

Dnana

nsDoa

'n^an ann o ^ i ^ y n p

iaMti>

rr^an

m

maaao

d i p n r o m p < m1? n a n 1 ?

1 3 3 ianaMi » n i M ' x o n n t P S M o"?atp i n » . D ' V i ^ y n o nn^ir"? n , ! ? a n n a ^ n r r

, a - n y n Vy

oniM'xo

- w m naitPM-in n ^ y a

m u

.aniK'XD ny-iaon M'm nr ,-ioMtt>a D N r n n o n p n n n o « 1 ? D ' e n s o n n x p - i n n nan sjiD 1 * 7 j w n o n o ' - r p a

nasi

dm o x y a y r m ^ p n o ' a naitp1?

, r r a o r n o n p n n r r n dm n a m . | « a n y . k x o ' b » - i p s m 'mi , y r ianaMi n o 1 ? , n p i " 7 n o n "?apn n a a dmi , n « r n nayta 1 ? D i p o

mn

, y a ' nan i"7 ^ i d t m p n o n o n p n a «"7 dm y \ r m"?b> not? n « n a m"? dmi , y a n l a ianaMi n r n o v n t f , b m - p i ^ y , n o « n .D^iyn monpa -ipm m y a o n a i

dhdik^ mpoatp

i^ms

.i 1 ? p;id i ' m p n o n o ' - t p a m^m nntt>BMa

n-nae>i , n n p o a

yan

nrtc m^m

- » a V i d ? [dVd1? - > 1 * r u i » * n n - n n ! ' » » n^yn - 1 « 3 p 1 1 1 * (nt) - * 3"nrv . ^ » » r n ' i .i'nni3Dn9 -• , l TIJni2

nna' -•>' (oip>6 . ' n a n n«aiV»]lD11

"tm [ ^ a - » mnn>5

rnwmn

.Pl-|DMi'3-» J ii^D , ®"IDDnD-i= I innniO

. » n o n p m ° rumps [nonpa 16

=r ' * eta h

.1 n'nn tnrvn

PROPOSITION I I I

227

the ground of the dependence of the entire series upon a first cause is without any justification, for assuming, as we did before, the existence of an infinite number of effects, [which are not interrelated among themselves as cause and effect], we likewise posit a first common cause for all the effects, and yet, we have shown, that those effects can be infinite, inasmuch as an infinite number is not impossible in the case of things which have no order in position or nature.

B y the same token, no impossibility will

happen if we assume those infinite effects to be each successively the cause of the other. T o be sure, it will be necessary for us [to posit at the beginning of the series] something [uncaused] to bring about the preponderance of the existence over the nonexistence [of the causes and effects within the series], since [by themselves] they all have only contingent existence. But still, we have already admitted the possibility of a first common cause which would not necessitate that the effects proceeding from it should be finite, even though it would bring about the existence of those effects. 13 A certain one14 of the commentators has attempted to prove this proposition by an argument which we quote verbatim: 'That which cannot be realized15 by itself, unless it be preceded by something infinite, will never be realized and cannot come into existence.' 16 Now, 17 if the 'precedence' [implied in Maimonides' proposition] were of a temporal nature, there might be some room for this reasoning, 18 though, I must say, even in temporal precedence the argument is not wholly immune from criticism.

For we see that

that which cannot arrive except by the precedence of what is infinite does actually arrive:

thus, for instance, the present day

in which we are is here, even though its arrival, according to the view of those who believe in the eternity of the universe, had to be preceded by something infinite. Indeed, it may be rejoined that in that case the precedence was only accidental." But still,

228

CRESCAS' CRITIQUE OF ARISTOTI.E

-WN n o ' i p a

nrn

o

,]»n

nn«

nm

pi^na

m i » D

"73«

.nnoNn

ant? -in« ,n3D3 - w k n a n p n

mman n n w

myaon 3"n

-p-is

1*7 m p a

osys

p«

, p a

,-rrm i o n i n ' a n s - i n t ?

