Philosophy of mathematics in the twentieth century (Q2711910)

The paper is devoted to the development of the philosophy of mathematics in the 20th century. Since the author claims that to understand it, it is necessary to have some knowledge of Kant's ideas, the paper begins with a presentation of the main theses of Kant's philosophy. Further the development of the philosophy of mathematics till 1931 (logicism, intuitionism, formalism) is discussed. In the next part the period after 1931 is considered. The changes in the classical doctrines made after 1931 are discussed (in particular ideas of Quine, Putnam, Hodes, Field and Wagner concerning logicism, ideas of Heyting, Dummett and Wittgenstein concerning intuitionism as well as the influence of studies in proof theory and of reverse mathematics on Hilbert's formalistic programme are presented). In the sequel works and ideas of Quine, Putnam, Gödel as well as Maddy, Hellman and Resnik are considered.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00015].