Table Of ContentSTUDIEN UND TEXTE
ZUR GEISTESGESCHICHTE
DES MITTELALTERS
BEGRtl'NDET VON
JOSEF KOCH
WEITERGEFtiHRT VON
PAUL WILPERT ALBERT ZIMMERMANN
UND
HERAUSGEGEBEN VON
JAN A. AERTSEN
IN ZUSAMMENARBEIT MIT
TZOTCHO BOIADjIEV, MARK D.JORDAN
UND ANDREAS SPEER (MANAGING EDITOW
BAND XLIX
ON REDUPLICATION
ON REDUPLICATION
Logical Iheories qf Qualification .
BY
ALLAN BACK
E.J BRILL
LEIDEN . NEW YORK· KOLN
1996
The paper in this book meets the guidelines for permanence and durability of the
Committee on Production Guidelines for Book Longevity of the Council on Library
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Library of Congress Cataloging-in-Publication Data
Back, Allan.
On reduplication : logical theories of qualification / by Allan
Back.
p. cm. - (Studien und Texte zur Geistesgeschichte des
Mittelalters, ISSN 0169-8125 ; Bd. 49)
Includes bibliographical references (p. ) and indexes.
ISBN 9004105395 (cloth: alk. paper)
1. Reduplication (Logic). 2. Logic, Medieval-History. I. Tide.
II. Series.
BC35.R43B33 1996
16o--dc20 95-53247
CIP
Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Back, Allan:
On reduplication : logical theories of qualification / by Allan
Back. - Leiden ; . . B rill, 1996
(Studien un des Mittelalters ; Bd. 49)
ISBN 90-,.....-,"',.,
NE:GT
:z
6>1
/~l ~ ~,/?
ISSN 0169-8125
ISBN 90 04 10539 5
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TABLE OF CONTENTS
Preface .......................................••...••.•.•.•..............•..•.....•........•..•..•• Xlll
Introduction ............................................................................................. xv
BOOK ONE ARISTOTLE'S THEORY OF QUA PROPOSITIONS ........ 1
I. Essential Qua Propositions ................................................................. 3
I. The Text .................................................................................... 3
II. Prior Analytics 49all-26 ........................................................... 7
III. Prior Analytics 49a27-b2 ......................................................... 14
IV. Conclusions and Modem Analysis .......................................... 22
II Essential Qua Propositions: Supplementary Texts ........................... 28
I. Aristotle on the Middle Term .................................................. 28
II. Ka8' Auro and Commensurate Universality ............................... 31
III. Senses of Ka8' "0 .................................................................... 39
V. The Meaning of Restrictive Essential Qua Propositions ........ .43
V. Symbolization of Restrictive Essential Qua Propositions ........ 47
VI. The Views of Later Greek Philosophers .................................. 50
III. Accidental Qua Propositions ............................................................ 54
I. The Fallacy of Secundum Quid Ad Simpliciter ........................ 54
II. On Interpretation 11 ................................................................ 58
III. The Greek Commentators on Qua Propositions ...................... 67
IV. Modem Analysis ..................................................................... 71
V. Formal Features ....................................................................... 78
Conclusions ............................................................................................. 83
BOOK TWO ORIGINS OF THE MEDIEVAL THEORY
OF REDUPLICATION ........................................................ 85
IV ~ Islamic Philosophers on Qua Propositions ....................................... 86
I. Alfarabi on On Interpretation 11 ............................................. 86
II. Ibn Sina (Avicenna) ................................................................. 91
1 Commentary on On Interpretation 11 ................................. 91
2. Commentary on the Fallacy of Quid Secundum
Ad Simpliciter ...................................................................... 96
3. Commentary on Prior Analytics 1.38 ................................... 98
III. Ibn Rushd (Averroes) ............................................................ 106
1. Commentary on Prior Analytics 1.38 ................................. 106
viii TABLE OF CONTENTS
2. Epitome on the Fallacy of
Secundum Quid Ad Simplicite. .................................... 108
V.Medieval Precursors of the Theory of Reduplication ................. 110
I. Boethius ................................................................................. III
1. ConditionalPr()positions ......... ~ .......................................... 111
2. The Fallacies of the Old Logic ........................................... 116
II. Peter Abelard ......................................................................... 119
1. Conditional Propositions .................................................... 120
2. Commentary on On Interpretation 11 ............................... 126 ..
III. Early Treatises on Fallacies in the Logica Nova .................... 131
IV. The Dialectica Monacensis ................................................... 135
V. William of Sherwood. ............................................................ 13 8
1. Reduplication in Simple Supposition.:. .............................. 138
2. Reduplication and Universal Quantification ...................... 141
3. Sherwood's Use of Prior Analytics 1.38 ............................ 142
f:l.
