Robert Kilwardby's Science of Logic: A Thirteenth-Century Intensional Logic

330 Pages·2019·1.943 MB·English

by  Paul Thom

Robert Kilwardby’s Science of Logic
Investigating Medieval Philosophy
Managing Editor
John Marenbon
Editorial Board
Margaret Cameron
Nadja Germann
Simo Knuuttila
Martin Lenz
Christopher J. Martin
volume 14
The titles published in thisseries are listed at brill.com/imp
Robert Kilwardby’s Science
of Logic
A Thirteenth-Century Intensional Logic
By
Paul Thom
leiden | boston
The Library of Congress Cataloging-in-Publication Data is available online at http://catalog.loc.gov
Typeface for the Latin, Greek, and Cyrillic scripts: “Brill”. See and download: brill.com/brill-typeface.
ISSN 1879-9787
ISBN 978-90-04-40846-3 (hardback)
ISBN 978-90-04-40877-7 (e-book)
Copyright 2019 by Koninklijke Brill NV, Leiden, The Netherlands.
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Contents
Acknowledgements  ix
List of Figures and Tables  x
Abbreviations  xviii
Introduction  1
1 Logic as Science and Art  8
1 The Evolution of Logic  9
2 The Art of Logic  10
3 Branches of the Science of Logic  11
4 The Science of Logic as Sermocinal  13
5 The Science of Logic Distinguished from Other Content in the
Organon  15
6 Kilwardby’s Writings on Logic  17
7 Aspects of Kilwardby’s Thought  17
8 Formalisation  21
2 The Logic of Terms: Categories and Complex Terms  23
1 The Categories  24
2 Complex Terms  32
3 Formal Language  41
4 Models  42
5 Theorems  44
3 The Logic of Terms: Relations between Terms  48
1 The Predicables  48
2 Genus and Species  49
3 Differentia  54
4 Proprium  64
5 Accident  69
6 Formal Analysis  71
7 Formal Language  71
8 Models  72
9 Truth in a Model  72
10 Postulates  73
11 Theorems  74
vi Contents
4 The Logic of Statements: Assertoric Statements  79
1 Propositions and Statements  79
2 Assertoric Statements  81
3 Truth  82
4 Ut nunc assertorics  84
5 Simpliciter Assertorics  88
6 Natural simpliciter Assertorics  90
7 Opposition and Equipollence  91
8 Conversion  96
9 Non-Aristotelian Consequences among Assertorics  97
10 Formal Analysis  98
11 Theorems  99
5 The Logic of Statements: Necessity and Possibility Statements  106
1 Modal Statements  106
2 Necessity Statements  108
3 Possibility Statements  126
4 Formal Analysis  126
5 Formal Language  127
6 Models  127
7 Theorems  128
6 The Logic of Statements: Contingency Statements  138
1 Unampliated Contingencies  139
2 Kilwardby’s Examples  144
3 Ampliated Contingencies  146
4 Kilwardby’s Rules for the Truth of Ampliated Contingency
Statements  148
5 Kilwardby’s Examples  149
6 Formal Analysis  153
7 Theorems  154
7 The Logic of Inferences: Consequences  161
1 Consequences According to the Relations between Terms  161
2 Formal Consequences  164
3 Pure Rules of Consequence  167
4 Rules of Consequence and Conversion  168
5 Rules of Consequence and Opposition  168
6 Rules of Consequence, Opposition and Repugnance  170
7 Rules of Consequence and Possibility  172
8 Rules of Consequence and Assertion  172
Contents vii
9 Rules of Consequence and Denial  172
10 Essential Consequences  173
11 Essential Consequence and Essential Inseparability  179
12 Syllogistic Consequences  179
13 Formal Analysis  181
14 Truth Conditions  182
15 Postulates  182
16 Theorems  182
8 The Logic of Inferences: Assertoric Syllogisms  185
1 Syllogistic Figures and Moods  185
2 Reduction  188
3 Perfection  195
4 Being Said of All  197
5 Families of Syllogism  201
6 Principles, Validity, Perfectibility  202
7 Mixed ut nunc / simpliciter Inferences  205
8 Summary  206
9 Formal Analysis  207
10 Generative Rules  207
11 Theorems  209
9 The Logic of Inferences: Necessity Syllogisms  221
1 Family 3. The LLL Family  221
2 Principles for LL Premises  222
3 Being Said of All  222
4 Reduction  224
5 Summary  231
6 Family 4. The LX L Family  231
l
7 Principles for L / X Premises  232
l
8 Being Said of All  232
9 Inferences Related to the Perfect Syllogisms  237
10 Reduction  241
11 Summary  243
12 Formal Analysis  244
13 Theorems  244
10 The Logic of Inferences: Contingency Syllogisms  250
1 Unrestricted Syllogistic Conversion in Family 3  250
2 Unrestricted Syllogistic Conversion in Family 4  257
3 Family 5. The Q’ Q’ Q’ Family  258
viii Contents
4 Family 6. The QX Q Family  262
l
5 Family 7. The QLQ Family  266
6 Formal Analysis  272
11 The Logic of Inferences: Non-perfectible Inferences  282
1 xq Premises  282
2 Realised Modals  292
3 Formal Analysis  296
4 Envoi  301
References  303
Modern Author Index  307
Subject Index  308
Ancient an Medieval Author Index  310