[Full Book] Aristotle On Mathematical Infinity

Aristotle on Mathematical Infinity PDF
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Publisher: Franz Steiner Verlag
Author: Theokritos Kouremenos
Category : Philosophy
Languages : en
Pages : 131

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Aristotle On Mathematical Infinity

Aristotle And Mathematics by Theokritos Kouremenos, Aristotle On Mathematical Infinity Books available in PDF, EPUB, Mobi Format. Download Aristotle On Mathematical Infinity books, 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.


[Full Book] Mathematics In Aristotle

Mathematics in Aristotle PDF
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Publisher: Routledge
Author: Thomas Heath
Category : Philosophy
Languages : en
Pages : 306

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Mathematics In Aristotle

Aristotle And Mathematics by Thomas Heath, Mathematics In Aristotle Books available in PDF, EPUB, Mobi Format. Download Mathematics In Aristotle books, 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.


[Full Book] Aristotle And Mathematics

Aristotle and Mathematics PDF
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Publisher: BRILL
Author: John J. Cleary
Category : Philosophy
Languages : en
Pages : 598

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Aristotle And Mathematics

Aristotle And Mathematics by John J. Cleary, Aristotle And Mathematics Books available in PDF, EPUB, Mobi Format. Download Aristotle And Mathematics books, This book examines Aristotle's critical reaction to the mathematical cosmology of Plato's Academy, and traces the aporetic method by which he developed his own cosmological and metaphysical views, which underpin his philosophy of mathematics.


[Full Book] Science And Mathematics In Ancient Greek Culture

Science and Mathematics in Ancient Greek Culture PDF
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Publisher: Oxford University Press on Demand
Author: Reader in Ancient History C J Tuplin
Category : History
Languages : en
Pages : 379

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Science And Mathematics In Ancient Greek Culture

Aristotle And Mathematics by Reader in Ancient History C J Tuplin, Science And Mathematics In Ancient Greek Culture Books available in PDF, EPUB, Mobi Format. Download Science And Mathematics In Ancient Greek Culture books, With contributions from a number of respected scholars, these papers locate science within ancient Greek society and culture. The writers investigate its impact upon that society and argue that it was both motivated and constrained by unscientific cultural interests and affected by the paradigms of the day.


[Full Book] An Aristotelian Realist Philosophy Of Mathematics

An Aristotelian Realist Philosophy of Mathematics PDF
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Publisher: Springer
Author: J. Franklin
Category : Mathematics
Languages : en
Pages : 308

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An Aristotelian Realist Philosophy Of Mathematics

Aristotle And Mathematics by J. Franklin, An Aristotelian Realist Philosophy Of Mathematics Books available in PDF, EPUB, Mobi Format. Download An Aristotelian Realist Philosophy Of Mathematics books, 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.


[Full Book] Philosophy Of Mathematics

Philosophy of Mathematics PDF
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Publisher: John Wiley & Sons
Author: David Bostock
Category : Mathematics
Languages : en
Pages : 332

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Philosophy Of Mathematics

Aristotle And Mathematics by David Bostock, Philosophy Of Mathematics Books available in PDF, EPUB, Mobi Format. Download Philosophy Of Mathematics books, Philosophy of Mathematics: An Introduction provides a critical analysis of the major philosophical issues and viewpoints in the concepts and methods of mathematics - from antiquity to the modern era. Offers beginning readers a critical appraisal of philosophical viewpoints throughout history Gives a separate chapter to predicativism, which is often (but wrongly) treated as if it were a part of logicism Provides readers with a non-partisan discussion until the final chapter, which gives the author?s personal opinion on where the truth lies Designed to be accessible to both undergraduates and graduate students, and at the same time to be of interest to professionals


[Full Book] Plato S Forms Mathematics And Astronomy

Plato   s forms  mathematics and astronomy PDF
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Publisher: Walter de Gruyter GmbH & Co KG
Author: Theokritos Kouremenos
Category : Literary Criticism
Languages : en
Pages : 158

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Plato S Forms Mathematics And Astronomy

Aristotle And Mathematics by Theokritos Kouremenos, Plato S Forms Mathematics And Astronomy Books available in PDF, EPUB, Mobi Format. Download Plato S Forms Mathematics And Astronomy books, 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.


