Philosophy of Mathematics in Antiquity and in Modern Times

Inbunden, Engelska, 2023

AvUlrich Felgner

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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?).

Produktinformation

Utgivningsdatum2023-06-11
Mått155 x 235 x 24 mm
Vikt664 g
FormatInbunden
SpråkEngelska
SerieScience Networks. Historical Studies
Antal sidor317
Upplaga2023
FörlagBirkhauser Verlag AG
ISBN9783031273032
OriginaltitelPhilosophie der Mathematik in der Antike und in der Neuzeit

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Ulrich Felgner is a retired professor of mathematics at the University of Tübingen. He studied at the Universities of Giessen, Besancon and Frankfurt/M, received his doctorate in 1968 in Tübingen and habilitated in Heidelberg in 1973. He worked as a Professor at the Universities of Heidelberg, Freiburg and Tübingen. His main areas of research are Algebra, Mathematical Logic, Set Theory, as well as Foundations, History and Philosophy of Mathematics.

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.