The Logical Syntax Of Greek Mathematics
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The Logical Syntax of Greek Mathematics
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.
Form and Clarity in Euclid’s ›Elements‹
Author: Anna-Maria Gasser
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2024-07-22
As of yet, the remarkable and highly influential textual form of Euclidean mathematics has not been considered from a literary-aesthetic perspective. By its extreme standardization and seeming non-literariness it appears to defy such an approach. This book nonetheless attempts precisely a literary-aesthetic study of the language and style of Euclid’s Elements, focusing on book I. It aims to find out what is literary about the form and what motivates this form as form. In doing so, it employs the concept of clarity, asking: How is the textual form related to logical and communicative clarity? That is, how far is the omnipresent standardization necessary for the accomplishment and successful communication of the proofs? Based on a close analysis of the standardization at all levels of the text (lexicon, grammar, structure, and especially diagram), it argues that the textual form of the Elements is standardized beyond logical-communicative purposes, and that it is in this sense ‘aesthetic’. The book exposes the unexpected literary dimension of Euclid’s Elements, provides a new interpretation of the peculiar form of the work, and offers a model for determining the role of clarity (not only) in Greek theoretical mathematics.
Metadata and Semantic Research
Author: Emmanouel Garoufallou
language: en
Publisher: Springer Nature
Release Date: 2023-08-09
This book constitutes the refereed post proceedings of the 16th Research Conference on Metadata and Semantic Research, MTSR 2022, held in London, UK, during November 7–11, 2022. The 21 full papers and 4 short papers included in this book were carefully reviewed andselected from 79 submissions. They were organized in topical sections as follows: metadata, linked data, semantics and ontologies - general session, and track on Knowledge IT Artifacts (KITA), Track on digital humanities and digital curation, and track on cultural collections and applications, track on digital libraries, information retrieval, big, linked, social & open data, and metadata, linked data, semantics and ontologies - general session, track on agriculture, food & environment, and metadata, linked Data, semantics and ontologies - general, track on open repositories, research information systems & data infrastructures, and metadata, linked data, semantics and ontologies - general, metadata, linked data, semantics and ontologies - general session, and track on european and national projects.