Philosophy of Mathematics in Antiquity and in Modern Times

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.