Reduplication and the Locus Ex Usu ................................. 143
5. The Fallacy of Secundum Quid Et Simpliciter
and Sherwood's Theory of Determination ........................ 145
6. Conclusions ....................................................................... 148
BOOK THREE MEDIEVA L PHILOSOPHERS ON
REDUPLICATIVE PROPOSITIONS ............................... 149
VI. Reduplicative Propositions as Determinations ...... ~ ........................ 151
I. Early Theories of Determination ........................................... 152
II. Albert's Theory of Determination ......................................... 152
III. Albert on On Interpretation 11 .............................................. 163
IV. Ockham' s Consequences for Accidental Qua
Propositions ............................................. :. ............................ 167
VII. The Fallacy of Secundum Quid Et Simpliciter ............................... 174
I. Peter of Spain ........................................................................ f74
II. Lambert of Auxerre ....... ~ ....................................................... 180
III. Albert the Great ....................................... :. .. ,. .... ~ .................... 181
IV. Giles of Rome ........................................................................ 185
V. Thomas Aquinas ................................................................... 188
VI. Raymond Lull [pseudo]. ........................................................ 189
VII. William of Ockham ............................................................... 189
VIII. Walter Burleigh ..................................... ~ ............................... 204
IX. John Buridan ...........................................................................2 04
X. John of Comubia ................................................................... 205
VIII. The Exposition of Reduplicative Propositions ............................... 208
I. Albert the Great ..................................................................... 209
II. Robert Kilwardby .................................................................. 215
TABLE OF CONTENTS IX
III. Peter of Spain ........................................................................ 216
VIII-12
A. Qua Propositions in the Syncategoremata ........................ 217
B. The Tractatus De Exponibilibus ...................................... 221
IV. Raymond Lull [pseudo] ......................................................... 229
V. John Duns Scotus .................................................................. 230
VI. William of Ockham ............................................................... 234
A. Reduplicative as Causal Hypothetical
Propositions ...................................................................... 234
B. The Analysis of Reduplicative Propositions .................... 239
C. The Negation of Reduplicative Propositions .................... 251
D. Consequences of Reduplicative Propositions ................... 254
VII. Walter Burleigh ..................................................................... 257
A. The Division of Reduplicative Propositions .................... 258
B. The Negation of Reduplicative Propositions .................... 267
VIII. John Buridan .......................................................................... 271
IX. [Pseudo-] Aquinas .... ~ ............................................................ 274
X. John of Comu bi a [Pseudo-Scotus] ........................................ 274
IX. The Conversion of Reduplicative Propositions .............................. 279
I. Albert the Great ..................................................................... 279
II. William ofOckham ............................................................... 283
III. John Buridan .......................................................................... 287
X, The Reduplicative Syllogistic ......................................................... 288
I. Albert the Great ..................................................................... 288
II. William of Ockham ............................................................... 298
III. Walter Burleigh ..................................................................... 305
IV. John Buridan .......................................................................... 309
XI. The Supposition of Reduplicative Propositions ............................. 312
I. Thomas Aquinas .................................................................... 312
II. Walter Burleigh ........................· . ............................................ 315
III. Paul of Venice ....................................................................... 318
xn.
