[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] 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] An Aristotelian Realist Philosophy Of Mathematics

An Aristotelian Realist Philosophy of Mathematics PDF
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Publisher: Palgrave Macmillan
Author: James Franklin
Category : Mathematics
Languages : en
Pages : 320

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An Aristotelian Realist Philosophy Of Mathematics

Aristotle And Mathematics by James Franklin, An Aristotelian Realist Philosophy Of Mathematics Books available in PDF, EPUB, Mobi Format. Download An Aristotelian Realist Philosophy Of Mathematics books, An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge.


[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] On Fictionalism In Aristotle S Philosophy Of Mathematics

On Fictionalism in Aristotle s Philosophy of Mathematics PDF
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Publisher:
Author: Young Kee Cho
Category :
Languages : en
Pages : 510

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On Fictionalism In Aristotle S Philosophy Of Mathematics

Aristotle And Mathematics by Young Kee Cho, On Fictionalism In Aristotle S Philosophy Of Mathematics Books available in PDF, EPUB, Mobi Format. Download On Fictionalism In Aristotle S Philosophy Of Mathematics books, The aim of this dissertation is to show that Aristotle's ontology cannot provide a model for mathematics. To show this, I argue that (i) mathematical objects must be seen as fictional entities in the light of Aristotle's metaphysics, and (ii) Aristotle's mathematical fictionalism is not compatible with his metaphysical realism. My interpretation differs from that of other fictionalists in denying this compatibility. For Aristotle, mathematical objects are "something resulting from abstraction ([Greek phrase])." For example, geometry investigates a man not qua man, but qua solid or figure. Traditionally, Aristotle's abstraction has been interpreted as an epistemic process by which a universal concept is obtained from particulars; I rather show his abstraction as a linguistic analysis or conceptual separation by which a certain group of properties are selected: e. g., if a science, X, studies a qua triangle, X studies the properties which belong to a in virtue of a's being a triangle and ignores a's other properties. Aristotle's theory of abstraction implies a mathematical naïve realism, in that mathematical objects are properties of sensible objects. But the difficulty with this mathematical naïve realism is that, since most geometrical objects do not have physical instantiations in the sensible world, things abstracted from sensible objects cannot supply all the necessary objects of mathematics. This is the so-called "precision problem." In order to solve this problem, Aristotle abandons his mathematical realism and claims that mathematical objects exist in sensibles not as actualities but 'as matter ([Greek phrase]).' This claim entails a mathematical fictionalism in metaphysical terms. Most fictionalist interpretations argue that the fictionality of mathematical objects does not harm the truth of mathematics for Aristotle, insofar as objects' matter is abstracted from sensibles. None of these interpretations, however, is successful in reconciling Aristotle's mathematical fictionalism with his realism. For Aristotle, sciences are concerned with 'what is ([Greek phrase])' and not with 'what is not ([Greek phrase]).' Aristotle's concept of truth rests on a realist correspondence to 'what is ([Greek phrase])': "what is true is to say of what is that it is or of what is not that it is not." Thus, insofar as mathematical objects are fictional, Aristotle's metaphysics cannot account for the truth of 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] Analysis And Science In Aristotle

Analysis and Science in Aristotle PDF
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Publisher: SUNY Press
Author: Patrick Hugh Byrne
Category : Philosophy
Languages : en
Pages : 303

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Analysis And Science In Aristotle

Aristotle And Mathematics by Patrick Hugh Byrne, Analysis And Science In Aristotle Books available in PDF, EPUB, Mobi Format. Download Analysis And Science In Aristotle books, Presents a new interpretation of Aristotle's Analytics (the Prior and Posterior Analytics) as a unified whole, and argues that to "loose up"or solve -- rather than to reduce or break up -- is the principle meaning which best characterizes the Analytics. Offering a new interpretation of Aristotle's Analytics (the Prior and Posterior Analytics) as a unified whole, Patrick H. Byrne argues that a non-deductive form of ancient mathematical analysis influenced Aristotle's thinking. Reading the Analytics with this perspective in mind sheds new light on Aristotle's theories of the syllogism, demonstration, and the principles of science. The book begins with a brief survey of ancient geometrical analysis and an investigation of Aristotle's uses of the Greek term, analuein. Byrne argues that "to loose up" or solve -- rather than to reduce or break up -- is the principal meaning which best characterizes Aristotle's Analytics. Extending this line of reasoning, he argues that for Aristotle scientific analysis commonly begins with knowledge of a "mere fact" (a conclusion) and seeks a rigorous demonstration which expresses knowledge of the "reasoned fact". Moreover, genuine analysis of a fact into a reasoned fact cannot be accomplished unless the premises of demonstrations are themselves reasoned facts. Hence the processes which yield the immediate principles (especially definitions) are next investigated through detailed examinations of key examples which Aristotle provides.


[Full Book] Iamblichus On The General Science Of Mathematics

Iamblichus  On the General Science of Mathematics PDF
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Publisher: Bloomsbury Publishing
Author: John Dillon
Category : Mathematics
Languages : en
Pages : 176

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Iamblichus On The General Science Of Mathematics

Aristotle And Mathematics by John Dillon, Iamblichus On The General Science Of Mathematics Books available in PDF, EPUB, Mobi Format. Download Iamblichus On The General Science Of Mathematics books, On the General Science of Mathematics is the third of four surviving works out of ten by Iamblichus (c. 245 CE–early 320s) on the Pythagoreans. He thought the Pythagoreans had treated mathematics as essential for drawing the human soul upwards to higher realms described by Plato, and downwards to understand the physical cosmos, the products of arts and crafts and the order required for an ethical life. His Pythagorean treatises use edited quotation to re-tell the history of philosophy, presenting Plato and Aristotle as passing on the ideas invented by Pythagoras and his early followers. Although his quotations tend to come instead from Plato and later Pythagoreanising Platonists, this re-interpretation had a huge impact on the Neoplatonist commentators in Athens. Iamblichus' cleverness, if not to the same extent his re-interpretation, was appreciated by the commentators in Alexandria.


[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] Aristotle On Mathematics Ontological And Epistemological Aspects

Aristotle on Mathematics   Ontological and Epistemological Aspects PDF
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Publisher:
Author: David Paraskos-Williams
Category :
Languages : en
Pages : 110

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Aristotle On Mathematics Ontological And Epistemological Aspects

Aristotle And Mathematics by David Paraskos-Williams, Aristotle On Mathematics Ontological And Epistemological Aspects Books available in PDF, EPUB, Mobi Format. Download Aristotle On Mathematics Ontological And Epistemological Aspects books,


[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] An Aristotelian Realist Philosophy Of Mathematics

An Aristotelian Realist Philosophy of Mathematics PDF
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Publisher: Palgrave Macmillan
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] 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.


[Full Book] A Manual Of Greek Mathematics

A Manual of Greek Mathematics PDF
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Publisher: Courier Corporation
Author: Sir Thomas L. Heath
Category : Mathematics
Languages : en
Pages : 576

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A Manual Of Greek Mathematics

Aristotle And Mathematics by Sir Thomas L. Heath, A Manual Of Greek Mathematics Books available in PDF, EPUB, Mobi Format. Download A Manual Of Greek Mathematics books, Originally published: Oxford: Clarendon Press, 1931; previously published by Dover Publications in 1963.


[Full Book] Ptolemy S Philosophy

Ptolemy s Philosophy PDF
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Publisher: Princeton University Press
Author: Jacqueline Feke
Category : Mathematics
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.