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.
Download or read book Plato s Forms Mathematics and Astronomy written by Theokritos Kouremenos and published by . This book was released on 2018 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.
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.
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.
Download or read book Plato s Philosophy of Mathematics written by Anders Wedberg and published by Praeger. This book was released on 1977 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Science and the Sciences in Plato written by John Peter Anton and published by Academic Resources Corp. This book was released on 1980 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ptolemy s Philosophy written by Jacqueline Feke and published by Princeton University Press. This book was released on 2020-10-13 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: A stimulating intellectual history of Ptolemy's philosophy and his conception of a world in which mathematics reigns supreme 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.
Download or read book Plato s Cosmology and its Ethical Dimensions written by Gabriela Roxana Carone and published by Cambridge University Press. This book was released on 2005-10-31 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although a great deal has been written on Plato's ethics, his cosmology has not received so much attention in recent times and its importance for his ethical thought has remained underexplored. By offering accounts of Timaeus, Philebus, Politicus and Laws X, the book reveals a strongly symbiotic relation between the cosmic and human sphere. It is argued that in his late period Plato presents a picture of an organic universe, endowed with structure and intrinsic value, which both urges our respect and calls for our responsible intervention. Humans are thus seen as citizens of a university that can provide a context for their flourishing even in the absence of good political institutions. The book sheds light on many intricate metaphysical issues in late Plato and brings out the close connections between his cosmology and the development of his ethics.
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 A Very Short Introduction written by Julia Annas and published by OUP Oxford. This book was released on 2003-02-13 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lively and accessible introduction to Plato focuses on the philosophy and argument of his writings, drawing the reader into Plato's way of doing philosophy, and the general themes of his thinking. This is not a book to leave the reader standing in the outer court of introduction and background information, but leads directly into Plato's argument. It looks at Plato as a thinker grappling with philosophical problems in a variety of ways, rather than a philosopher with a fully worked-out system. It includes a brief account of Plato's life and the various interpretations that have been drawn from the sparse remains of information. It stresses the importance of the founding of the Academy and the conception of philosophy as a subject. Julia Annas discusses Plato's style of writing: his use of the dialogue form, his use of what we today call fiction, and his philosophical transformation of myths. She also looks at his discussions of love and philosophy, his attitude to women, and to homosexual love, explores Plato's claim that virtue is sufficient for happiness, and touches on his arguments for the immortality of the soul and his ideas about the nature of the universe. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Download or read book Plato Was Not a Mathematical Platonist written by Elaine Landry and published by Cambridge University Press. This book was released on 2023-01-31 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Plato s Philosophy of Science written by Andrew Gregory and published by Bristol Classical Press. This book was released on 2000 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text seeks to reassess Plato's views on how we might investigate and explain the natural world.
Download or read book Early Greek Science written by G E R Lloyd and published by Random House. This book was released on 2012-09-30 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this new series leading classical scholars interpret afresh the ancient world for the modern reader. They stress those questions and institutions that most concern us today: the interplay between economic factors and politics, the struggle to find a balance between the state and the individual, the role of the intellectual. Most of the books in this series centre on the great focal periods, those of great literature and art: the world of Herodotus and the tragedians, Plato and Aristotle, Cicero and Caesar, Virgil, Horace and Tacitus. This study traces Greek science through the work of the Pythagoreans, the Presocratic natural philosophers, the Hippocratic writers, Plato, the fourth-century B.C. astronomers and Aristotle. G. E. R. Lloyd also investigates the relationships between science and philosophy and science and medicine; he discusses the social and economic setting of Greek science; he analyses the motives and incentives of the different groups of writers.
Download or read book Plato s Philosophy of Mathematics written by Paul Pritchard and published by . This book was released on 1995 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Plato s Mathematical Imagination written by Robert Sherrick Brumbaugh and published by Bloomington : Indiana University Press. This book was released on 1954 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Plato Lysis written by Plato and published by Scribe Publishing. This book was released on 2018-03-22 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: For someone whose influence has been so profound on Western thinking remarkably little is known of the Greek philosopher and thinker Plato. Due to the means and social status of his family Plato was most probably educated by some of Athens' finest teachers. The curriculum would have been rich and varied and include the doctrines of Cratylus and Pythagoras as well as Parmenides. Two major events shaped Plato's life whilst he was a young man. The first was a meeting with the great philosopher Socrates. Socrates's methods of debate impressed Plato and he soon became a devoted follower. From here would flow Plato's career as one of the finest minds civilization has produced. Major event number two was the on-going rivalry between Athens and Sparta which erupted into the Peloponnesian War. This was, in fact, several 'stop-start' wars fought during the period 431-404 BCE. Plato served in the cause of Athens and its Allies between 409 and 404 B.C.E. The comprehensive defeat of Athens by Sparta ended the Athenian democracy, although after a brief oligarchy it was restored. Plato traveled for a dozen years throughout the Mediterranean, studying mathematics with the Pythagoreans in Italy, as well as geometry, geology, astronomy and religion in Egypt. It was during this time that Plato began his writings, a remarkable number of which survive to this day. The writings themselves are usually classified into three distinct periods although there is some uncertainty as to the exact order in which they were written. Having now returned to Athens Plato embarked upon an extraordinary undertaking. In around 385 B.C.E., he established a school of learning, known as the Academy. The extensive curriculum included astronomy, biology, mathematics, political theory and philosophy. Plato hoped that those who studied there would be future leaders who would be better equipped thorough its teachings to understand how to build a better government. Plato would preside over its teachings until his death in Athens around 348 B.C.E.
Download or read book Aristotle on Mathematical Infinity written by Theokritos Kouremenos and published by Franz Steiner Verlag. This book was released on 1995 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
