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Parsons, Terence / Парсонс, Теренс - Articulating Medieval Logic / Разборки со средневековой логикой

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Parsons, Terence / Парсонс, Теренс - Articulating Medieval Logic / Разборки со средневековой логикой
Articulating Medieval Logic / Разборки со средневековой логикой
Год издания: 2014
Автор: Parsons, Terence / Парсонс, Теренс
Жанр или тематика: Монография
Издательство: Oxford University Press
ISBN: 978-0-19-968884-5
Язык: Английский
Формат: PDF
Качество: Издательский макет или текст (eBook)
Интерактивное оглавление: Да
Количество страниц: 331
Описание: Теренс Парсонс пытается разобраться, что в «аристотелевой логике» от Аристотеля и стоиков, а что — от средневековых схоластов, и какой аппарат матлогики может ухватить средневековый вклад. В приложениях рассматривается то, что можно назвать «средневековой матлогикой» — символизмы, использовавшиеся самими схоластами.
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 full 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.
Примеры страниц

List of Tables
Preface xii
xiii
Introduction 1
1. An Overview of Aristotelian Logic as seen by Medieval Logicians
Categorical propositions
Logical relations among categorical propositions
Th e square of opposition
Issues concerning empty terms
1.4.1 Universal affi rmatives
1.4.2 Particular negatives
Conversions
Syllogisms
Infi nite negation
Formal validity
2. Aristotle’s Proofs of Conversions and Syllogisms
2.1 Formal derivations
2.2 Proofs of the conversion principles
2.2.1 Conversion of universal negatives
2.2.2 Conversion of universal affi rmatives (conversion per accidens)
2.2.3 Conversion of particular affi rmatives
2.3 Reduction of all syllogisms to perfect ones
2.3.1 Figure 1 syllogisms
2.3.2 Reduction to the fi rst fi gure
2.3.3 Figure 2 syllogisms
2.3.4 Barocho
2.3.5 Figure 3 syllogisms
2.3.6 First fi gure indirect moods
2.4 Proving the fi rst fi gure syllogisms
2.5 Propositions with repeated terms
2.6 Th e indispensability of exposition and expository syllogism
2.7 A contemporary assessment of Aristotle’s basic theory
2.7.1 Generalized quantifi ers
2.7.2 Axiomatizing generalized quantifi ers
2.7.3 A qualifi cation concerning existential import
2.8 Singular propositions
2.9 13th-century texts
2.10 Summary of Aristotle’s rules of proof
viii
contents
3. Quantifying Predicates, Singular Term Predicates, Negative Terms
Expanded notation
Equipollences
Semantics and rules
Singular terms as predicates
Infi nitizing negation and conversion
3.5.1 Conversion by contraposition and obversion
3.6 Completeness of the rules
3.6.1 Verbs other than the copula
3.7 Summary of the rules of proof used so far
4. Linguish
4.1 Basics
4.2 Categorical propositional logical forms
4.3 Rules of inference
4.3.1 Some theorems that may be of interest
4.3.1.1 Symmetry of ‘is’
4.4 Signifi cation and supposition
4.5 Truth conditions
4.5.1 Affi rmative and negative propositions and existential import
4.6 Validity
4.7 Completeness of the rules
5. Expanding the Notation
5.1 Adjectives
5.2 Intransitive verbs
5.2.1 Being
5.3 Transitive verbs
5.4 Additional rules for parasitic terms
5.5 Some complex terms
5.5.1 Attributive adjectives and participles modifying nouns
5.5.2 Participles of transitive verbs with their objects
5.5.3 Terms modifi ed by complex terms
5.6 Relative clauses
5.6.1 Semantics of relative clauses
5.6.2 Representing ordinary language Latin (and English)
5.7 Genitives
5.7.1 What the genitive means
5.7.2 Relational common nouns
5.7.3 Non-relational uses
5.7.4 Non-relational possessives
5.7.5 Complex terms with genitives
5.8 Demonstratives
5.9 Molecular propositions
5.9.1 Constructions with free markers
6. Some Illustrative Topics
6.1 Relational expressions and De Morgan’s challenge
6.1.1 Dealing with explicit relational expressions
6.1.2 Dealing with parasitic terms
6.2 Buridan on subjects and predicates
6.2.1 Identifying subjects and predicates
6.2.2 Subjects and predicates in Linguish
