Plato S Problem

Author: M. Panza
Publisher: Springer
ISBN: 1137298138
Size: 61.27 MB
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What is mathematics about? And how can we have access to the reality it is supposed to describe? The book tells the story of this problem, first raised by Plato, through the views of Aristotle, Proclus, Kant, Frege, Gödel, Benacerraf, up to the most recent debate on mathematical platonism.

Platonism And Anti Platonism In Mathematics

Author: Mark Balaguer
Publisher: Oxford University Press on Demand
ISBN: 9780195143980
Size: 75.39 MB
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In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He establishes that both platonism and anti-platonism are defensible views and introduces a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, proceeding to defend anti-platonism (in particular, mathematical fictionalism) against various attacks--most notably the Quine-Putnam indispensability attack.

Plato S Ghost

Author: Jeremy Gray
Publisher: Princeton University Press
ISBN: 9781400829040
Size: 75.19 MB
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Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method--debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.

Plato

Author: A.E. Taylor
Publisher: Routledge
ISBN: 041562780X
Size: 20.88 MB
Format: PDF
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This book provides an introduction to Plato’s work that gives a clear statement of what Plato has to say about the problems of thought and life. In particular, it tells the reader just what Plato says, and makes no attempt to force a system on the Platonic text or to trim Plato’s works to suit contemporary philosophical tastes. The author also gives an account that has historical fidelity - we cannot really understand the Republic or the Gorgias if we forget that the Athens of the conversations is meant to be the Athens of Nicias or Cleon, not the very different Athens of Plato’s own manhood. To understand Plato’s thought we must see it in the right historical perspective.

Plato

Author: Julia Annas
Publisher: Sterling Publishing Company, Inc.
ISBN: 9781402770524
Size: 64.22 MB
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"Julia Annas provides an incisive exploration of the many-sided and elusive genius whose wide-ranging, bold, and influential ideas continue to challenge, provoke, and inspire us today"--Cover, p. 4.

From Plato To Platonism

Author: Lloyd P. Gerson
Publisher: Cornell University Press
ISBN: 0801469171
Size: 79.65 MB
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Was Plato a Platonist? While ancient disciples of Plato would have answered this question in the affirmative, modern scholars have generally denied that Plato’s own philosophy was in substantial agreement with that of the Platonists of succeeding centuries. In From Plato to Platonism, Lloyd P. Gerson argues that the ancients were correct in their assessment. He arrives at this conclusion in an especially ingenious manner, challenging fundamental assumptions about how Plato’s teachings have come to be understood. Through deft readings of the philosophical principles found in Plato's dialogues and in the Platonic tradition beginning with Aristotle, he shows that Platonism, broadly conceived, is the polar opposite of naturalism and that the history of philosophy from Plato until the seventeenth century was the history of various efforts to find the most consistent and complete version of “anti-naturalism." Gerson contends that the philosophical position of Plato—Plato’s own Platonism, so to speak—was produced out of a matrix he calls “Ur-Platonism.” According to Gerson, Ur-Platonism is the conjunction of five “antis” that in total arrive at anti-naturalism: anti-nominalism, anti-mechanism, anti-materialism, anti-relativism, and anti-skepticism. Plato’s Platonism is an attempt to construct the most consistent and defensible positive system uniting the five “antis.” It is also the system that all later Platonists throughout Antiquity attributed to Plato when countering attacks from critics including Peripatetics, Stoics, and Sceptics. In conclusion, Gerson shows that Late Antique philosophers such as Proclus were right in regarding Plotinus as “the great exegete of the Platonic revelation."

Timaeus

Author: Plato
Publisher: Hackett Publishing
ISBN: 1585108138
Size: 66.24 MB
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Both an ideal entrée for beginning readers and a solid text for scholars, the second edition of Peter Kalkavage's acclaimed translation of Plato's Timaeus brings enhanced accessibility to a rendering well known for its faithfulness to the original text. An extensive essay offers insights into the reading of the work, the nature of Platonic dialogue, and the cultural background of the Timaeus. Appendices on music, astronomy, and geometry provide additional guidance. A brief outline of the themes of the work, a detailed glossary, and a selected bibliography are also included.

Introducing Philosophy Of Mathematics

Author: Michele Friend
Publisher: Routledge
ISBN: 1317493796
Size: 56.65 MB
Format: PDF, ePub
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What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.

Plato S Parmenides

Author: Plato
Publisher: Univ of California Press
ISBN: 0520224035
Size: 72.23 MB
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"Scolnicov’s aim is to provide a new translation of Plato’s Parmenides, with a commentary designed to show that the arguments of the second half of the dialogue, the purpose of which has long been a matter of scholarly dispute, make sense as an attempt to establish the necessary logical and epistemological conditions for Plato’s own theory of forms and participation. In particular, Scolnicov attempts to show that the otherwise bewildering concatenation of arguments and hypotheses answers to a style of argument paralleled in other dialogues. Scolnicov also argues that the dialogue is intended as a serious rebuttal of Parmenides’ monist philosophy. Scolnicov’s thesis is thus diametrically opposed to those who think that the dialogue is intended as a successful critique of Plato’s own theory in the light of arguments adapted from Parmenides."—Denis O’Brien, author of Etudes sur Parménide; Empedocles' Cosmic Cycle: A Reconstruction from the Fragments and Secondary Sources "Scolnicov’s introduction presents a very clear account of Parmenides’ method and the contrast that Plato’s use of hypothesis presents to it as early as the Meno. Scolnicov then offers a clear account of Plato’s method and the way it establishes an idea of philosophical method in general: not a reasoning from first principles but a disclosing of the principles at the foundation of one’s prior convictions in order to test those principles. He subsequently takes up the principle of noncontradiction in particular before tackling the questions Parmenidean philosophy might raise about the doctrine of participation. An immensely clear and interesting introduction and way into the Parmenides."—Georgia Warnke, author of Justice and Interpretation: Studies in Contemporary German Social Thought