Publication at Faculty of Arts |
2008
Abstract
This work deals with basic principles of arithmetic and calculus from the perspective of modern logic. The central line of the text examines the concept of real number or, more precisely, the concept of continuum in its development, beginning with Eudoxus, Descartes and Leibniz, through Bolzano, Cantor and Dedekind, to Frege, Brouwer, Hilbert and Wittgenstein.
Every significant movement in the philosophy of mathematics (Platonism, formalism, intuitionism, logicism, constructivism, structuralism etc.) is covered, not abstractly, but against the background of particular results or phenomena of modern logic and mathematics.