The logical syntax of Greek mathematics / Fabio Acerbi.

Format:

Book

Author/Creator:

Acerbi, Fabio, author.

Series:

Sources and studies in the history of mathematics and physical sciences.

Sources and studies in the history of mathematics and physical sciences

Language:

English

Subjects (All):

Mathematics, Greek.

Physical Description:

1 online resource (401 pages)

Edition:

1st ed.

Place of Publication:

Cham, Switzerland : Springer, [2021]

Summary:

The aim of this monograph is to describe Greek mathematics as a literary product, studying its style from a logico-syntactic point of view and setting parallels with logical and grammatical doctrines developed in antiquity.

Contents:

Intro

TABLE OF CONTENTS

LIMINALIA

1. THE THREE STYLISTIC CODES OF GREEK MATHEMATICS

1.1. THE DEMONSTRATIVE CODE

1.2. THE PROCEDURAL CODE

1.3. THE ALGORITHMIC CODE

1.4. PUNCTUATING GREEK MATHEMATICAL TEXTS

1.5. THE ELEMENTS AND ITS LEXICAL CONTENT

2. VALIDATION AND TEMPLATES

2.1. ARISTOTLE AND GALEN ON LINGUISTIC TEMPLATES

2.2. SUBSENTENTIAL VALIDATION: FORMULAIC TEMPLATES

2.3. SENTENTIAL VALIDATION: SYNTACTIC TEMPLATES

2.4. LARGE-SCALE VALIDATION: ANALYSIS AND SYNTHESIS

2.4.1. Geometric analysis and synthesis

2.4.2. Validating algorithms and procedures by the "givens"

3. THE PROBLEM OF MATHEMATICAL GENERALITY

3.1. THE PRESENTIAL VALUE OF THE VERB "TO BE" IN THE SETTING-OUT

3.2. THE FUNCTION OF THE DENOTATIVE LETTERS

3.3. THE INDEFINITE STRUCTURE

3.4. ONTOLOGICAL COMMITMENT

3.5. OVERSYMMETRIZED DIAGRAMS

4. THE DEDUCTIVE MACHINE

4.1. ENUNCIATION AND CONCLUSION

4.2. SUPPOSITIONS AND "SETTING-OUT"

4.2.1. Determination

4.3. THE ROLE OF CONSTRUCTIONS

4.4. ANAPHORA

4.5. PROOF

4.5.1. The logic of relations

4.5.2. Metamathematical markers: potential and analogical proofs, references to the obvious, optative mood, personal verb forms

4.5.3. Postposed arguments

4.5.4. Instantiated and non-instantiated citations of theorems

4.5.5. Assumptions and coassumptions

5. THE LOGICAL SYNTAX

5.1. QUANTIFICATION

IMPLICIT AND EXPLICIT GENERALITY

5.1.1. Quantifiers

5.1.2. Determiners of arbitrariness

5.1.3. Determiners of indefiniteness

5.1.4. Generalizing qualifiers

5.1.5. The use of the article

5.1.6. Ordinals as variables

5.1.7. The indefinite conditionals of Stoic logic

5.2. MODALS

5.2.1. Reductions to the impossible

5.2.2. Arguments "for a contrapositive"

5.3. SENTENTIAL OPERATORS

5.3.1. Conditional

5.3.2. Paraconditional.

5.3.3. Negation

5.3.4. Disjunction

5.3.5. Conjunction

5.3.6. Syllogistic connectors

APPENDICES

APPENDIX A. PROBLEMS IN THE GREEK MATHEMATICAL CORPUS

APPENDIX B. THEOREMS OF THE DATA THAT HAVE A SYNTHETIC COUNTERPART AND EXTANT SOURCES ON GREEK ANALYSIS AND SYNTHESIS

APPENDIX C. ONOMASTICON

BIBLIOGRAPHY

INDICES

INDEX NOMINUM

INDEX FONTIUM

INDEX LOCORUM

INDEX RERUM.

Notes:

Includes bibliographical references and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

3-030-76959-3

OCLC:

1258366109