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Philosophy of mathematics in antiqui...

Felgner, Ulrich.

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Philosophy of mathematics in antiquity and in modern times

Record Type:	Electronic resources : Monograph/item
Title/Author:	Philosophy of mathematics in antiquity and in modern times/ by Ulrich Felgner.
Author:	Felgner, Ulrich.
Published:	Cham :Springer International Publishing : : 2023.,
Description:	xi, 317 p. :ill., digital ;24 cm.
[NT 15003449]:	The concept of mathematics -- Plato's philosophy of mathematics -- The Aristotelian conception of mathematics -- The axiomatic method of Euclid -- Finitism in Greek mathematics -- The paradoxes of Zeno -- On certainty in mathematics -- The Cartesian nativism, the Prometheus myth, Augustinian illuminism, and Cartesian rationalism -- John Locke's thoughts on mathematics -- Rationalism -- Empiricism in mathematics -- Immanuel Kant's conception of mathematics -- Psychologism in mathematics -- Logicism -- The concept of "set" -- Contemporary Platonism -- The problem of non-constructive proofs of existence -- The formal and the contentual position -- Dedekind and the emergence of structuralism -- Hilbert's critical philosophy -- Epilogue -- Index of names -- Index of subjects -- Index of abbreviations.
Contained By:	Springer Nature eBook
Subject:	Mathematics - Philosophy -
Online resource:	https://doi.org/10.1007/978-3-031-27304-9
ISBN:	9783031273049

Philosophy of mathematics in antiquity and in modern times
Felgner, Ulrich.

Philosophy of mathematics in antiquity and in modern times[electronic resource] /by Ulrich Felgner. - Cham :Springer International Publishing :2023. - xi, 317 p. :ill., digital ;24 cm. - Science networks. historical studies,v. 622296-6080 ;. - Science networks. historical studies,v. 62..

The concept of mathematics -- Plato's philosophy of mathematics -- The Aristotelian conception of mathematics -- The axiomatic method of Euclid -- Finitism in Greek mathematics -- The paradoxes of Zeno -- On certainty in mathematics -- The Cartesian nativism, the Prometheus myth, Augustinian illuminism, and Cartesian rationalism -- John Locke's thoughts on mathematics -- Rationalism -- Empiricism in mathematics -- Immanuel Kant's conception of mathematics -- Psychologism in mathematics -- Logicism -- The concept of "set" -- Contemporary Platonism -- The problem of non-constructive proofs of existence -- The formal and the contentual position -- Dedekind and the emergence of structuralism -- Hilbert's critical philosophy -- Epilogue -- Index of names -- Index of subjects -- Index of abbreviations.

»Philosophy of Mathematics« is understood, in this book, as an effort to clarify such questions that mathematics itself raises but cannot answer with its own methods. These include, for example, questions about the ontological status of mathematical objects (e.g., what is the nature of mathematical objects?) and the epistemological status of mathematical theorems (e.g., from what sources do we draw when we prove mathematical theorems?) The answers given by Plato, Aristotle, Euclid, Descartes, Locke, Leibniz, Kant, Cantor, Frege, Dedekind, Hilbert and others will be studied in detail. This will lead us to deep insights, not only into the history of mathematics, but also into the conception of mathematics as it is commonly held in the present time. The book is a translation from the German, however revised and considerably expanded. Various chapters have been completely rewritten.

ISBN: 9783031273049

Standard No.: 10.1007/978-3-031-27304-9doiSubjects--Topical Terms:

562905
Mathematics
--Philosophy

LC Class. No.: QA8.4

Dewey Class. No.: 510.1

Philosophy of mathematics in antiquity and in modern times
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240 1 0 $a Philosophie der Mathematik in der Antike und in der Neuzeit. $l English
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505 0 $a The concept of mathematics -- Plato's philosophy of mathematics -- The Aristotelian conception of mathematics -- The axiomatic method of Euclid -- Finitism in Greek mathematics -- The paradoxes of Zeno -- On certainty in mathematics -- The Cartesian nativism, the Prometheus myth, Augustinian illuminism, and Cartesian rationalism -- John Locke's thoughts on mathematics -- Rationalism -- Empiricism in mathematics -- Immanuel Kant's conception of mathematics -- Psychologism in mathematics -- Logicism -- The concept of "set" -- Contemporary Platonism -- The problem of non-constructive proofs of existence -- The formal and the contentual position -- Dedekind and the emergence of structuralism -- Hilbert's critical philosophy -- Epilogue -- Index of names -- Index of subjects -- Index of abbreviations.
520 $a »Philosophy of Mathematics« is understood, in this book, as an effort to clarify such questions that mathematics itself raises but cannot answer with its own methods. These include, for example, questions about the ontological status of mathematical objects (e.g., what is the nature of mathematical objects?) and the epistemological status of mathematical theorems (e.g., from what sources do we draw when we prove mathematical theorems?) The answers given by Plato, Aristotle, Euclid, Descartes, Locke, Leibniz, Kant, Cantor, Frege, Dedekind, Hilbert and others will be studied in detail. This will lead us to deep insights, not only into the history of mathematics, but also into the conception of mathematics as it is commonly held in the present time. The book is a translation from the German, however revised and considerably expanded. Various chapters have been completely rewritten.
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