LEADER 03827nam 2200517 450 001 9910485585903321 005 20230622200746.0 010 $a3-030-76959-3 035 $a(CKB)5590000000503304 035 $a(MiAaPQ)EBC6676264 035 $a(Au-PeEL)EBL6676264 035 $a(OCoLC)1258366109 035 $a(PPN)259391182 035 $a(EXLCZ)995590000000503304 100 $a20220326d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe logical syntax of Greek mathematics /$fFabio Acerbi 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (401 pages) 225 1 $aSources and studies in the history of mathematics and physical sciences 311 $a3-030-76958-5 320 $aIncludes bibliographical references and index. 327 $aIntro -- 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. 327 $a5.3.3. Negation -- 5.3.4. Disjunction -- 5.3.5. Conjunction -- 5.3.6. Syllogistic connectors -- APPENDICES -- APPENDIX A. PROBLEMS IN THE GREEK MATHEMATICAL CORPUS -- APPENDIX B. THEOREMS OF THE DATA THAT HAVE A SYNTHETIC COUNTERPART AND EXTANT SOURCES ON GREEK ANALYSIS AND SYNTHESIS -- APPENDIX C. ONOMASTICON -- BIBLIOGRAPHY -- INDICES -- INDEX NOMINUM -- INDEX FONTIUM -- INDEX LOCORUM -- INDEX RERUM. 410 0$aSources and studies in the history of mathematics and physical sciences. 606 $aMathematics, Greek 606 $aMatemàtica grega$2thub 606 $aHistòria$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematics, Greek. 615 7$aMatemàtica grega 615 7$aHistòria 676 $a510.938 700 $aAcerbi$b Fabio$0611846 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910485585903321 996 $aThe Logical Syntax of Greek Mathematics$91985022 997 $aUNINA