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Logical Syntax of Greek Mathematics 1st ed. 2021 [Kõva köide]

  • Formaat: Hardback, 396 pages, kõrgus x laius: 235x155 mm, kaal: 776 g, 9 Illustrations, color; 3 Illustrations, black and white; XII, 396 p. 12 illus., 9 illus. in color., 1 Hardback
  • Sari: Sources and Studies in the History of Mathematics and Physical Sciences
  • Ilmumisaeg: 23-Jun-2021
  • Kirjastus: Springer Nature Switzerland AG
  • ISBN-10: 3030769585
  • ISBN-13: 9783030769581
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Logical Syntax of Greek Mathematics 1st ed. 2021Suurem pilt
  • Formaat: Hardback, 396 pages, kõrgus x laius: 235x155 mm, kaal: 776 g, 9 Illustrations, color; 3 Illustrations, black and white; XII, 396 p. 12 illus., 9 illus. in color., 1 Hardback
  • Sari: Sources and Studies in the History of Mathematics and Physical Sciences
  • Ilmumisaeg: 23-Jun-2021
  • Kirjastus: Springer Nature Switzerland AG
  • ISBN-10: 3030769585
  • ISBN-13: 9783030769581
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783030769581.html
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. In this way, major philosophical themes such as the expression of mathematical generality and the selection of criteria of validity for arguments can be treated without anachronism. Thus, the book is of interest for both historians of ancient philosophy and specialists in Ancient Greek, in addition to historians of mathematics.

This volume is divided into five parts, ordered in decreasing size of the linguistic units involved. The first part describes the three stylistic codes of Greek mathematics; the second expounds in detail the mechanism of "validation"; the third deals with the status of mathematical objects and the problem of mathematical generality; the fourth analyzes the main features of the "deductive machine," i.e. the suprasentential logical system dictated by the traditional division of a mathematical proposition into enunciation, setting-out, construction, and proof; and the fifth deals with the sentential logical system of a mathematical proposition, with special emphasis on quantification, modalities, and connectors. A number of complementary appendices are included as well. 

Arvustused

This book is an English version, with expansions and improvements ... . this book is not an argument to be read cover-to-cover, but rather serves as a repository for many of the insights and views that the author developed over his  years of working on these sources. ... This is an important book on the language of Greek mathematical texts, and scholars of these sources will find much that is useful in its pages. (Nathan Sidoli, MAA Reviews, March 29, 2024)





This is a deep and detailed linguistic study of ancient Greek mathematical texts. This wide-ranging book exploits the resources of several disciplines including classical philology, manuscript studies, statistical analysis, and computational linguistics, as well as the history and philosophy of mathematics. It will doubtless be much used as a reference work in those disciplines. (Paul Thom, Mathematical Reviews, May, 2022)

Liminalia ix
1 The Three Stylistic Codes Of Greek Mathematics
1(36)
1.1 The demonstrative code
2(10)
1.2 The procedural code
12(7)
1.3 The algorithmic code
19(4)
1.4 Punctuating greek mathematical texts
23(2)
1.5 The Elements and its lexical content
25(12)
2 Validation And Templates
37(44)
2.1 Aristotle and Galen on linguistic templates
39(3)
2.2 Subsentential validation: formulaic templates
42(6)
2.3 Sentential validation: syntactic templates
48(5)
2.4 Large-scale validation: analysis and synthesis
53(28)
2.4.1 Geometric analysis and synthesis
53(15)
2.4.2 Validating algorithms and procedures by the "givens"
68(13)
3 The Problem Of Mathematical Generality
81(22)
3.1 The presential value of the verb "to be" in the setting-out
84(2)
3.2 The function of the denotative letters
86(11)
3.2.1 Denotative letters as "letter-labels"
90(7)
3.3 The indefinite structure
97(6)
34 Ontological Commitment
103(10)
3.5 Oversymmetrized diagrams
110(3)
4 The Deductive Machine
113(98)
4.1 Enunciation and conclusion
113(8)
4.2 Suppositions and "setting-out"
121(27)
4.2.1 Determination
143(5)
4.3 The role of constructions
148(15)
4.4 Anaphora
163(3)
4.5 Proof
166(45)
4.5.1 The logic of relations
166(1)
4.5.1.1 Aristotle and Galen on relations
166(3)
4.5.1.2 Relations and predicates
169(2)
4.5.1.3 The fundamental criterion: the position of the relational operator
171(8)
4.5.1.4 Interactions between relations and the deductive machine: transitivity, symmetry, stability
179(15)
4.5.2 Metamathematical markers: potential and analogical proofs, references to the obvious, optative mood, personal verbal forms
194(6)
4.5.3 Postposed arguments
200(2)
4.5.4 Instantiated and non-instantiated citations of theorems
202(3)
4.5.5 Assumptions and coassumptions
205(6)
5 The Logical Syntax
211(106)
5.1 Quantification; implicit and explicit generality
211(31)
5.1.1 Quantifiers
213(9)
5.1.2 Determiners of arbitrariness
222(4)
5.1.3 Determiners of indefiniteness
226(7)
5.1.4 Generalizing qualifiers
233(6)
5.1.5 The use of the article
239(3)
5.16 Ordinals as variables
242(7)
5.1.7 The indefinite conditionals of Stoic logic
246(3)
5.2 Modals
249(16)
5.2.1 Reductions to the impossible
251(9)
5.2.2 Arguments "for a contrapositive"
260(5)
5.3 Sentential operators
265(52)
5.3.1 Conditional
265(4)
5.3.2 Paraconditional
269(7)
5.3.3 Negation
276(7)
5.3.4 Disjunction
283(7)
5.3.5 Conjunction
290(14)
5.3.6 Syllogistic connectors
304(13)
APPENDICES
317(14)
A Problems in the Greek mathematical corpus
319(3)
B Theorems of the Data that have a synthetic counterpart and extant sources on Greek analysis and synthesis
322(3)
C Onomasticon
325(6)
Bibliography 331(20)
Indices 351(2)
Index Nominum 353(7)
Index Fontium 360(1)
Index Locorum 361(18)
Index Rerum 379