[Full Book] Universal Mathematics In Aristotelian Thomistic Philosophy

Universal Mathematics in Aristotelian Thomistic Philosophy PDF
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Publisher:
Author: Charles B. Crowley
Category : Interprétation (Philosophie)
Languages : en
Pages : 221

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Universal Mathematics In Aristotelian Thomistic Philosophy

Aristotle And Mathematics by Charles B. Crowley, Universal Mathematics In Aristotelian Thomistic Philosophy Books available in PDF, EPUB, Mobi Format. Download Universal Mathematics In Aristotelian Thomistic Philosophy books,


[Full Book] Existence In A Way

Existence in a Way PDF
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Publisher:
Author: Eva Maria Cadavid
Category : Mathematics
Languages : en
Pages : 342

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Existence In A Way

Aristotle And Mathematics by Eva Maria Cadavid, Existence In A Way Books available in PDF, EPUB, Mobi Format. Download Existence In A Way books, "There is no one Aristotelian text devoted to mathematics. Instead, Aristotle's view can be found in Posterior Analytics, Metaphysics, De Anima, and Physics. These texts show that Aristotle believed we could have mathematical knowledge and that mathematics is an ideal science. Aristotle's views on the ontology of mathematical objects are less clear. He says in Metaphysics XIII.2 that mathematical objects exist neither separately from nor in sensible objects. He concludes that they either do not exist or have a qualified existence. Aristotle's comments on mathematical objects have given rise to different interpretations. These include accusations of naïveté about mathematics, incoherence, and even a Platonic ontology about mathematics. In the past 30 years, the work of scholars such as Ian Mueller, Julia Annas, and Jonathan Lear have challenged these interpretations. Their work calls attention to the need to clarify Aristotle's comments on the existence of mathematical objects. This dissertation analyzes the interpretations of Mueller, Annas, and Lear, and building from them, defends a fictionalist account of mathematical objects in Aristotle. There is an apparent inconsistency in Aristotle that arises from his claim that there is mathematical knowledge, which implies the existence of objects that perfectly exemplify mathematical properties, and his claim that there are no non-sensible substances. But no sensible object perfectly exemplifies mathematical properties. There are four propositions that would resolve the apparent inconsistency. They are the following: (I) there are no mathematical truths; (II) not all existing things are sensible objects; (III) mathematical truths do not require the existence of mathematical objects as substances; and (IV) mathematical objects are sensible substances. The first proposition can be quickly discarded as an option because there is textual evidence against it. The challenge is to determine which of the other three propositions is the best interpretation. There is some textual evidence for each as well as some unwanted implications. The dissertation examines and evaluates the evidence for propositions II-IV and defends a fictionalist account as a version of the (III) proposition"--Leaves v-vi.


[Full Book] An Historical Introduction To The Philosophy Of Mathematics A Reader

An Historical Introduction to the Philosophy of Mathematics  A Reader PDF
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Publisher: Bloomsbury Publishing
Author: Russell Marcus
Category : Philosophy
Languages : en
Pages : 896

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An Historical Introduction To The Philosophy Of Mathematics A Reader

Aristotle And Mathematics by Russell Marcus, An Historical Introduction To The Philosophy Of Mathematics A Reader Books available in PDF, EPUB, Mobi Format. Download An Historical Introduction To The Philosophy Of Mathematics A Reader books, A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject. An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject. Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers.


[Full Book] The Continuous The Discrete And The Infinitesimal In Philosophy And Mathematics

The Continuous  the Discrete and the Infinitesimal in Philosophy and Mathematics PDF
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Publisher: Springer Nature
Author: John L. Bell
Category : Mathematics
Languages : en
Pages : 313

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The Continuous The Discrete And The Infinitesimal In Philosophy And Mathematics

Aristotle And Mathematics by John L. Bell, The Continuous The Discrete And The Infinitesimal In Philosophy And Mathematics Books available in PDF, EPUB, Mobi Format. Download The Continuous The Discrete And The Infinitesimal In Philosophy And Mathematics books, 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.


[Full Book] Ptolemy S Philosophy

Ptolemy s Philosophy PDF
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Publisher: Princeton University Press
Author: Jacqueline Feke
Category : Science
Languages : en
Pages : 256

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Ptolemy S Philosophy

Aristotle And Mathematics by Jacqueline Feke, Ptolemy S Philosophy Books available in PDF, EPUB, Mobi Format. Download Ptolemy S Philosophy books, 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.


