Plato Was Not a Mathematical Platonist

Plato Was Not a Mathematical Platonist

Author: Elaine Landry

Publisher: Cambridge University Press

Published: 2023-01-31

Total Pages: 103

ISBN-13: 1009313800

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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.


Platonism and Anti-Platonism in Mathematics

Platonism and Anti-Platonism in Mathematics

Author: Mark Balaguer

Publisher: Oxford University Press, USA

Published: 2001

Total Pages: 234

ISBN-13: 9780195143980

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In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible. (Philosophy)


Explorations in Ancient and Modern Philosophy

Explorations in Ancient and Modern Philosophy

Author: M. F. Burnyeat

Publisher: Cambridge University Press

Published: 2012-06-14

Total Pages: 393

ISBN-13: 0521750725

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The first of two volumes collecting the published work of one of the greatest living ancient philosophers, M.F. Burnyeat.


Plato and Pythagoreanism

Plato and Pythagoreanism

Author: Phillip Sidney Horky

Publisher: Oxford University Press

Published: 2016

Total Pages: 328

ISBN-13: 0190465700

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Was Plato a Pythagorean? Plato's students and earliest critics thought so, but later scholars have been more skeptical. Plato and Pythagoreanism reconsiders this question by arguing that a specific type of Pythagorean philosophy, called "mathematical" Pythagoreanism, played a profound role in Plato's philosophy.


The Nature of Mathematical Knowledge

The Nature of Mathematical Knowledge

Author: Philip Kitcher

Publisher: Oxford University Press, USA

Published: 1984

Total Pages: 300

ISBN-13: 0195035410

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This book argues against the view that mathematical knowledge is a priori, contending that mathematics is an empirical science and develops historically, just as natural sciences do. Kitcher presents a complete, systematic, and richly detailed account of the nature of mathematical knowledge and its historical development, focusing on such neglected issues as how and why mathematical language changes, why certain questions assume overriding importance, and how standards of proof are modified.


Plato's Problem

Plato's Problem

Author: M. Panza

Publisher: Springer

Published: 2013-01-21

Total Pages: 323

ISBN-13: 1137298138

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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, Naturalism, and Mathematical Knowledge

Platonism, Naturalism, and Mathematical Knowledge

Author: James Robert Brown

Publisher: Routledge

Published: 2013-06-17

Total Pages: 195

ISBN-13: 1136580387

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This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. Not only does this engaging book present the Platonist-Naturalist debate over mathematics in a comprehensive fashion, but it also sheds considerable light on non-mathematical aspects of a dispute that is central to contemporary philosophy.


Plato’s forms, mathematics and astronomy

Plato’s forms, mathematics and astronomy

Author: Theokritos Kouremenos

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2018-05-22

Total Pages: 158

ISBN-13: 3110601869

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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.


From Plato to Platonism

From Plato to Platonism

Author: Lloyd P. Gerson

Publisher: Cornell University Press

Published: 2013-11-27

Total Pages: 360

ISBN-13: 0801469171

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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 are 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."