Aristotle And Mathematics

Author : John J. Cleary
Publisher : BRILL
Page : 597 pages
File Size : 47,8 Mb
Release : 2016-06-21
Category : Philosophy
ISBN : 9789004320901

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Aristotle and Mathematics by John J. Cleary Pdf

John Cleary here explores the role which the mathematical sciences play in Aristotle's philosophical thought, especially in his cosmology, metaphysics, and epistemology. He also thematizes the aporetic method by means of which he deals with philosophical questions about the foundations of mathematics. The first two chapters consider Plato's mathematical cosmology in the light of Aristotle's critical distinction between physics and mathematics. Subsequent chapters examine three basic aporiae about mathematical objects which Aristotle himself develops in his science of first philosophy. What emerges from this dialectical inquiry is a different conception of substance and of order in the universe, which gives priority to physics over mathematics as the cosmological science. Within this different world-view, we can better understand what we now call Aristotle's philosophy of mathematics.

Author : Thomas Heath
Publisher : St. Augustine's Press
Page : 0 pages
File Size : 53,7 Mb
Release : 1998
Category : Mathematics, Ancient
ISBN : 1855065649

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Mathematics in Aristotle by Thomas Heath Pdf

This is a detailed exposition of Aristotelian mathematics and mathematical terminology. It contains clear translations of all the most important passages on mathematics in the writings of Aristotle, together with explanatory notes and commentary by Heath. Particularly interesting are the discussions of hypothesis and related terms, of Zeno's paradox, and of the relation of mathematics to other sciences. The book includes a comprehensive index of the passages translated.

Author : Thomas Heath
Publisher : Routledge
Page : 310 pages
File Size : 42,8 Mb
Release : 2015-08-14
Category : Philosophy
ISBN : 9781317380603

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Mathematics in Aristotle by Thomas Heath Pdf

Originally published in 1949. This meticulously researched book presents a comprehensive outline and discussion of Aristotle’s mathematics with the author's translations of the greek. To Aristotle, mathematics was one of the three theoretical sciences, the others being theology and the philosophy of nature (physics). Arranged thematically, this book considers his thinking in relation to the other sciences and looks into such specifics as squaring of the circle, syllogism, parallels, incommensurability of the diagonal, angles, universal proof, gnomons, infinity, agelessness of the universe, surface of water, meteorology, metaphysics and mechanics such as levers, rudders, wedges, wheels and inertia. The last few short chapters address ‘problems’ that Aristotle posed but couldn’t answer, related ethics issues and a summary of some short treatises that only briefly touch on mathematics.

Author : Theokritos Kouremenos,Aristotle
Publisher : Franz Steiner Verlag
Page : 142 pages
File Size : 49,5 Mb
Release : 1995
Category : History
ISBN : 3515068511

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Aristotle on Mathematical Infinity by Theokritos Kouremenos,Aristotle Pdf

Aristotle was the first not only to distinguish between potential and actual infinity but also to insist that potential infinity alone is enough for mathematics thus initiating an issue still central to the philosophy of mathematics. Modern scholarship, however, has attacked Aristotle's thesis because, according to the received doctrine, it does not square with Euclidean geometry and it also seems to contravene Aristotle's belief in the finitude of the physical universe. This monograph, the first thorough study of the issue, puts Aristotle's views on infinity in the proper perspective. Through a close study of the relevant Aristotelian passages it shows that the Stagirite's theory of infinity forms a well argued philosophical position which does not bear on his belief in a finite cosmos and does not undermine the Euclidean nature of geometry. The monograph draws a much more positive picture of Aristotle's views and reaffirms his disputed stature as a serious philosopher of mathematics. This innovative and stimulating contribution will be essential reading to a wide range of scholars, including classicists, philosophers of science and mathematics as well as historians of ideas.

Author : Andreas Graeser
Publisher : Unknown
Page : 344 pages
File Size : 55,7 Mb
Release : 1987
Category : Mathematics
ISBN : UOM:39015012438894

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Mathematics and Metaphysics in Aristotle by Andreas Graeser Pdf

Author : J. Franklin
Publisher : Springer
Page : 308 pages
File Size : 40,8 Mb
Release : 2014-04-09
Category : Mathematics
ISBN : 9781137400734

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An Aristotelian Realist Philosophy of Mathematics by J. Franklin Pdf

Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.

Author : Sir Thomas Little Heath,Thomas L. Heath
Publisher : Burns & Oates
Page : 316 pages
File Size : 51,5 Mb
Release : 1993
Category : Mathematics
ISBN : CHI:39683513

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Mathematics in Aristotle by Sir Thomas Little Heath,Thomas L. Heath Pdf

This is a detailed exposition of Aristotelian mathematics and mathematical terminology. It contains clear translations of all the most important passages on mathematics in the writings of Aristotle, together with explanatory notes and commentary by Heath. Particularly interesting are the discussions of hypothesis and related terms, of Zeno's paradox, and of the relation of mathematics to other sciences. The book includes a comprehensive index of the passages translated. Copyright © Libri GmbH. All rights reserved.