[Full Book] Philosophy Of Mathematics And Mathematical Practice In The Seventeenth Century

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century PDF
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Publisher: Oxford University Press on Demand
Author: Paolo Mancosu
Category : Drama
Languages : en
Pages : 275

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Philosophy Of Mathematics And Mathematical Practice In The Seventeenth Century

Aristotle And Mathematics by Paolo Mancosu, Philosophy Of Mathematics And Mathematical Practice In The Seventeenth Century Books available in PDF, EPUB, Mobi Format. Download Philosophy Of Mathematics And Mathematical Practice In The Seventeenth Century books, The seventeenth century saw dramatic advances in mathematical theory and practice than any era before or since. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, analytic geometry, the geometry of indivisibles, the arithmetic of infinites, and the calculus had been developed. Although many technical studies have been devoted to these innovations, Paolo Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Beginning with the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relationship between empiricist epistemology and infinitistic theorems in geometry, and the debates concerning the foundations of the Leibnizian calculus In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics.


[Full Book] The Essence Of Numbers

The Essence of Numbers PDF
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Publisher: Springer Nature
Author: Frédéric Patras
Category : Mathematics
Languages : en
Pages : 176

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The Essence Of Numbers

Aristotle And Mathematics by Frédéric Patras, The Essence Of Numbers Books available in PDF, EPUB, Mobi Format. Download The Essence Of Numbers books, This book considers the manifold possible approaches, past and present, to our understanding of the natural numbers. They are treated as epistemic objects: mathematical objects that have been subject to epistemological inquiry and attention throughout their history and whose conception has evolved accordingly. Although they are the simplest and most common mathematical objects, as this book reveals, they have a very complex nature whose study illuminates subtle features of the functioning of our thought. Using jointly history, mathematics and philosophy to grasp the essence of numbers, the reader is led through their various interpretations, presenting the ways they have been involved in major theoretical projects from Thales onward. Some pertain primarily to philosophy (as in the works of Plato, Aristotle, Kant, Wittgenstein...), others to general mathematics (Euclid's Elements, Cartesian algebraic geometry, Cantorian infinities, set theory...). Also serving as an introduction to the works and thought of major mathematicians and philosophers, from Plato and Aristotle to Cantor, Dedekind, Frege, Husserl and Weyl, this book will be of interest to a wide variety of readers, from scholars with a general interest in the philosophy or mathematics to philosophers and mathematicians themselves.


[Full Book] Pythagoras Revived

Pythagoras Revived PDF
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Publisher: Oxford University Press on Demand
Author: Dominic J. O'Meara
Category : Philosophy
Languages : en
Pages : 251

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Pythagoras Revived

Aristotle And Mathematics by Dominic J. O'Meara, Pythagoras Revived Books available in PDF, EPUB, Mobi Format. Download Pythagoras Revived books, The Pythagorean idea that number is the key to understanding reality inspired Neoplatonist philosophers in the fourth and fifth centuries to develop theories in physics and metaphysics based on mathematical models. The theories produced by this revived interest in Pythagoreanism were to becomeinfluential in medieval and early modern philosophy, and this book makes use of some newly-discovered evidence to examine for the first time the development of those theories.


[Full Book] Knowledge And Demonstration

Knowledge and Demonstration PDF
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Publisher: Springer Science & Business Media
Author: Orna Harari
Category : Philosophy
Languages : en
Pages : 162

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Knowledge And Demonstration

Aristotle And Mathematics by Orna Harari, Knowledge And Demonstration Books available in PDF, EPUB, Mobi Format. Download Knowledge And Demonstration books, This study explores the theoretical relationship between Aristotle’s theory of syllogism and his conception of demonstrative knowledge. More specifically, I consider why Aristotle’s theory of demonstration presupposes his theory of syllogism. In reconsidering the relationship between Aristotle’s two Analytics, I modify this widely discussed question. The problem of the relationship between Aristotle’s logic and his theory of proof is commonly approached from the standpoint of whether the theory of demonstration presupposes the theory of syllogism. By contrast, I assume the theoretical relationship between these two theories from the start. This assumption is based on much explicit textual evidence indicating that Aristotle considers the theory of demonstration a branch of the theory of syllogism. I see no textual reasons for doubting the theoretical relationship between Aristotle’s two Analytics so I attempt to uncover here the common theoretical assumptions that relate the syllogistic form of reasoning to the cognitive state (i. e. , knowledge), which is attained through syllogistic inferences. This modification of the traditional approach reflects the wider objective of this essay. Unlike the traditional interpretation, which views the Posterior Analytics in light of scientific practice, this study aims to lay the foundation for a comprehensive interpretation of the Posterior Analytics, considering this work from a metaphysical perspective. One of my major assertions is that Aristotle’s conception of substance is essential for a grasp of his theory of demonstration in general, and of the role of syllogistic logic in particular.