The Logical Syntax of Greek Mathematics (Sources and Studies in the History of Mathematics and Physical Sciences)

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