Articulating medieval logic:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford University Press
2014
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XI, 331 S. |
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Datensatz im Suchindex
| _version_ | 1804152015249473536 |
|---|---|
| adam_text | Contents
List of
Tables
xii
Preface
xiii
Introduction
1
1.
An Overview of Aristotelian Logic as seen by Medieval Logicians
6
1.1
Categorical propositions
6
1.2
Logical relations among categorical propositions
9
1.3
The square of opposition
10
1.4
Issues concerning empty terms
12
1.4.1
Universal affirmatives
12
1.4.2
Particular negatives
12
1.5
Conversions
14
1.6
Syllogisms
15
1.7
Infinite negation
18
1.8
Formal validity
18
2.
Aristotle s Proofs of Conversions and Syllogisms
21
2.1
Formal derivations
21
2.2
Proofs of the conversion principles
25
2.2.1
Conversion of universal negatives
26
2.2.2
Conversion of universal affirmatives (conversion per accidens)
27
2.2.3
Conversion of particular affirmatives
28
2.3
Reduction of all syllogisms to perfect ones
30
2.3.1
Figure
1
syllogisms
30
2.3.2
Reduction to the first figure
31
2.3.3
Figure
2
syllogisms
32
2.3.4
Barocho
33
2.3.5
Figure
3
syllogisms
34
2.3.6
First figure indirect moods
38
2.4
Proving the first figure syllogisms
39
2.5
Propositions with repeated terms
40
2.6
The indispensability of exposition and expository syllogism
41
2.7
A contemporary assessment of Aristotle s basic theory
43
2.7.1
Generalized quantifiers
43
2.7.2
Axiomatizing generalized quantifiers
48
2.7.3
A qualification concerning existential import
49
2.8
Singular propositions
50
2.9 13th-century
texts
51
2.10
Summary of Aristotle s rules of Droof
53
Vlil
CONTENTS
3.
Quantifying Predicates, Singular Term Predicates, Negative Terms
56
3.1
Expanded notation
56
3.2
Equipollences
60
3.3
Semantics and rules
62
3.4
Singular terms as predicates
67
3.5
Infinitizing negation and conversion
72
3.5.1
Conversion by contraposition and obversion
74
3.6
Completeness of the rules
77
3.6.1
Verbs other than the copula
77
3.7
Summary of the rules of proof used so far
77
4.
Linguisti
81
4.1
Basics
81
4.2
Categorical propositional logical forms
87
4.3
Rules of inference
90
4.3.1
Some theorems that maybe of interest
92
4.3.1.1
Symmetry of is
93
4.4
Signification and supposition
95
4.5
Truth conditions
98
4.5.1
Affirmative and negative propositions and existential import
109
4.6
Validity
110
4.7
Completeness of the rules
113
5.
Expanding the Notation
123
5.1
Adjectives
123
5.2
Intransitive verbs
126
5.2.1
Being
128
5.3
Transitive verbs
129
5.4
Additional rules for parasitic terms
133
5.5
Some complex terms
134
5.5.1
Attributive adjectives and participles modifying nouns
134
5.5.2
Participles of transitive verbs with their obj ects
135
5.5.3
Terms modified by complex terms
138
5.6
Relative clauses
140
5.6.1
Semantics of relative clauses
142
5.6.2
Representing ordinary language Latin (and English)
143
5.7
Genitives
145
5.7.1
What the genitive means
146
5.7.2
Relational common nouns
147
5.7.3
Non-relational uses
148
5.7.4
Non-relational
possessives 150
5.7.5
Complex terms with genitives
152
5.8
Demonstratives
153
5.9
Molecular propositions
155
5.9.1
Constructions with free markers
158
6.
Some
Illustrative
Topics
160
6.1 Relational
expressions and
De
Morgan s challenge
160
6.1.1
Dealing with explicit relational expressions
161
6.1.2
Dealing with parasitic terms
162
6.2 Buridan
on subjects and predicates
164
6.2.1
Identifying subjects and predicates
164
6.2.2
Subjects and predicates in Linguish
167
6.2.3
Agreeing with
Buridan
(mostly)
169
6.2.4
The asymmetry of subjects and predicates
173
6.2.4.1
Way
1 :
Quantifier signs
173
6.2.4.2
Way
2:
Negative signs
175
6.3
Simple and complex terms
176
6.3.1
Some interesting constructions
176
6.3.2
Simple and complex terms
180
6.3.2.1
The first type of determinable/deter
minant
pairs
181
6.3.2.2
The second type of determinable/determinant pairs
181
7.
Modes of Personal Supposition
184
7.1
Introduction to medieval theory
184
7.2
The
14th-century
definitions of the modes
186
7.3
Clarification of the definitions
189
7.3.1
The nature of ascent and descent
190
7.3.2
Occurrences of terms have modes of supposition
190
7.3.3
Repeated occurrences must be ignored
190
7.3.4
Empty terms
192
7.4
Causes of the modes
193
7.5
Restricted descent and parasitic terms
197
7.6
A variant account of merely confused supposition
199
7.7
Useful inferences
202
7.7.1
Superiors and inferiors
202
7.7.2
Monotonicity
205
7.7.3
Parasitic terms
206
7.7.4
Additional useful inferences and
non-
inferences
207
7.8
Refining the theory: Distinguishing two kinds of distributive supposition
209
7.9
Causes of the refined modes
211
7.9.1
Modes of supposition in Linguish
212
7.10
Useful inferences again
214
7.10.1
Complete induction
214
7.10.2
Switching scopes (thereby switching modes of supposition)
216
7.10.3
Algorithms
217
7.11
Modes of supposition as analyses of quantification
218
7.11.1
Categorical propositions whose terms are non-parasitic and simple
220
7.11.2
Categorical propositions whose terms are simple with one or more
parasitic terms
221
7.11.3
Categorical propositions with complex terms
221
7.11.4
Rules from inferior to superior and from superior to inferior
222
7.12
Global
quantificational import
223
7.12.1
What are modes of common personal supposition?
