Greek Mathematical Philosophy
Author: Edward A. Maziarz
Publisher:
Published: 1995
Total Pages: 296
ISBN-13:
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Greek Mathematical Thought and the Origin of Algebra
Author: Jacob Klein
Publisher: Courier Corporation
Published: 2013-04-22
Total Pages: 246
ISBN-13: 0486319814
DOWNLOAD EBOOKImportant study focuses on the revival and assimilation of ancient Greek mathematics in the 13th-16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. 1968 edition. Bibliography.
Introduction to Mathematical Philosophy
Author: Bertrand Russell
Publisher:
Published: 1920
Total Pages: 224
ISBN-13:
DOWNLOAD EBOOKThe Origin of the Logic of Symbolic Mathematics
Author: Burt C. Hopkins
Publisher: Indiana University Press
Published: 2011-09-07
Total Pages: 593
ISBN-13: 0253005272
DOWNLOAD EBOOKBurt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts—especially mathematical concepts and the process of mathematical abstraction that generates them—have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkins explores how Husserl and Klein arrived at their conclusion and its philosophical implications for the modern project of formalizing all knowledge.
The Logical Syntax of Greek Mathematics
Author: Fabio Acerbi
Publisher: Springer
Published: 2021-06-23
Total Pages: 396
ISBN-13: 9783030769581
DOWNLOAD EBOOKThe 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 Shaping of Deduction in Greek Mathematics
Author: Reviel Netz
Publisher: Cambridge University Press
Published: 2003-09-18
Total Pages: 356
ISBN-13: 9780521541206
DOWNLOAD EBOOKThe 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.
Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century
Author: Paolo Mancosu
Publisher: Oxford University Press, USA
Published: 1999
Total Pages: 290
ISBN-13: 0195132440
DOWNLOAD EBOOK1. Philosophy of Mathematics and Mathematical Practice in the Early Seventeenth Century p. 8 1.1 The Quaestio de Certitudine Mathematicarum p. 10 1.2 The Quaestio in the Seventeenth Century p. 15 1.3 The Quaestio and Mathematical Practice p. 24 2. Cavalieri's Geometry of Indivisibles and Guldin's Centers of Gravity p. 34 2.1 Magnitudes, Ratios, and the Method of Exhaustion p. 35 2.2 Cavalieri's Two Methods of Indivisibles p. 38 2.3 Guldin's Objections to Cavalieri's Geometry of Indivisibles p. 50 2.4 Guldin's Centrobaryca and Cavalieri's Objections p. 56 3. Descartes' Geometrie p. 65 3.1 Descartes' Geometrie p. 65 3.2 The Algebraization of Mathematics p. 84 4. The Problem of Continuity p. 92 4.1 Motion and Genetic Definitions p. 94 4.2 The "Causal" Theories in Arnauld and Bolzano p. 100 4.3 Proofs by Contradiction from Kant to the Present p. 105 5. Paradoxes of the Infinite p. 118 5.1 Indivisibles and Infinitely Small Quantities p. 119 5.2 The Infinitely Large p. 129 6. Leibniz's Differential Calculus and Its Opponents p. 150 6.1 Leibniz's Nova Methodus and L'Hopital's Analyse des Infiniment Petits p. 151 6.2 Early Debates with Cluver and Nieuwentijt p. 156 6.3 The Foundational Debate in the Paris Academy of Sciences p. 165 Appendix Giuseppe Biancani's De Mathematicarum Natura p. 178 Notes p. 213 References p. 249 Index p. 267.
Introducing Greek Philosophy
Author: Rosemary Wright
Publisher: Routledge
Published: 2014-12-05
Total Pages: 240
ISBN-13: 1317492463
DOWNLOAD EBOOKAimed at students of classics and of philosophy who would like a taste of the subject before being committed to a full course and at those who have already started and need to find their bearings in what may seem at first a complex maze of names and schools, "Introducing Greek Philosophy" is a concise, lively, philosophically aware introduction to ancient Greek philosophy. The book begins with the Milesians in Asia Minor before moving over to the developments in the western Greek world, then focusing on Socrates, Plato and Aristotle in Athens, finishing with the Hellenistic schools and their arrival in Rome, where the main ideas are set out in the Latin poetry of Lucretius and the prose of Cicero.The book eschews the method of most histories of ancient philosophy of addressing one thinker after another through the centuries. Instead, after a basic mapping of the territory, it takes the great themes that the Greeks were engaged in from the earliest times, and looks at them individually, their development in argument and counter-argument, from the beginnings of recorded Greek history, through the various upheavals of tyrannies, democracies, oligarchies and kingships, to their introduction into Rome in the first century BC.
Principia Mathematica
Author: Alfred North Whitehead
Publisher:
Published: 1910
Total Pages: 688
ISBN-13:
DOWNLOAD EBOOKThe Metaphysics of the Pythagorean Theorem
Author: Robert Hahn
Publisher: State University of New York Press
Published: 2017-05-01
Total Pages: 301
ISBN-13: 1438464916
DOWNLOAD EBOOKBringing together geometry and philosophy, this book undertakes a strikingly original study of the origins and significance of the Pythagorean theorem. Thales, whom Aristotle called the first philosopher and who was an older contemporary of Pythagoras, posited the principle of a unity from which all things come, and back into which they return upon dissolution. He held that all appearances are only alterations of this basic unity and there can be no change in the cosmos. Such an account requires some fundamental geometric figure out of which appearances are structured. Robert Hahn argues that Thales came to the conclusion that it was the right triangle: by recombination and repackaging, all alterations can be explained from that figure. This idea is central to what the discovery of the Pythagorean theorem could have meant to Thales and Pythagoras in the sixth century BCE. With more than two hundred illustrations and figures, Hahn provides a series of geometric proofs for this lost narrative, tracing it from Thales to Pythagoras and the Pythagoreans who followed, and then finally to Plato's Timaeus. Uncovering the philosophical motivation behind the discovery of the theorem, Hahn's book will enrich the study of ancient philosophy and mathematics alike.