Author : Thomas L. Heath
Publisher : Unknown
Page : 0 pages
File Size : 49,5 Mb
Release : 1970
Category : Electronic
ISBN : OCLC:1014743432

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Mathematics in Aristotle by Thomas L. Heath Pdf

Author : W.S. Anglin
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461208754

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Mathematics: A Concise History and Philosophy by W.S. Anglin Pdf

This is a concise introductory textbook for a one-semester (40-class) course in the history and philosophy of mathematics. It is written for mathemat ics majors, philosophy students, history of science students, and (future) secondary school mathematics teachers. The only prerequisite is a solid command of precalculus mathematics. On the one hand, this book is designed to help mathematics majors ac quire a philosophical and cultural understanding of their subject by means of doing actual mathematical problems from different eras. On the other hand, it is designed to help philosophy, history, and education students come to a deeper understanding of the mathematical side of culture by means of writing short essays. The way I myself teach the material, stu dents are given a choice between mathematical assignments, and more his torical or philosophical assignments. (Some sample assignments and tests are found in an appendix to this book. ) This book differs from standard textbooks in several ways. First, it is shorter, and thus more accessible to students who have trouble coping with vast amounts of reading. Second, there are many detailed explanations of the important mathematical procedures actually used by famous mathe maticians, giving more mathematically talented students a greater oppor tunity to learn the history and philosophy by way of problem solving.

Author : Aristote
Publisher : Unknown
Page : 291 pages
File Size : 45,5 Mb
Release : 1970
Category : Mathematics, Greek
ISBN : 0198143613

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Mathematics in Aristotle by Aristote Pdf

Author : Edward A. Maziarz,Thomas Greenwood
Publisher : Unknown
Page : 296 pages
File Size : 51,8 Mb
Release : 1995
Category : Mathematics, Greek
ISBN : PSU:000025472257

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Greek Mathematical Philosophy by Edward A. Maziarz,Thomas Greenwood Pdf

Author : Charles B. Crowley
Publisher : Unknown
Page : 246 pages
File Size : 45,9 Mb
Release : 1980
Category : Mathematics
ISBN : UOM:39015017349674

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Universal Mathematics in Aristotelian-Thomistic Philosophy by Charles B. Crowley Pdf

Author : Theokritos Kouremenos
Publisher : Walter de Gruyter GmbH & Co KG
Page : 158 pages
File Size : 48,7 Mb
Release : 2018-05-22
Category : Literary Criticism
ISBN : 9783110601862

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Plato’s forms, mathematics and astronomy by Theokritos Kouremenos Pdf

Plato’s view that mathematics paves the way for his philosophy of forms is well known. This book attempts to flesh out the relationship between mathematics and philosophy as Plato conceived them by proposing that in his view, although it is philosophy that came up with the concept of beings, which he calls forms, and highlighted their importance, first to natural philosophy and then to ethics, the things that do qualify as beings are inchoately revealed by mathematics as the raw materials that must be further processed by philosophy (mathematicians, to use Plato’s simile in the Euthedemus, do not invent the theorems they prove but discover beings and, like hunters who must hand over what they catch to chefs if it is going to turn into something useful, they must hand over their discoveries to philosophers). Even those forms that do not bear names of mathematical objects, such as the famous forms of beauty and goodness, are in fact forms of mathematical objects. The first chapter is an attempt to defend this thesis. The second argues that for Plato philosophy’s crucial task of investigating the exfoliation of the forms into the sensible world, including the sphere of human private and public life, is already foreshadowed in one of its branches, astronomy.

Author : John L. Bell
Publisher : Springer Nature
Page : 313 pages
File Size : 50,6 Mb
Release : 2019-09-09
Category : Mathematics
ISBN : 9783030187071

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The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics by John L. Bell Pdf

This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.

Author : Stewart Shapiro,Geoffrey Hellman
Publisher : Oxford University Press
Page : 320 pages
File Size : 41,8 Mb
Release : 2020-12-01
Category : Philosophy
ISBN : 9780192537492

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The History of Continua by Stewart Shapiro,Geoffrey Hellman Pdf

Mathematical and philosophical thought about continuity has changed considerably over the ages. Aristotle insisted that continuous substances are not composed of points, and that they can only be divided into parts potentially. There is something viscous about the continuous. It is a unified whole. This is in stark contrast with the prevailing contemporary account, which takes a continuum to be composed of an uncountably infinite set of points. This vlume presents a collective study of key ideas and debates within this history. The opening chapters focus on the ancient world, covering the pre-Socratics, Plato, Aristotle, and Alexander. The treatment of the medieval period focuses on a (relatively) recently discovered manuscript, by Bradwardine, and its relation to medieval views before, during, and after Bradwardine's time. In the so-called early modern period, mathematicians developed the calculus and, with that, the rise of infinitesimal techniques, thus transforming the notion of continuity. The main figures treated here include Galileo, Cavalieri, Leibniz, and Kant. In the early party of the nineteenth century, Bolzano was one of the first important mathematicians and philosophers to insist that continua are composed of points, and he made a heroic attempt to come to grips with the underlying issues concerning the infinite. The two figures most responsible for the contemporary orthodoxy regarding continuity are Cantor and Dedekind. Each is treated in an article, investigating their precursors and influences in both mathematics and philosophy. A new chapter then provides a lucid analysis of the work of the mathematician Paul Du Bois-Reymond, to argue for a constructive account of continuity, in opposition to the dominant Dedekind-Cantor account. This leads to consideration of the contributions of Weyl, Brouwer, and Peirce, who once dubbed the notion of continuity "the master-key which . . . unlocks the arcana of philosophy". And we see that later in the twentieth century Whitehead presented a point-free, or gunky, account of continuity, showing how to recover points as a kind of "extensive abstraction". The final four chapters each focus on a more or less contemporary take on continuity that is outside the Dedekind-Cantor hegemony: a predicative approach, accounts that do not take continua to be composed of points, constructive approaches, and non-Archimedean accounts that make essential use of infinitesimals.