i n « .o'Vi^y d^d a n v n n n m s w

i n «

nnttV n*?y

.nm rrVsn 'Vys viVs Nin

,mna

'Vys

i o n s

'nVa

i3níí> n » i

D^iVyn

vn

,nmpnn

. n ^ y

.n'bon ^ y n

,nnsn

nxo*

'lj'pntp

,nitfitynn

i m n

m*a

Nim

moiNn

,-pMn

'irrcn nr

m w i n

,]nptnn

-iD«D3i , - i D s n m m i n n

nsd'i

viba

insane*

«"7«

n*?y

niN'xn

i n n n n V nb>y n n «

p i s n n y m x n

nxro

nanpnn

Kim ,D^yn

id«D3i

n ^ s n

^ s n

rryrnn

,pnynn

-10N03

,ynDnm

nyun

-iiN32 ,nn0K0

nrrnxn

Nim . m a n .cnsfr

'írrcn np^'tto , j m n ^ i n ,nosy3

r n « u o 3

oxys

' w m

torn , p n

anvn

uddi p n .nonpnn

«in m«3i

u d o 'irtflntp no1? n«t

nDKnn

-p**31 n » 3 3

«im

-iDNnn nyunn mn

.rrbBQ

'»no

new 'iri»n

.nosnm minn i b d 3 ntanntp ids ,pr n V m ,nnDRB n y 3 i « n 3 p 11 ^ d a » n D [3"n ' a 3 . « • " c r t y ) 19

.» ™«m

'3 «in

i"?k n n " n » 1 ? , v b y - n i y n i t p - p n x t p n o i .> t ca) - ' » " ^ » n 1 ? pV 2 r«wi7

npV'sois

.» nonpnn n n [ n o n p a nrn 1 .•> rn'® in [Vn7

.-> 3'ino

P R O P O S I T I O N IV

229

to admit that something is possible when accidental and to deny its possibility when essential, needs to be demonstrated."Granted, however, that the distinction between accidental and essential holds true in the case of things which precede one another in time, it has no place in the case of things which precede one another only as causes, but co-exist in time. Admitting, therefore, as we must, that things which co-exist in time can be infinite in number, by what show of reason can we confine that possibility only to things that are all equally the effects of one cause and deny that possibility of the same effects when they are arranged among themselves as the effects of each other? But what this proposition really means to bring out, and what conclusion thereof is actually needful for our purpose, is the fact that there must exist a first cause, which is uncaused by anything else, regardless of the view whether its effects, when they are one the cause of the other, are infinite or finite." PROPOSITION IV P R O O F of the fourth proposition which reads: 'Change exists in four categories: in the category of substance, which is generation and corruption; in the category of quantity, which is growth and diminution; in the category of quality, which is alteration; and in the category of place, which is the movement of translation. It is this change in place that is called motion proper'. 1 Inasmuch as some kinds of change are in time while others are in no-time, by taking the term change in an unrestricted, absolute' sense, the proposition will have been proved to be true. [That the term change is to be here so understood] is quite self-evident, for change in the categories of quantity, quality, and place is in time, whereas that in the category of substance is in no-time, J as has been shown in the book De Generatione et Corruptione The following argument, however, may be urged against the author. Why did he enumerate only these four categories, when as

230

CRESCAS' CRITIQUE OF ARISTOTLE

,-io»n 'nc

,nnoNon

'ir»

,-i«n

bobv

bu

- i n b d n x o ' - 1 3 3 'U'tpntp - i k u o

no1?» n1?« .^yerren

~i«na m n w o n

d « i ,]dt n b n n nrraai

'ir®

pnyn

rom

.nnoNon

,n»ai nia'tai mo33

nrn ] v y a miD

rom

Kim

^ye'Gn .twin

"inbq

nxo ron

,-ioNn

'B 1 ?

nra n u

-pm

.'iron noin u

norotp

.nnD«D no

pan

nya-mn mm

-iono3

a«

nron

.nirrn nrnaai

,'irtfn i n n n®« n o N o a

i V í u n e w nyun1? q p o j a x y 3 -ipn 'irtpn m m -p-r

axon

i1?« m n

.nn«»

ron

.nron nn"

nan

Nim

-rso nron

nrnsn

,nnoNon

nsD3

ibd-in

.nroinp no ,pnynn in« ,p nvn1? '3

ron»

' w e n i n " no1? .nsa 1 ?

d j m t a 'U'tpn ,-id«i

ron

nynnnp

noss

nrD unan 1 ?« n i y n a

-inípw nn« , m B 3

nVn nyun1?

