The Significance of the Mathematical Element in the Philosophy of Plato ... PDF Download

Author: Irving Elgar Miller
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 104

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Author: Irving Elgar Miller
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 0

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Author: Irving Elgar 1869 Miller
Publisher: Wentworth Press
ISBN: 9781373874580
Category : History
Languages : en
Pages : 98

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This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author: Irving Elgar Miller
Publisher: Theclassics.Us
ISBN: 9781230213873
Category :
Languages : en
Pages : 38

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1904 edition. Excerpt: ...dialogues "of search."8 Even positions are taken in which the speaker does not necessarily believe, for the sake of the argument. Thrasymachus says: "I may be in earnest or not, but what is that to you?--to refute the argument is your business."9 Glaucon maintains the cause of injustice, though confessedly not believing it," in order that he may see how the position can be refuted.10 In the Gorgias (462) Socrates gives Polus a lesson in the method of argumentation.. In the Phtzdo (ioo ff.) there is quite a long digression on method. The Parmenides is from one point of view, taken as a whole, an exposition of method. When Socrates is involved in certain difficulties regarding the Ideas, Parmenides explains that this arises out of his attempting to define the beautiful, the just, the good, and the ideas generally, without sufficient previous training. The special lack in his training is pointed out, and it is indicated wherein he could get better training. Parmenides is asked to give an illustration of the method which he has indicated. This he proceeds reluctantly to do. On the side of form, the dialogue Parmenides is the outcome.11 Soph., 218. "Soph., 218-21. 'Stat., 285-86. 8I use this terra to apply more widely than to the minor dialogues alone. 'Rep., 1:349. wRep., 2:358. PLATO'S DOGMATISM.12 It may seem a little inappropriate at first thought to discuss dogmatism under the general head of method. But there seems to be no better place for its discussion in this book without involving repetitions. The dogmatism of Plato has a bearing on method, even if it cannot be said to be a part of method. The term "dogmatic" is often used as a term of reproach. Plato was a dogmatist in the better sense of the...

Author: Irving Elgar Miller
Publisher: Mac Donnell Press
ISBN: 144609426X
Category : Literary Collections
Languages : en
Pages : 98

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Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.

Author: Irving Elgar Miller
Publisher: Forgotten Books
ISBN: 9781333807412
Category : Philosophy
Languages : en
Pages : 108

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Excerpt from The Significance of the Mathematical Element in the Philosophy of Plato: A Dissertation It was significant for the progress of mathematics that when Plato turned his attention toward this science he looked with the eyes of a philosopher. Hence I shall discuss what it was that his philosophic insight Saw in mathematics to attract him, and in what way the philosophic attitude of mind which he brought to bear on the study of this subject served to further the progress of the science. On the other hand, the interaction Of the mathematical and the philosophic elements was an important factor in the development] of Plato's philosophic system. The main part of this book will be given up to the task of showing the in uence of mathematics upon the formulation of philosophic problems, in the determination of) method, and as affecting the content of philosophy. In the first chapter I have put the mathematical element in the foreground wth special reference to showing the significance to mathematics of the philosophical element. In the remaining chapters I have put the philosophical element into the foreground and have sought to show the in uence upon it of the mathematical element. This has involved a duplication in the treatment of certain topics and considerable cross-reference at certain points. This element of repetition might have been avoided by a unification of treatment under the lead of the philosophical aspect, with the mathematical as incidental and subsidiary. But I have thought that the advantages of giving the mathematical element a more unified discussion on its own account counterbalanced the disadvantages from the other point of v1ew. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works."

Author: Elaine Landry
Publisher: Cambridge University Press
ISBN: 1009313800
Category : Philosophy
Languages : en
Pages : 103

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This Element shows that Plato keeps a clear distinction between mathematical and metaphysical realism and the knife he uses to slice the difference is method. The philosopher's dialectical method requires that we tether the truth of hypotheses to existing metaphysical objects. The mathematician's hypothetical method, by contrast, takes hypotheses as if they were first principles, so no metaphysical account of their truth is needed. Thus, we come to Plato's methodological as-if realism: in mathematics, we treat our hypotheses as if they were first principles, and, consequently, our objects as if they existed, and we do this for the purpose of solving problems. Taking the road suggested by Plato's Republic, this Element shows that methodological commitments to mathematical objects are made in light of mathematical practice; foundational considerations; and, mathematical applicability. This title is also available as Open Access on Cambridge Core.

Author: Theokritos Kouremenos
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110601869
Category : Literary Criticism
Languages : en
Pages : 158

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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: W.R. Knorr
Publisher: Springer Science & Business Media
ISBN: 9401017549
Category : Philosophy
Languages : en
Pages : 389

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The present work has three principal objectives: (1) to fix the chronology of the development of the pre-Euclidean theory of incommensurable magnitudes beginning from the first discoveries by fifth-century Pythago reans, advancing through the achievements of Theodorus of Cyrene, Theaetetus, Archytas and Eudoxus, and culminating in the formal theory of Elements X; (2) to correlate the stages of this developing theory with the evolution of the Elements as a whole; and (3) to establish that the high standards of rigor characteristic of this evolution were intrinsic to the mathematicians' work. In this third point, we wish to counterbalance a prevalent thesis that the impulse toward mathematical rigor was purely a response to the dialecticians' critique of foundations; on the contrary, we shall see that not until Eudoxus does there appear work which may be described as purely foundational in its intent. Through the examination of these problems, the present work will either alter or set in a new light virtually every standard thesis about the fourth-century Greek geometry. I. THE PRE-EUCLIDEAN THEORY OF INCOMMENSURABLE MAGNITUDES The Euclidean theory of incommensurable magnitudes, as preserved in Book X of the Elements, is a synthetic masterwork. Yet there are detect able seams in its structure, seams revealed both through terminology and through the historical clues provided by the neo-Platonist commentator Proclus.

Author: Thomas Bedürftig
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110470772
Category : Mathematics
Languages : en
Pages : 474

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The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today‘s mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally – First nonstandard steps Retrospection