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Author : Edward A. Maziarz
Publisher :
ISBN 13 :
Total Pages : 296 pages
Book Rating : 4.0/5 ( download)
Download or read book Greek Mathematical Philosophy written by Edward A. Maziarz and published by . This book was released on 1995 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jacob Klein
Publisher : Courier Corporation
ISBN 13 : 0486319814
Total Pages : 246 pages
Book Rating : 4.4/5 (863 download)
Download or read book Greek Mathematical Thought and the Origin of Algebra written by Jacob Klein and published by Courier Corporation. This book was released on 2013-04-22 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Important 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.
Author : Bertrand Russell
Publisher :
ISBN 13 :
Total Pages : 224 pages
Book Rating : 4.3/5 (91 download)
Download or read book Introduction to Mathematical Philosophy written by Bertrand Russell and published by . This book was released on 1920 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Burt C. Hopkins
Publisher : Indiana University Press
ISBN 13 : 0253005272
Total Pages : 593 pages
Book Rating : 4.2/5 (53 download)
Download or read book The Origin of the Logic of Symbolic Mathematics written by Burt C. Hopkins and published by Indiana University Press. This book was released on 2011-09-07 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Burt 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.
Author : Reviel Netz
Publisher : Cambridge University Press
ISBN 13 : 9780521541206
Total Pages : 356 pages
Book Rating : 4.5/5 (412 download)
Download or read book The Shaping of Deduction in Greek Mathematics written by Reviel Netz and published by Cambridge University Press. This book was released on 2003-09-18 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Fabio Acerbi
Publisher : Springer
ISBN 13 : 9783030769581
Total Pages : 396 pages
Book Rating : 4.7/5 (695 download)
Download or read book The Logical Syntax of Greek Mathematics written by Fabio Acerbi and published by Springer. This book was released on 2021-06-23 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Paolo Mancosu
Publisher : Oxford University Press, USA
ISBN 13 : 0195132440
Total Pages : 290 pages
Book Rating : 4.1/5 (951 download)
Download or read book Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century written by Paolo Mancosu and published by Oxford University Press, USA. This book was released on 1999 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. 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.
Author : Rosemary Wright
Publisher : Routledge
ISBN 13 : 1317492463
Total Pages : 240 pages
Book Rating : 4.3/5 (174 download)
Download or read book Introducing Greek Philosophy written by Rosemary Wright and published by Routledge. This book was released on 2014-12-05 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed 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.
Author : Alfred North Whitehead
Publisher :
ISBN 13 :
Total Pages : 688 pages
Book Rating : 4.3/5 (91 download)
Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ian Mueller
Publisher : Courier Dover Publications
ISBN 13 :
Total Pages : 404 pages
Book Rating : 4.3/5 (555 download)
Download or read book Philosophy of Mathematics and Deductive Structure in Euclid's Elements written by Ian Mueller and published by Courier Dover Publications. This book was released on 2006 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of Euclid's Elements, this text provides an understanding of the classical Greek conception of mathematics and its similarities to modern views as well as its differences. It focuses on philosophical, foundational, and logical questions -- rather than focusing strictly on historical and mathematical issues -- and features several helpful appendixes.
Author : Robert Hahn
Publisher : State University of New York Press
ISBN 13 : 1438464916
Total Pages : 301 pages
Book Rating : 4.4/5 (384 download)
Download or read book The Metaphysics of the Pythagorean Theorem written by Robert Hahn and published by State University of New York Press. This book was released on 2017-05-01 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bringing 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.
Author : Thomas Little Heath
Publisher : Dalcassian Publishing Company
ISBN 13 :
Total Pages : 468 pages
Book Rating : 4./5 ( download)
Download or read book A history of Greek mathematics written by Thomas Little Heath and published by Dalcassian Publishing Company. This book was released on 1921-01-01 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bharath Sriraman
Publisher : Birkhäuser
ISBN 13 : 331961231X
Total Pages : 357 pages
Book Rating : 4.3/5 (196 download)
Download or read book Humanizing Mathematics and its Philosophy written by Bharath Sriraman and published by Birkhäuser. This book was released on 2017-11-07 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift contains numerous colorful and eclectic essays from well-known mathematicians, philosophers, logicians, and linguists celebrating the 90th birthday of Reuben Hersh. The essays offer, in part, attempts to answer the following questions set forth by Reuben himself as a focus for this volume: Can practicing mathematicians, as such, contribute anything to the philosophy of math? Can or should philosophers of math, as such, say anything to practicing mathematicians? Twenty or fifty years from now, what will be similar, and what will, or could, or should be altogether different: About the philosophy of math? About math education? About math research institutions? About data processing and scientific computing? The essays also offer glimpses into Reuben’s fertile mind and his lasting influence on the mathematical community, as well as revealing the diverse roots, obstacles and philosophical dispositions that characterize the working lives of mathematicians. With contributions from a veritable “who’s who” list of 20th century luminaries from mathematics and philosophy, as well as from Reuben himself, this volume will appeal to a wide variety of readers from curious undergraduates to prominent mathematicians.
