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The Unity Of Mathematics In Platos Republic
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Book Synopsis Plato’s forms, mathematics and astronomy by : Theokritos Kouremenos
Download or read book Plato’s forms, mathematics and astronomy written by Theokritos Kouremenos and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-05-22 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Explorations in Ancient and Modern Philosophy by : M. F. Burnyeat
Download or read book Explorations in Ancient and Modern Philosophy written by M. F. Burnyeat and published by Cambridge University Press. This book was released on 2012-06-14 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of two volumes collecting the published work of one of the greatest living ancient philosophers, M.F. Burnyeat.
Book Synopsis The Teleology of Action in Plato's Republic by : Andrew Payne
Download or read book The Teleology of Action in Plato's Republic written by Andrew Payne and published by Oxford University Press. This book was released on 2017-10-06 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many discussions of ancient philosophy, teleology is acknowledged as an important theme. How do we act for a particular end or purpose? One common answer describes humans as acting with the intention of achieving a goal. A person selects particular actions with the thought that these actions will lead to that goal. Andrew Payne accepts that this is one good answer to our question but proposes that it is not the only one. In Plato's Republic, Socrates appeals to a different understanding of how humans act for the sake of ends as they live together in political communities and pursue knowledge. As they carry out activities that are necessary for human flourishing, their actions can produce unintended results that signal the full completion of human capacities. For example, performing the actions of a just individual can help promote the establishment of a just society as an unintended result. Such unintended results qualify as ends or purposes of human action. This volume fully explores this functional teleology of action in Plato's Republic.
Book Synopsis One over Many by : Necip Fikri Alican
Download or read book One over Many written by Necip Fikri Alican and published by State University of New York Press. This book was released on 2021-10-01 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finalist for the 2022 PROSE Award in the Philosophy category presented by the Association of American Publishers One over Many is a groundbreaking interpretation of Plato's philosophical outlook, solving longstanding problems in the scholarly literature. Its originality and its strength consist in replacing the metaphysical dualism of the traditional interpretation with the paradigm of unitary pluralism: one world with a gradation of reality, including three different types of Forms, as well as the entire spectrum of sensible phenomena, with intermediate ontological constructs in between. The model thus combines a monism of worlds with a pluralism of things, positing a unitary reality of infinite possibilities through ontological stratification. This tightly integrated collection of essays, conceived and developed by the author in pursuit of corrective intervention in Plato’s metaphysics, combines his previously published work with newly drafted material for the present volume. The book replaces the standard view of Plato as a metaphysical dualist with a novel interpretation providing greater explanatory power through the paradigm of unitary pluralism in a single reality built on ontological diversity.
Book Synopsis The Embodied Self in Plato by : Orestis Karatzoglou
Download or read book The Embodied Self in Plato written by Orestis Karatzoglou and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-04-06 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book argues that, rather than being conceived merely as a hindrance, the body contributes constructively in the fashioning of a Platonic unified self. The Phaedo shows awareness that the indeterminacy inherent in the body infects the validity of any scientific argument but also provides the subject of inquiry with the ability to actualize, to the extent possible, the ideal self. The Republic locates bodily desires and needs in the tripartite soul. Achievement of maximal unity is dependent upon successful training of the rational part of the soul, but the earlier curriculum of Books 2 and 3, which aims at instilling a pre-reflectively virtuous disposition in the lower parts of the soul, is a prerequisite for the advanced studies of Republic 7. In the Timaeus, the world soul is fashioned out of Being, Sameness, and Difference: an examination of the Sophist and the Parmenides reveals that Difference is to be identified with the Timaeus’ Receptacle, the third ontological principle which emerges as the quasi-material component that provides each individual soul with the alloplastic capacity for psychological growth and alteration.
Book Synopsis The Principle of Non-contradiction in Plato's Republic by : Laurence Bloom
Download or read book The Principle of Non-contradiction in Plato's Republic written by Laurence Bloom and published by Lexington Books. This book was released on 2017-03-08 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plato’s formulation of the Principle of Non-contradiction (PNC) in Republic IV is the first full statement of the principle in western philosophy. His use of the principle might seem to suggest that he endorses the PNC. After all, how could one possibly deny so fundamental a principle—especially when it seems difficult to deny it without relying on it. However, the endorsement in the text is qualified. Socrates refers to the principle as one that he and his interlocutors will hypothesize and warns that if it should ever be shown to be false, all that follows from it will also be refuted. Scholars who have noticed this issue have tended to assume that the truth of the hypothesis in question can be guaranteed. Laurence Bloom argues against unthinkingly accepting this claim. He suggests that what emerges from the text is more sophisticated: Plato’s concession that the PNC is hypothetical is a textual clue pointing us to a complex philosophical argument that grounds the PNC, as well as the sort of reasoning it grounds, in form. Indeed, in framing the problem in this way, we can read the Republic as providing an extended argument for form. The argument for forms that emerges is complex and difficult. It is not and cannot be a normal, discursive argument. Indeed, the argument cannot even be one that assumes the PNC; if it did so, it would fall prey to a vicious circularity. Rather, the argument rests on the very possibility of our hypothesizing the PNC in the first place. Our ability to hypothesize the PNC—and perhaps our inability not to hypothesize it—is the linchpin. When we ask questions such as “to what objects does the PNC apply?” or “how is it possible that we apply the PNC?,” we are asking questions that lead us to the existence of form. The Principle of Non-contradiction in Plato’s Republic also explores the soul of the knower—the very entity to which and by which the principle is applied in the text—and its underlying unity.