Applications of Reduplicative Propositions .................................. 319
l. Sophisms ................................................................................ 319
A. Peter of Spain .................................................................... 319
B. William ofOckham ............................................ :~ ........... 324
C. . Walter Burleigh ................................................................ 325
II. Reduplication in Defence of Nominalism ............................. 328
A. Pro: William ofOckham .................................................. 328
B. Contra: Walter Burleigh ................................................... 330
III. Simple Supposition as Reduplic3;tive .................................... 331
A. William ofOckham .......................................................... 332
B. Walter Burleigh ................................................................ 334
x TABLE OF CONTENTS
IV. Theology ................................................................................ 336
A. Thomas Aquinas ............................................................... 336
B. John Duns Scotus ............................................................. 340
C. William of Ockham .......................................................... 348
D. Francis of Mayron ............................................................ 350
BOOK FOUR THE POST-MEDIEVAL PERIOD ................................ 353
XIII. Classifications and Truth Conditions
of Qua Propositions ........................................................................ 356
I. The Division of Qua Propositions ............................................. 357
A. The Binary Classification: Reduplicative or Specificative ... 359
1. Marsilius of Inghen ............................................................ 359
2. Gaspar Lax ......................................................................... 361
3. Peter of Fonseca ................................................................. 362
4. Rudolph Goclenius ............................................................. 363
5. Joachim Jungius ................................................................. 364
6. John Brunnemann .............................................................. 366
7. Andreas Schubartius .......................................................... 367
B. Ternary Classifications .......................................................... 367
1. Albert of Saxony ................................................................ 368
2. John Wycliffe ..................................................................... 368
3. Paul of Venice .................................................................... 369
4. John De Magistris .............................................................. 370
5. Peter of Ailly ...................................................................... 371
6. George of Brussels ............................................................. 372
7. John Major ......................................................................... 373
8. Peter Tartaretus .................................................................. 374
9. Jodocus Trutvetter .............................................................. 375
10. Domingo De Soto .............................................................. 376
C. Other Classifications .............................................................. 379
1. Stephen Brulifer ................................................................. 379
2. Zachary Coke ..................................................................... 380
3. John Scherzer ..................................................................... 380
4. Ludovicus Lossada ............................................................. 381
5. Jacob Dedelley ................................................................... 381
D. General Remarks ................................................................... 383
II. The Exposition of Reduplicative Propositions ............................ 385
1. The Medieval Analysis .......................................................... 386
2. The Compact Analysis ........................................................... 387
3. The Elimination of a Formal Analysis ................................... 392
4. Other Sorts of Reduplicative Propositions .....•....................... 394
5. Simple Propositions With Reduplicated Extremes ................ 398
III. Negative Reduplicative Forms ................................................... .400
TA BLE OF CONTENTS Xl
XIV. Inference Patterns of Reduplicative Propositions:
Supposition, Consequences, and Syllogisms ............................... .405
I. The Supposition of Reduplicative Terms ........... .406
,0 •••••••••••••••••••••••
I. Paul of Venice ................................................ '. ................... 406
2. Peter Tartaretus .................................................................. 408
3. Gaspar Lax .......................................................................... 409
4. Domingo De Soto .............................................................. 411
5. John Wycliffe ..................................................................... 411
II. Consequences ........................................................................ 414
III. Syllogistic .......................................... , ................................... 415
XV. Inference Patterns of Accidental Qua Propositions ....................... .422
I. The Fallacy of Secundum Quid Et Simpliciter .............. ~ ....... .423
I. Albert of Saxony .......................................... ~ ..................... 423
2. John Versor ........................................................................ 426
3. Ludovicus Lossada ............................................................. 428
II. Consequences of Parts and Wholes ....................................... .429
III. Accidental Consequences ...................................................... 430
XVI. Sophisms and Applications ........................................................... .435
I. Sophisms ................................................................................ 435
II. Inferences "and Syllogisms .................................................... .442
III. Leibniz: Reduplication, Identity, and Relations ................... .450
IV. Reduplication and Concrete Terms ...................................... .460
Conclusions ........................................................................................... 464
BOOK FIVE CONTEMPORARY PERSPECTIVES ON
QUA PROPOSITIONS .................................................................. 467
XVII.Modern Views on Reduplication ................................................... 468
I. Aristotelian Views in the Modem Setting .............................' 468
A. Reduplicative Propositions in Critical Philosophy .......... .468
I. Wilhelm Krug ................................................................. 468
2. Bernard Bolzano ............................................................. 471
B. The Fallacy of Secundum Quid et Simpliciter .................. 473
1. Richard Whately and Auguste De Morgan .................... .474
2. John Stuart Mill .............................................................. 477
II. The Neo-Scholastics .............................................................. 478
I. Wilhelm Pesch ................................................................ 478
2. Jacques Maritain ............................................................. 480
3.E. M. Barth ..................................................................... 481
xii TABLE OF CONTENTS
III. Contemporary Research on Qua Propositions ...................... .483
1. Gottlob Frege .................................................................. 483
2. David Wiggins ................................................................ 485
3. Douglas Browning .......................................................... 487
4. Kit Fine ........................................................................... 489
5. Bangs Tapscott ............................................................... 493
6. C. L. Hamblin ................................................................ 497
7. Mereology ...................................................................... 498
XVIII. Results .................................................................................. 500
I. Summary of the History of the Development
of the Theory of Reduplication .............................................. 500
II. A Theory of Reduplication .................................................... 507
III. Applications ........................................................................... 522
Bibliography ........................................................................................... 529
Index of Numbered Propositions ............................................................. 539
General Index .......................................................................................... 541