223
7.12.2
Causes of the modes and global import
225
7.12.3
Parasitic terms
226
8.
Relatives (Anaphoric Words)
227
8.1
Relatives of identity
227
8.2
Reflexive pronouns
229
8.3
Relatives in Linguish
233
8.3.1
The semantics of relatives that fall within the scope of their antecedents
234
8.3.2
Rules of inference for indexed expressions
236
8.4
Non-reflexive relatives of identity
239
8.5
Applying the singulation theory
244
8.6
An application of relatives to syllogistic
252
8.7
Donkey anaphora
254
8.8
Common term relatives of identity and diversity
256
9.
Comparison of Medieval Logic with Contemporary Logic
259
9.1
The expressive power of medieval logic
259
9.1.1
Medieval logic without anaphoric pronouns
260
9.1.2
Medieval logic with anaphoric expressions
261
9.2
Representing medieval logic within modern predicate logic with identity
262
9.3
Representing modern logic within medieval logic: The problem of
existential import
262
9.4
Representing modern logic within medieval logic: Grammatical issues
265
9.5
First-order arithmetic in medieval logic
269
9.5.1
Peano s postulates
269
9.5.2
Definition of addition
271
9.5.3
Multiplication
275
10.
Ampliation and Restriction
276
10.1
Univocation as the source of ampliation and restriction
276
10.2
Ampliation and restriction by tenses
280
10.2.1
Tenses
280
10.2.2
A Complexity: Ambiguity or disjunction?
280
10.2.3
Coordination of times in tensed sentences
281
10.2.3.1
Coordination of times between subject and predicate
281
10.2.3.2
Tenses with relative clauses
282
10.2.3.3
Coordination of times among parts of the subject or predicate
285
10.2.3.4
Subclauses
and coordination of tense
285
10.2.4
Buridan s special use of appellation
286
10.2.5
Tenses in Linguish
288
10.2.5.1
If singular terms are not subject to restriction and ampliation
294
10.2.6
Infinitizing negation
294
10.3
Ampliation by modal terms
295
10.3.1
What are modal propositions?
295
10.3.2
Modal propositions: Semantics
296
10.33
Differences between medieval and modern readings
297
103.4
Modal propositions in Linguish
298
10.4
Ampliation due to semantic words
299
10.4.1
Looking ahead
299
10.5
Ampliation due to words which pertain to the soul
300
10.6
Promising and owing
302
Appendix: Artificial Quantifiers in Early loth-Century Logic
306
1.
The signs
307
2.
What the signs mean
308
3.
The signs are, in a sense, logically dispensable
310
4.
A doubt: Certain examples do not work as advertised
311
5.
Another doubt: The paradigm use of sign
ď
is incoherent
313
6.
Some examples from John Major
315
Selected Bibliography
319
Index
328
Terence Parsons presents a new study of the development and logical complexity of
medieval logic. Basic principles of logic were used by Aristotle to prove conversion
principles and reduce syllogisms. Medieval logicians expanded Aristotle s notation
in several ways, such as quantifying predicate terms, as in No donkey is every animal ,
and allowing singular terms to appear in predicate position, as in Not every donkey
is Brownie ; with the enlarged notation come additional logical principles. The
resulting system of logic is able to deal with relational expressions, as in
De
Morgan s
puzzles about heads of horses. A crucial issue is a mechanism for dealing with anaphoric
pronouns, as in Every woman loves her mother . Parsons illuminates the ways in
which medieval logic is as rich as contemporary first-order symbolic logic, though
its fall potential was not envisaged at the time. Along the way, he provides a detailed
exposition and examination of the theory of modes of common personal supposition,
and the useful principles of logic included with it. An appendix discusses the artificial
signs introduced in the fifteenth century to alter quantifier scope.
|
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| spelling | Parsons, Terence 1939- Verfasser (DE-588)1069691178 aut Articulating medieval logic Terence Parsons Oxford Oxford University Press 2014 XI, 331 S. txt rdacontent n rdamedia nc rdacarrier Geschichte 500-1500 gnd rswk-swf Logik (DE-588)4036202-4 gnd rswk-swf Logik (DE-588)4036202-4 s Geschichte 500-1500 z DE-604 Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027178468&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027178468&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Parsons, Terence 1939- Articulating medieval logic Logik (DE-588)4036202-4 gnd |
| subject_GND | (DE-588)4036202-4 |
| title | Articulating medieval logic |
| title_auth | Articulating medieval logic |
| title_exact_search | Articulating medieval logic |
| title_full | Articulating medieval logic Terence Parsons |
| title_fullStr | Articulating medieval logic Terence Parsons |
| title_full_unstemmed | Articulating medieval logic Terence Parsons |
| title_short | Articulating medieval logic |
| title_sort | articulating medieval logic |
| topic | Logik (DE-588)4036202-4 gnd |
| topic_facet | Logik |
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