Philosophy of mathematics in antiquity and in modern times / Ulrich Felgner.
Felgner, Ulrich, author.
2023
QA8.4
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Title Philosophy of mathematics in antiquity and in modern times / Ulrich Felgner.
Author Felgner, Ulrich, author.
Uniform Title Philosophie der Mathematik in der Antike und in der Neuzeit. English
ISBN 9783031273049 (electronic bk.)
3031273044 (electronic bk.)
9783031273032
3031273036
DOI https://doi.org/10.1007/978-3-031-27304-9
Published Cham : Birkhäuser, [2023]
Copyright ©2023
Language English
Language Note Translated from the German.
Description 1 online resource (xi, 317 pages) : illustrations.
Other Standard Identifiers 10.1007/978-3-031-27304-9 doi
Call Number QA8.4
Dewey Decimal Classification 510.1
Summary 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.
Bibliography, etc. Note Includes bibliographical references and indexes.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Series Science networks historical studies ; v. 62.
Available in Other Form Philosophy of mathematics in antiquity and in modern times.
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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.

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