Plato Was Not a Mathematical Platonist

Plato Was Not a Mathematical Platonist
Author: Elaine Landry
Publisher: Cambridge University Press
Total Pages: 103
Release: 2023-01-31
Genre: Philosophy
ISBN: 1009313800

Download Plato Was Not a Mathematical Platonist Book in PDF, Epub and Kindle

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
Total Pages: 234
Release: 2001
Genre: Mathematics
ISBN: 9780195143980

Download Platonism and Anti-Platonism in Mathematics Book in PDF, Epub and Kindle

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
Total Pages: 393
Release: 2012-06-14
Genre: History
ISBN: 0521750725

Download Explorations in Ancient and Modern Philosophy Book in PDF, Epub and Kindle

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
Total Pages: 328
Release: 2016
Genre: History
ISBN: 0190465700

Download Plato and Pythagoreanism Book in PDF, Epub and Kindle

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.

Platonism, Naturalism, and Mathematical Knowledge

Platonism, Naturalism, and Mathematical Knowledge
Author: James Robert Brown
Publisher: Routledge
Total Pages: 195
Release: 2013-06-17
Genre: Philosophy
ISBN: 1136580387

Download Platonism, Naturalism, and Mathematical Knowledge Book in PDF, Epub and Kindle

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 Problem

Plato's Problem
Author: M. Panza
Publisher: Springer
Total Pages: 323
Release: 2013-01-21
Genre: Mathematics
ISBN: 1137298138

Download Plato's Problem Book in PDF, Epub and Kindle

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.

The Nature of Mathematical Knowledge

The Nature of Mathematical Knowledge
Author: Philip Kitcher
Publisher: Oxford University Press, USA
Total Pages: 300
Release: 1984
Genre: Electronic books
ISBN: 0195035410

Download The Nature of Mathematical Knowledge Book in PDF, Epub and Kindle

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 forms, mathematics and astronomy

Plato’s forms, mathematics and astronomy
Author: Theokritos Kouremenos
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 158
Release: 2018-05-22
Genre: Literary Criticism
ISBN: 3110601869

Download Plato’s forms, mathematics and astronomy Book in PDF, Epub and Kindle

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
Total Pages: 360
Release: 2013-11-27
Genre: Philosophy
ISBN: 0801469171

Download From Plato to Platonism Book in PDF, Epub and Kindle

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."