The Logical Syntax of Greek Mathematics
The Logical Syntax of Greek Mathematics

Author: Fabio Acerbi

Publisher: Springer Nature

Published: 2021-06-21

Total Pages: 396

ISBN-13: 3030769593

DOWNLOAD EBOOK

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.

The Logical Syntax of Greek Mathematics
The Logical Syntax of Greek Mathematics

Author: Fabio Acerbi

Publisher: Springer

Published: 2021-06-23

Total Pages: 396

ISBN-13: 9783030769581

DOWNLOAD EBOOK

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.

Shadows of Syntax
Shadows of Syntax

Author: Jared Warren

Publisher: Oxford University Press

Published: 2020-07-20

Total Pages: 336

ISBN-13: 0190086165

DOWNLOAD EBOOK

What is the source of logical and mathematical truth? This volume revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. In Shadows of Syntax, Jared Warren offers the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. He argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims. In Part I, Warren explains exactly what conventionalism amounts to and what linguistic conventions are. Part II develops an unrestricted inferentialist theory of the meanings of logical constants that leads to logical conventionalism. This conventionalist theory is elaborated in discussions of logical pluralism, the epistemology of logic, and of the influential objections that led to the historical demise of conventionalism. Part III aims to extend conventionalism from logic to mathematics. Unlike logic, mathematics involves both ontological commitments and a rich notion of truth that cannot be generated by any algorithmic process. To address these issues Warren develops conventionalist-friendly but independently plausible theories of both metaontology and mathematical truth. Finally, Part IV steps back to address big picture worries and meta-worries about conventionalism. This book develops and defends a unified theory of logic and mathematics according to which logical and mathematical truths are reflections of our linguistic rules, mere shadows of syntax.

Form and Clarity in Euclid’s ›Elements‹
Form and Clarity in Euclid’s ›Elements‹

Author: Anna-Maria Gasser

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2024-07-22

Total Pages: 486

ISBN-13: 3110670461

DOWNLOAD EBOOK

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
Metadata and Semantic Research

Author: Emmanouel Garoufallou

Publisher: Springer Nature

Published: 2023-08-09

Total Pages: 318

ISBN-13: 3031391411

DOWNLOAD EBOOK

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.

The Cambridge Companion to Ancient Logic
The Cambridge Companion to Ancient Logic

Author: Luca Castagnoli

Publisher: Cambridge University Press

Published: 2023-03-31

Total Pages: 445

ISBN-13: 1107062942

DOWNLOAD EBOOK

A state-of-the-art overview of ancient logic for students and scholars, with in-depth analyses of its central themes.

The Platonic Mind
The Platonic Mind

Author: Peter D. Larsen

Publisher: Taylor & Francis

Published: 2024-11-26

Total Pages: 582

ISBN-13: 104018507X

DOWNLOAD EBOOK

Plato is one of the most widely read and studied philosophers of all time. A pivotal figure in the history of philosophy, his work is foundational to the Western philosophical tradition. The Platonic Mind provides an extensive survey of his work, not only placing it in its historical context but also exploring its contemporary significance. Comprising over 30 specially commissioned chapters by an international team of contributors, the volume is divided into three clear parts: Reading Plato’s Dialogues Themes From Plato Plato’s Influences and Significance Within these sections key topics are addressed including the nature of reality and the physical world; human cognition, including knowledge, sense perception, and affective states; society, politics, and law; his method of inquiry and literary style; his influence on subsequent thinkers and traditions; and studies on a wide range of individual Platonic dialogues. Plato’s work is central to the study of ancient philosophy, Greek philosophy, history of philosophy, metaphysics, philosophy of mind, political philosophy, epistemology, philosophy of science, ethics, philosophy of language, legal philosophy, and philosophy of religion. As such The Platonic Mind is essential reading for all students and researchers in philosophy. It will also be of interest to those studying Plato in related disciplines such as politics, law, ancient history, literature, and religious studies.

The Shaping of Deduction in Greek Mathematics
The Shaping of Deduction in Greek Mathematics

Author: Reviel Netz

Publisher: Cambridge University Press

Published: 2003-09-18

Total Pages: 356

ISBN-13: 9780521541206

DOWNLOAD EBOOK

The aim of this book is to explain the shape of Greek mathematical thinking. It can be read on three levels: as a description of the practices of Greek mathematics; as a theory of the emergence of the deductive method; and as a case-study for a general view on the history of science. The starting point for the enquiry is geometry and the lettered diagram. Reviel Netz exploits the mathematicians' practices in the construction and lettering of their diagrams, and the continuing interaction between text and diagram in their proofs, to illuminate the underlying cognitive processes. A close examination of the mathematical use of language follows, especially mathematicians' use of repeated formulae. Two crucial chapters set out to show how mathematical proofs are structured and explain why Greek mathematical practice manages to be so satisfactory. A final chapter looks into the broader historical setting of Greek mathematical practice.