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Philosophy of mathematics in antiquity and in modern times

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Philosophy of mathematics in antiquity and in modern times/ by Ulrich Felgner.
作者:	Felgner, Ulrich.
出版者:	Cham :Springer International Publishing : : 2023.,
面頁冊數:	xi, 317 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Geometry. -
電子資源:	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:

579899
Geometry.

LC Class. No.: QA8.4

Dewey Class. No.: 510.1

Philosophy of mathematics in antiquity and in modern times
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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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