.no pnyn

naai

u p

'3 .nn'Dxi? nrn« nm «"71 ,nyunn ib» nm,emtio m«a pnynn pnyn

u

,nn'02£3 n r o v » no

.»mo

im'n

n3 pnynn

«"7 nrh ,vnt3p "733 «in noixs nmosntp yi-rtp nob» . m t u nm nrbi .m«

n w o pnyn 13 norovp v1?« non p"?n -iropj .n3«3 pnynn

[«im-«3 neo [HD39 .* pnynn [pnyn 13

.1 n'n'i ^p^ N'm [n'rru .>a Minn pnyn [pnynn 14 ,»pnyni8

."vioip

P R O P O S I T I O N IV

231

a matter of common knowledge change exists as well in the other categories5, as e. g., position6, action and passion?7 [The solution of this difficulty may be given as follows]: Every change has two aspects 8 . First, it may be regarded with respect to the substratum, in which case change means the transition of that which underlies the change from one accident to another®. In this respect, change exists in the other categories10, and is in no-time. Second, change may also be regarded with respect to the matter of the change, that matter being, e. g., quantity, quality, and place". In this respect it exists in that category in which the matter of the change is to be found". It is change in this latter respect that the author has in mind in this proposition 13 . But inasmuch as change in the category of substance is consequent upon the motion existing in those [three] categories14, the author has enumerated those four categories. In this he has followed the path trod by Aristotle in the Metaphysics.IS This would seem to be the right 16 solution of the difficulty. There still remains for us to explain why he has restricted the use of the term motion proper to change in the category of place, that is, to translation, when, as a matter of fact, motion in the category of quantity is likewise a change in place, inasmuch as it always entails some act of translation. 17 This question has already been raised by Altabrizi, 18 in answer to which he says that the term motion proper is applied by the author to locomotion because the act of translation therein is perceptible; but he does not apply it to growth because the act of translation therein is not perceptible. It would seem, however, that in growth there is no translation in place at all, for plants, as is well known, grow in all directions, and consequently there is no definite part therein of which translation from one place to another can be truly affirmed." It is for this reason that the Master has restricted the use of the term motion proper to translation in place.

232

CRESCAS* C R I T I Q U E OF ARISTOTLE 'Bronn p n s n

n K ' X ' i 'U'tp n y u n

bsv

,]i»&nn

nnoi«n

^ a n

n^'onn

no-tpnn

n w a a

. ^ y s n "?« n s n p «*? "?3K ,Q"TpB> n o ' S 1 ? 1 « 1 3 0 K i n '13'® nj?13D "?3tP 1 1 0 « H3H rrn'P

13DD ' U ' t p n t p n o 1 ? , n y i 3 n

it£>N , n « n ^

.nr

-|snn'

n « n o « p u n p n y m n D s n m n ' i n n i d s ,]»r n ^ i r a

-isp« 130D 'i3B>n " 7 3 « ,my-n

"?3 | ' « t p n n

.ns1? n y u n n

.^ysiran

^ys'tp

db> p n : r u

-i0«03

D33' n s n

nro

n e w 'U'tpn n o n D 3 ' n n a

ton

.•'SDVsnon ]iono pi^nn n n

w a i n

«V

'3

no 1 ? 1 ^ 0 3 « i n ,"?ysn "?« n o n ]» n « ^ ' «int? n o « ci3o«i n3m . n 3 3 «inte no n x o n33ti> no nio^tp «'na» n y u n n m3t2> noi uootp n o ]'3 nyunntp no 1 ?

«intp v V y p n r

. v ^ p n o 3 n'n'tioi ,n3 « m i -1103 n a n n ' n ,13002» n o 3 n ' n a o i m o W « m n3n ,|'3B> n o s «intP3i ,n3 « i m 1103 m o W i 1 ? n ' n nr"7i ."1103 nio^tp i 1 ? i ' « nr^i r n 3 3 v ' n y «mtt> - r s o ^ 3 « ,no ."?ysn "?« n a n p n«'2£' nyunnt? n o « n n n"?i3D02> n o * 7 , n y i 3 n " ? ' n o « 133'« n r n - n s n t ? n « T 1 3 3 o " 7 i « i 'sVi

,nsion

-ie>d3 n « 3 n n B >

,nyi3n n ' n ' » p

» -WK UDB .i - p e s ' = p n r ® i

103

,-i"T33n "?y

d« 3 " n n ' ,ny3n3 p

-jsnnnn

as p n x ' 1 3 3 n r n

- m n -nan»

Aato •"> ntw ojdd ' B T I Van » « p n * -1»« CUOD) w n p

N'nisoi [n'msom »0^) - 1 'i n:n [ ¡ r n n

n

x

'

n

w

.Mnyunn] v 1 ?«®^

»

s

"73x7

i f « warn 'u®rt 6 3 « )

.>=pt' mm [«in 10

[ n y m n j v ^ t w - ^ (ra wmi -

.«»p^nn [ p i ^ r m

"> N'n [n'n -

13

p* n ' n ' i o i

.3 ID 03(13 DM->a h d ' s b ' n o a n ~ n i n r v n

niD1?» n o » m m HD3 h d k i

' n ^ nt^i

. y y u n » « m » n o a y y u n o n m o ^ i f Nim , r a r

. n o n i o 1 ? » ! b ' y s i 1 ? w v "72N , n D 3 r o n î a w . - n o a n i o b w i V y s i1?