Author : Ian Hacking
Publisher : Cambridge University Press
ISBN 13 : 1107729823
Total Pages : 307 pages
Book Rating : 4.1/5 (77 download)
Download or read book Why Is There Philosophy of Mathematics At All? written by Ian Hacking and published by Cambridge University Press. This book was released on 2014-01-30 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities.
Author : Barbara M. Sattler
Publisher : Cambridge University Press
ISBN 13 : 9781108745215
Total Pages : 437 pages
Book Rating : 4.7/5 (452 download)
Download or read book The Concept of Motion in Ancient Greek Thought written by Barbara M. Sattler and published by Cambridge University Press. This book was released on 2021-10-31 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the birth of the scientific understanding of motion. It investigates which logical tools and methodological principles had to be in place to give a consistent account of motion, and which mathematical notions were introduced to gain control over conceptual problems of motion. It shows how the idea of motion raised two fundamental problems in the 5th and 4th century BCE: bringing together being and non-being, and bringing together time and space. The first problem leads to the exclusion of motion from the realm of rational investigation in Parmenides, the second to Zeno's paradoxes of motion. Methodological and logical developments reacting to these puzzles are shown to be present implicitly in the atomists, and explicitly in Plato who also employs mathematical structures to make motion intelligible. With Aristotle we finally see the first outline of the fundamental framework with which we conceptualise motion today.
Author : John Baird Callicott
Publisher :
ISBN 13 : 9781516554270
Total Pages : 386 pages
Book Rating : 4.5/5 (542 download)
Download or read book Greek Natural Philosophy written by John Baird Callicott and published by . This book was released on 2017-12-21 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Greek Natural Philosophy presents the primary sources on the Presocratics in a straightforward way in order to tell a coherent story about the astonishing development of natural philosophy in ancient Greece and its relevance today. The book begins with historical influences on the birth of natural philosophy, especially literacy and the ecosystem services provided by the natural environment of ancient Greece. It argues that the individual philosophers' thoughts about the nature of the cosmos, living things, humankind, and human culture were linked by a "diachronic dialectic of ideas." Each philosopher's speculations were subjected to a critique by the next generation who crafted more subtle theories. The dialectical transition is traced from the mythopoeic worldview of Hesiod to the rational worldview of Thales and his Milesian successors, followed by Xenophanes and Heraclitus, then Parmenides and his Eleatic successors, and the qualitative pluralisms of Anaxagoras and Empedocles. An entirely fresh interpretation is provided of the Atomists and later Pythagoreans, whose work culminated in the ideas upon which Galileo, Newton, and the other architects of modern science, continued to build. In the span of only two centuries, the Presocratics developed the basic principles of philosophy and natural science, ecology, mathematical astronomy, the atomic theory of matter, an inertial theory of motion, and the possibility that our solar system is only one of infinitely many scattered throughout infinite time and space. The concluding chapter traces natural philosophy through subsequent centuries until its abandonment in 20th century philosophy, leading to the moribund state of philosophy by the end of that century. The authors show how environmental philosophy represents a return to natural philosophy and a model for the revival of philosophy's vigor and relevance in the 21st century. Greek Natural Philosophy is suitable for undergraduate and graduate courses in ancient Greek philosophy or in environmental philosophy, and will be of interest to scholars in these fields.
Author : Jacqueline Feke
Publisher : Princeton University Press
ISBN 13 : 069121039X
Total Pages : 250 pages
Book Rating : 4.6/5 (912 download)
Download or read book Ptolemy's Philosophy written by Jacqueline Feke and published by Princeton University Press. This book was released on 2020-10-13 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: A stimulating intellectual history of Ptolemy's philosophy and his conception of a world in which mathematics reigns supreme The Greco-Roman mathematician Claudius Ptolemy is one of the most significant figures in the history of science. He is remembered today for his astronomy, but his philosophy is almost entirely lost to history. This groundbreaking book is the first to reconstruct Ptolemy’s general philosophical system—including his metaphysics, epistemology, and ethics—and to explore its relationship to astronomy, harmonics, element theory, astrology, cosmology, psychology, and theology. In this stimulating intellectual history, Jacqueline Feke uncovers references to a complex and sophisticated philosophical agenda scattered among Ptolemy’s technical studies in the physical and mathematical sciences. She shows how he developed a philosophy that was radical and even subversive, appropriating ideas and turning them against the very philosophers from whom he drew influence. Feke reveals how Ptolemy’s unique system is at once a critique of prevailing philosophical trends and a conception of the world in which mathematics reigns supreme. A compelling work of scholarship, Ptolemy’s Philosophy demonstrates how Ptolemy situated mathematics at the very foundation of all philosophy—theoretical and practical—and advanced the mathematical way of life as the true path to human perfection.
