Ways into the Logic of Alexander of Aphrodisias (Philosophia Antiqua 62)

195 Pages·1995·6.99 MB·English

by  Kevin L. Flannery

PHILOSOPHIA ANTIQUA
A SERIES OF STUDIES
ON ANCIENT PHILOSOPHY
FOUNDED BY]. H. WASZINK AND W.]. VERDENIUS
EDITED BY
J. MANSFELD, D.T. RUNIA
J.C.M. VAN WIND EN
VOLUME LXII
KEVIN L. F1.ANNERY , s.].
WAYS INTO THE LOGIC OF
ALEXANDER OF APHRODISIAS
WAYS INTO THE LOGIC
OF
ALEXANDER OF APHRODISIAS
BY
KEVIN L. FLANNERY, S.].
E.J. BRILL
LEIDEN . NEW YORK· KOLN
1995
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
Resources.
Library of Congress Cataloging-in-Publication Data
Flannery, Kevin L.
Ways into the logic of Alexander of Aphrodisias / by Kevin L.
Flannery.
p. cm. - (Philosophia antiqua, ISSN 0079-1687; v. 62)
Includes bibliographical references (p. ) and indexes.
ISBN 9004099980 (cloth: alk. paper)
I. Alexander, of Aphrodisias. 2. Logic, Ancient. 1. Title.
H. Series.
B535.A64F57 1995
160'.92-dc20 94-42819
CIP
Die Deutsche Bibliothek - CIP-Einheitsaufnalune
Flannery, Kevin L.:
Ways into the logic of Alexander of Aphrodisias / by Kevin L.
Flannery. - Leiden ; New York; Koln: Brill, 1995
(Philosophia antiqua ; Vol. 62)
ISBN 90--{)4-09998--{)
NE:GT
ISSN 0079-1687
ISBN 90 04 09998 0
© Copyright 1995 by EJ. Brill, Leiden, The Netherlands
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PRINTED IN THE NETHERLANDS
Dedicated to
FRANCIS R. and MARY C. FLANNERY
(my parents)

