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The aim of this paper is to indicate some connections between Leibniz's and Kant's philosophical ideas on the one hand and Hilbert's and Gödel's philosophy of mathematics on the other. We shall be interested mainly in issues connected with Hilbert's program and Gödel's incompleteness theorems.Hilbert's program -which gave rise to one of the important domains of mathematical logic, i.e., to proof theory, and to one of the three main theories in the contemporary philosophy of mathematics, i.e., to formalism -arose in a crisis situation in the foundations of mathematics on the turn of the nineteenth century. 2 Main controversy centered around the problem of the legitimacy of abstract objects, in particular of the actual infinity. Some paradoxes were discovered in Cantor's set theory but they could be removed by appropriate modifications of the latter. The really embarrassing contradiction was discovered a bit later by Russell in Frege's system of logic.Hilbert's program was on the one hand a protest against proposals of overcoming those difficulties and securing the edifice of mathematics by restricting the subject and methods of the latter (cf. Brouwer's intuitionism as well as propo

Author

Editors Essays in the Philosophy and Histor

Publisher

Brill Academic Pub

Published

2010

Language

EN

ISBN

9789042030916

Subjects

History, Philosophy, Mathematics