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Philosophy of Mathematics in Antiquity and in Modern Times

»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...

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Hlavní autor: Felgner, Ulrich (Autor)
Korporativní autor: SpringerLink (Online service)
Médium: Elektronický zdroj E-kniha
Jazyk:angličtina
Vydáno: Cham : Springer International Publishing : Imprint: Birkhäuser, 2023.
Vydání:1st ed. 2023.
Edice:Science Networks. Historical Studies, 62
Témata:
Mathematical logic.
Geometry.
Mathematical Logic and Foundations.
On-line přístup:https://doi.org/10.1007/978-3-031-27304-9
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Obsah:
  • 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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