The logical syntax of Greek mathematics / / Fabio Acerbi

• Record Nr.: UNINA9910485585903321
• Autore: Acerbi Fabio
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2021]; ©2021
• ISBN: 3-030-76959-3
• Descrizione fisica: 1 online resource (401 pages)
• Collana: Sources and studies in the history of mathematics and physical sciences
• Disciplina: 510.938
• Soggetti: Mathematics, Greek; Matemàtica grega; Història; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.