6.2.3 Agreeing with Buridan (mostly)
6.2.4 Th e asymmetry of subjects and predicates
6.2.4.1 Way 1: Quantifi er signs
6.2.4.2 Way 2: Negative signs
6.3 Simple and complex terms
6.3.1 Some interesting constructions
6.3.2 Simple and complex terms
6.3.2.1 Th e fi rst type of determinable/determinant pairs
6.3.2.2 Th e second type of determinable/determinant pairs
7. Modes of Personal Supposition
7.1 Introduction to medieval theory
7.2 Th e 14th-century defi nitions of the modes
7.3 Clarifi cation of the defi nitions
7.3.1 Th e nature of ascent and descent
7.3.2 Occurrences of terms have modes of supposition
7.3.3 Repeated occurrences must be ignored
7.3.4 Empty terms
7.4 Causes of the modes
7.5 Restricted descent and parasitic terms
7.6 A variant account of merely confused supposition
7.7 Useful inferences
7.7.1 Superiors and inferiors
7.7.2 Monotonicity
7.7.3 Parasitic terms
7.7.4 Additional useful inferences and non-inferences
7.8 Refi ning the theory: Distinguishing two kinds of distributive supposition
7.9 Causes of the refi ned modes
7.9.1 Modes of supposition in Linguish
7.10 Useful inferences again
7.10.1 Complete induction
7.10.2 Switching scopes (thereby switching modes of supposition)
7.10.3 Algorithms
7.11 Modes of supposition as analyses of quantifi cation
7.11.1 Categorical propositions whose terms are non-parasitic and simple
7.11.2 Categorical propositions whose terms are simple with one or more
parasitic terms
7.11.3 Categorical propositions with complex terms
7.11.4 Rules from inferior to superior and from superior to inferior
7.12 Global quantifi cational import
7.12.1 What are modes of common personal supposition?
7.12.2 Causes of the modes and global import
7.12.3 Parasitic terms
8. Relatives (Anaphoric Words)
8.1 Relatives of identity
8.2 Refl exive pronouns
8.3 Relatives in Linguish
8.3.1 Th e semantics of relatives that fall within the scope of their antecedents
8.3.2 Rules of inference for indexed expressions
8.4 Non-refl exive relatives of identity
8.5 Applying the singulation theory
8.6 An application of relatives to syllogistic
8.7 Donkey anaphora
8.8 Common term relatives of identity and diversity
9. Comparison of Medieval Logic with Contemporary Logic
9.1 Th e expressive power of medieval logic
9.1.1 Medieval logic without anaphoric pronouns
9.1.2 Medieval logic with anaphoric expressions
9.2 Representing medieval logic within modern predicate logic with identity
9.3 Representing modern logic within medieval logic: Th e problem of
existential import
9.4 Representing modern logic within medieval logic: Grammatical issues
9.5 First-order arithmetic in medieval logic
9.5.1 Peano’s postulates
9.5.2 Defi nition of addition
9.5.3 Multiplication
10. Ampliation and Restriction
10.1 Univocation as the source of ampliation and restriction
10.2 Ampliation and restriction by tenses
10.2.1 Tenses
10.2.2 A Complexity: Ambiguity or disjunction?
10.2.3 Coordination of times in tensed sentences
10.2.3.1 Coordination of times between subject and predicate
10.2.3.2 Tenses with relative clauses
10.2.3.3 Coordination of times among parts of the subject or predicate
10.2.3.4 Subclauses and coordination of tense
10.2.4 Buridan’s special use of appellation
10.2.5 Tenses in Linguish
10.2.5.1 If singular terms are not subject to restriction and ampliation
10.2.6 Infi nitizing negation
10.3 Ampliation by modal terms
10.3.1 What are modal propositions?
10.3.2 Modal propositions: Semantics
10.3.3 Diff erences between medieval and modern readings
10.3.4 Modal propositions in Linguish
10.4 Ampliation due to semantic words
10.4.1 Looking ahead
10.5 Ampliation due to words which pertain to the soul
10.6 Promising and owing
Appendix: Artificial Quantifiers in Early 16th-Century Logic
The signs
What the signs mean
The signs are, in a sense, logically dispensable
A doubt: Certain examples do not work as advertised
Another doubt: The paradigm use of sign ‘d’ is incoherent
Some examples from John Major
Selected Bibliography
Index
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