TABLE OF CONfENTS
General Introduction .................... ............................................ XIX
Chapter One: Ecthesis
1.1 Introduction .............. ...................................................... 1
1.2 Expository matters .. ..... ... .... ............. ..... ....... ... ...... ......... 4
1.2.1 A modern treatment ......................... u................. 4
1.2.2 The definitional proof of e-conversion .............. 6
1.2.2.1 The context ............................................. 6
1.2.2.2 The basis of the definitional proof ....... 8
1.2.2.3 The definitional proof itself ................... 10
1.2.3 Perceptual ecthesis ............................................... 16
1.2.3.1 Perceptual e-conversion .......................... 16
1.2.3.2 The perceptual proof of Darapti .......... 19
1.2.4 Syllogistic ecthesis ................................................ 21
1.2.4.1 The proof of Darapti ............................. 21
1.2.4.2 The proof of e-conversion ..................... 23
1.2.4.3 The proofs of apodeictic Baroco
and Bocardo ............................................ 23
1.3 Interpretation ................................................................. 25
1.3.1 Definitional and perceptual proofs
compared ........ ....... ........ .............. ....... .............. .... 25
1.3.2 Alexander the Theophrastan .............................. 27
1.3.3 The role of quantifiers ........................................ 30
1.3.4 Light shed on the Darapti proof ....................... 35
1.3.5 Two Lukasiewiczian objections ........................... 38
1.3.5.1 The role of singulars .............................. 38
1.3.5.2 The logical status of the perceptual ..... 40
1.3.6 Syllogistic proofs: an inconsistency? ................... 45
1.3.6.1 Resolution ................................................ 46
1.3.6.2 Some texts in Alexander ........................ 49
1.4 Conclusion ....................................................................... 52
Chapter Two: The contents of On mixed premisses
2.1 Introduction .................................................................... 53
2.2 What Philoponus says about On mixed premisses ........... 59
Vlll TABLE OF CONTENTS
2.3 Pseudo-Amrnonius, in A.Pr.38"741· ................................. 65
2.3.1 Philoponus and pseudo-Ammonius
compared ... ..................................................... ...... 68
2.3.2 A difference re: the reductio solution ................ 70
2.4 The vexed question of hypothetical necessity ............. 74
2.4.1 Philoponus and pseudo-Ammonius .................... 74
2.4.2 Alexander, in A.Pr.140.14-28 .............................. 75
2.4.3 Alexander, in A.Pr.140.25-28 .............................. 78
2.4.4 Alexander, in A.Pr.140.29-34 .............................. 81
2.4.5 Alexander, in A.Pr.141.1-6 .................................. 83
2.4.6 Alexander, in A.Pr.141.6-16 ................................ 85
2.4.7 Alexander, in A.Pr.129-30 ................................... 86
2.5 The Arabic evidence ..................................................... 92
2.5.1 Averroes material and On mixed premisses ............ 92
2.5.2 Evidence in Averroes' Qyestions ........................... 94
2.5.3 The nature of the necessary ............................... 99
2.5.3.1 The 'Refutation' fragment ..................... 99
2.5.3.2 Alexander on grades of necessity .......... 101
2.5.3.3 Philoponus a plurimis naeuis
vindicatus .................................................... 106
2.6 Conclusion ...................................................................... 108
Chapter Three: Logical Matter
3.1 Introduction .................................................................... 109
3.2 What is matter? (initial remarks) .................................. 110
3.2.1 The modern conception ...................................... 110
3.2.2 Alexander's understanding .................................. 111
3.2.3 Dummy letters (modern) ..................................... 114
3.2.4 Dummy letters (ancient) ...................................... 116
3.2.5 Matter as "stuff"? ................................................ 118
3.3 Some relevant texts ....................................................... 123
3.3.1 in Top.21 ............................................................... 123
3.3.2 in Top.10 ............................................................... 125
3.3.3 in Metaph.148 ........................................................ 126
3.3.4 in A.Pr.13-14 ........................................................ 129
3.4 Natural deduction in Alexander ................................... 131
3.5 Can matter be said to "conclude"? ............................. 136
3.5.1 Premisses as efficient causes ................................ 142
3.6 Conclusion ...................................................................... 144
TABLE OF CONTENTS IX
Bibliography
Primary sources ..................................................................... 146
Secondary sources ................................................................. 148
Appendix: Logical Symbols and Conventions ..... ...... ...... .... ... 154
Index of passages cited ............................................................. 157
Index of names ..... ............... ........ .............. ....... ..... ... ... ...... ....... 166
Subject index ............................................................................. 170
TABLE OF CONTENTS (ANALYTICAL)
Chapter One: Ecthesis
1.1 [po 1J Introduction.
1.2 [po 4J The lie of the land: the different types of ecthetic
proof.
1.2.1 [po 4J A modern treatment. Lukasiewicz's analysis of
ecthesis has certain advantages (e.g., non-reliance on
conversion of the particular affinnative) but also one
disadvantage: the ectethen-or "that which is taken
out"-is not a singular.
1.2.2 [po 6J Alexander's definitional proof of conversion of the
universal negative.
1.2.2.1 [po 6J The context. It is important first of all to under
stand why Alexander presents various types of ecthetic
proof. The definitiona1 and perceptual proofs are
logically prior to the syllogistic itself. Of these two,
the perceptual proof is the better supported textu
ally.
1.2.2.2 [po 8J The basis of the definitional proof: the dictum de omni
et nullo. This gives us at least one formal rule: i.e.,
a rule (ke) which says that lCCX'tU 1tcxv'to~ and EV OACP
'tip work in opposite "directions."
1.2.2.3 [po lOJ The definitional proof of conversion of the univer
sal negative set out formally in two versions. The
first version points up areas of obscurity; closer
analysis reveals the need of two additional formal
rules (based on the dictum de omni): (uk) and (te).
These are used to move between standard syllogis
tic propositions like BiA and propositions about
singulars.t (See section 1.3.3.) Also involved in the
proof is the natural deduction procedure "existen
tial quantifier elimination" (or EE). These rules and
t See Appendix ("Logical Symbols and Conventions").