ni'tf n y u n

m v

.rvnoK n o i p n n

m v

y y u n o Nintp

, - n i n rrrrty

l'Ni

. • ? y s n "7« n s n

w n .moxya

on»

,moxya

ipn

idk'p

niyunn» o^in

103 , m p o n oVini

it»«

p-isn

,mpD

,|nwnn

rnoi«n

^ s n

n w n

noipnn

.p^rta onoi . r r o m

oipoo

pnyinîf

d"7ini nr V y n n n 3 ' n ' - i 3 » 3 n ^ y n n

-ïin33

onoi . m p o a

ntsw d V i n i ^ i p o 1 ? mpDO

p

db>;q

Qtyn Nina»

p a n nyura

anoi pnyro

nnnBQ . r r o m

» n r s D n n y y u n n - i í p í o ' 3 . n r s D a - i d d d h n y u n a , p ^ r a -ib>n îVboa

yyurv

-aino

"731 , p

ai iDDon y y u n n

133»

m*«

. y y u n n -133 ip^nty -ion1 a«

nn

.nu'na

n1?

nyunntp

n«rn

nonpna

pison

p n y n 3 ,ivii2nn nr3 Disn . r r r r o n in n r r n rryata l'Kty - i 3 - i " ? n y u n n o r ™ , n n p D

3

niai n a a u r w w s

[yjîunDn] maV®

o n a - 1 » ' n n o - 1 " 3 onon

.» nyyuruifo - » n ® t o ) - » nj'soa p » « ] h m - * îp^n

.rrninxy

i s î a i p D ^ s D i p a D O f j n

- » i-iDKi - » (ram) - » 1 wn [Nine> - 1 3 p m a i * u-dm -'n^yau

mn

1

10003 -

1

- ' ip^nn 17

(nyuro) 15

w n [Kin»6 ."> m n n y

»n-i3inon-»'?3piis

P R O P O S I T I O N VI

235

require a motive agent for its motion. But that second motivity will likewise be motion, and this will have to go on to infinity. 10 It seems to us, therefore, that the true definition of motion is the other definition mentioned by Aristotle, namely, that it is the actuality of that which is movable in so far as it is movable." His use of the term 'actuality' is meant to indicate that motion is not complete potentiality, but that it has some degree of energeia and entelecheia." His use of the qualification 'in so far as it is movable' is likewise meant to indicate that it has not a complete energeia and entelecheia. But, however the definition may be phrased, the proposition remains true, namely, that 'every motion is a change and transition from potentiality to actuality.'

PROPOSITION VI of the sixth proposition which reads: 'Of motions some are according to essence, some are according to accident, some are according to violence, and some are according to part 1 . Motion is according to essence, as when a body is translated from one place to another. It is according to accident, when, e. g., blackness which exists in a body is said to be translated from one place to another. It is according to violence, as, e. g., the motion of a stone upward brought about by a certain force applied to it in that direction. It is according to part, as, e. g., the motion of a nail in a boat, for when the boat is moved we say that the nail is likewise moved; and similarly, when something composed of several parts is moved as a whole, every part of it is likewise said to be moved.' 2 PROOF

The purpose of this proposition is to show that motion is classifiable.3 First, essential, 'as when a body is translated from one place to another' 4 , which may be either natural or violent, and voluntary motion, too, is to be included in this class. Second,

236

CRESCAS' CRITIQUE OF ARISTOTLE

y y u n ' t p 1133 , m p D 3

yyurvt?

îosyo yyurrip

istid

nrrn rrrnDxy .rrn-on ont ;otwn n y u n n o t m -ipn nnntpn n ' m s n .p^na -ib>n D K i ; n ^ y D V i 3 N n n y n n 3 , n n p o in nnpontf, p ^ m -ib>ni n n p o n ]'3 nttw tinsnm .rrynto ik nirn new,yyiannp o t t d paty nsn 1 ? m p o a i e w n y u n n Drrïzo n t i .yyurrtp d i i d i j - m 1 ? p V n a nt?« n y u n n orra» « m p"?n3 -ik>n nyiann "?ti>D3 n o «

bzx

,v"?y - m y n n 1 ? - p x t p n o

. a i p o 1 ? o i p o » d p an p n y n s

.mo^yn

m p » n t d ' n 1 ?^ nob .mpo 1 ? oip»o ^ a n otpa p n y

^an

nyiaratp 'e^i

iV^d"? n'osy n y u n n n'nn «V nan ,vpVn î p n y d3oni , 1 ^ 3 3 o n K'n b&b

nyunn o

.ntn'tp n o

n n .vp^n1? d n

o

n n .la1? ntrvtp n o V rrystî d n i i d d - i n n y n ' s V rvpitwi m i a n D'Dtî'jn v m ^ V s a

rrysta nyunntp

u r m ? nobw

a'yyuno m b p i - a u '^y3 d ' h i d ' h ^sVan n n n -îtm D'tawsn ,m^pi n3i33 -iNino i m w