Book Synopsis Science of Arithmetic by : Charles Wesley Vandewalker
Download or read book Science of Arithmetic written by Charles Wesley Vandewalker and published by . This book was released on 1924 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Republic written by By Plato and published by BookRix. This book was released on 2019-06-15 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Republic is a Socratic dialogue, written by Plato around 380 BCE, concerning the definition of justice, the order and character of the just city-state and the just man. The dramatic date of the dialogue has been much debated and though it must take place some time during the Peloponnesian War, "there would be jarring anachronisms if any of the candidate specific dates between 432 and 404 were assigned". It is Plato's best-known work and has proven to be one of the most intellectually and historically influential works of philosophy and political theory. In it, Socrates along with various Athenians and foreigners discuss the meaning of justice and examine whether or not the just man is happier than the unjust man by considering a series of different cities coming into existence "in speech", culminating in a city (Kallipolis) ruled by philosopher-kings; and by examining the nature of existing regimes. The participants also discuss the theory of forms, the immortality of the soul, and the roles of the philosopher and of poetry in society.
Book Synopsis Plato’s forms, mathematics and astronomy by : Theokritos Kouremenos
Download or read book Plato’s forms, mathematics and astronomy written by Theokritos Kouremenos and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-05-22 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Summoning Knowledge in Plato's Republic by : Nicholas D. Smith
Download or read book Summoning Knowledge in Plato's Republic written by Nicholas D. Smith and published by Oxford University Press. This book was released on 2019-07-04 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nicholas D. Smith presents an original interpretation of the Republic, considering it to be a book about knowledge and education. Over the course of Summoning Knowledge in Plato's Republic, he argues for four main theses. Firstly, the Republic is not just a work that has a lot to say about education; it is a book that depicts Socrates as attempting to engage his interlocutors in such a way as to help to educate them and also engages us, the readers, in a way that helps to educate us. Secondly, Plato does not suppose that education, properly understood, should have as its primary aim putting knowledge into souls that do not already have it. Instead, the education Plato discusses, represents occurring between Socrates and his interlocutors, and hopes to achieve in his readers is one that aims to arouse the power of knowledge in us and then to begin to train that power always to engage with what is more real, rather than what is less real. Thirdly, Plato's conception of knowledge is not the one typically presented in contemporary epistemology. It is, rather, the power of conceptualization by the use of exemplars. And finally, Plato engages this power of knowledge in the Republic in a way he represents as only a kind of second-best way to engage knowledge - and not as the best way, which would be dialectic. Instead, Plato uses images that summon the power of knowledge to begin the process by which the power may become fully realized.
Book Synopsis The Cambridge Companion to Plato's Republic by : Giovanni R. F. Ferrari
Download or read book The Cambridge Companion to Plato's Republic written by Giovanni R. F. Ferrari and published by Cambridge University Press. This book was released on 2007 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a fresh and comprehensive account of this outstanding work, which remains among the most frequently read works of Greek philosophy, indeed of Classical antiquity in general.
Book Synopsis From Riemann to Differential Geometry and Relativity by : Lizhen Ji
Download or read book From Riemann to Differential Geometry and Relativity written by Lizhen Ji and published by Springer. This book was released on 2017-10-03 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.
Book Synopsis Mathematics Useful for Understanding Plato by : Theon (of Smyrna.)
Download or read book Mathematics Useful for Understanding Plato written by Theon (of Smyrna.) and published by . This book was released on 1979 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Plato's Republic: Essays written by Plato and published by Editions Artisan Devereaux. This book was released on 1894 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Revolutions and Continuity in Greek Mathematics by : Michalis Sialaros
Download or read book Revolutions and Continuity in Greek Mathematics written by Michalis Sialaros and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-04-23 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together a number of leading scholars working in the field of ancient Greek mathematics to present their latest research. In their respective area of specialization, all contributors offer stimulating approaches to questions of historical and historiographical ‘revolutions’ and ‘continuity’. Taken together, they provide a powerful lens for evaluating the applicability of Thomas Kuhn’s ideas on ‘scientific revolutions’ to the discipline of ancient Greek mathematics. Besides the latest historiographical studies on ‘geometrical algebra’ and ‘premodern algebra’, the reader will find here some papers which offer new insights into the controversial relationship between Greek and pre-Hellenic mathematical practices. Some other contributions place emphasis on the other edge of the historical spectrum, by exploring historical lines of ‘continuity’ between ancient Greek, Byzantine and post-Hellenic mathematics. The terminology employed by Greek mathematicians, along with various non-textual and material elements, is another topic which some of the essays in the volume explore. Finally, the last three articles focus on a traditionally rich source on ancient Greek mathematics; namely the works of Plato and Aristotle.
Download or read book Plato's Republic written by Plato and published by Editions Artisan Devereaux. This book was released on 1894 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis What is a Mathematical Concept? by : Elizabeth de Freitas
Download or read book What is a Mathematical Concept? written by Elizabeth de Freitas and published by Cambridge University Press. This book was released on 2017-06-22 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leading thinkers in mathematics, philosophy and education offer new insights into the fundamental question: what is a mathematical concept?