^ b a n aœa n3n . m c

nyun

^ a 1 ? n ' n n D n nyiann nrrn nrèn . n ^ u o n îb» n'ynun n y u n n ,iV?33 m p o

m p » o "pa^an p n y

rrn o n t ,n"niDsy

.3in n 3 i a n»Ttf n n sp'rrn »3

.N^YON

,NV3BN

NVYATO

1

L A N , P « N N I M , O N » - M « ? . N Y A N A N NRND'NTP ,NR 'JBD ÍOSTTN / S M

M^PI

ÑAU

D'O^I T I K ^ I

-ID!« 1 ? vrw NN . - M A N ' D'B^NNA

I M

,NBYOB

N S N -PN I M

NO1? ,N"?YBN .D'DN

- I N 3 N N K1? NTO'TP NO >SB NRN NY-RM

DNTF KVK , N A N 3 I 3

NSO1?

TI«N

RNVP TMVI , TAENIA

MN

NMD'NA

INX

RIYNN NRRN D J D « I

BJBW

N O W

.NM

RIINS3

P « 1 ? M P ' ITFTO . N ^ Y A 1 ? W I N N M ' -IB>N

YYURVTP 'N » P A IN - [ M O M S I Y

-MAN

N I P ' NR NIANAI

,-I'INN N T S N A -RV , Y - I N 3

IRIS

IN 3NR

N

.INN"R M S N A N NAIATP

N NTPTOTF NO 1 ? ,NR N « T

I33I

YAAN1? UAA NRW IIYTS'TP LYICS^ -IÍPBK» N'N DNI .WON RINVANN O^INI NID'N 1 3 1 3 1 ? NR N ' N ' » YAAJ U R « "73« . ^ J N

-PN M P - I N

, N N A A D N B D D'JB *?3 "?Y NAN , N B Y O B P A N NYUN N'NNTP - P N

.bmZL HOD1? INDA ^«7

NODN

-1« A P IN U S EINRN [WK^I 9 NVN [NN'N-O -INI'112 - 1 TETAN [N:NI9

.MAP

[«IN]6

. > *=P NVYON

N3TP 1D3

. ' " P 1 1 " 1 " M A M [NINIS

[NVJ? ob -

•>

- 1 ' ' p V'-IAO - ' « 3 P 1 O NOI» [N«DD - =

[^Y-I KIN

239

PROPOSITION VI

Again, in his illustration of accidental motion, he uses the phrase 'blackness which exists in a body.'

This would seem to

imply that there can be no accidental motion except of something residing in some magnitude and capable of being translated from one magnitude to another." But as a matter of fact accidental motion may apply to the point at the extremity of a body, even though it does not exist in a body but at the extremity thereof. 13 As for his illustration of violent motion, which he finds in 'the motion of a stone upward,' he follows the well-known theory of the Greek, 14 namely, that the elements are endowed with natural motion in opposite directions, as, e. g., the motion of a stone downward and the motion of fire upward, whence it is inferred that of the four elements, one, i. e., earth, has absolute weight, fire has absolute lightness, while air and water have only relative weight and lightness. IS But this theory seems never to have been demonstrated and never will be. On the contrary, one may argue, that all the elements possess a certain amount of weight, but some possess more of it and some less.16 T h a t fire tends upwards may be due to the pressure of the air which pushes it upwards," as happens in the case of a stone which, upon being dropped into a crucible in which there is molten gold or lead or mercury, comes up to the top, because of the pressure of the metals which push it upward. The same may also be said to happen in the case of the elements air and water. That [air possesses some weight] is moreover supported by observation. For when we make a digging in the ground, the air immediately descends into the hollow and fills it up. 18

Though the opponent might claim that this last

phenomenon is due to the fact that a vacuum is impossible within the world, still it is not impossible that the descent of the air into the hollow is due to the weight which that element possesses.1»

But, whatever may be the explanation [of natural

motion], it is clear that the upward motion of a stone is due, as has been shown in the illustration, to some external force.

240

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