Without adopting one of the various views advocated in the foundations of mathematics, we may agree that mathematicians need and use a language, if only for the communication of their results and their problems. While mathematicians have been claiming the greatest possible exactness for their methods, they have been less sensitive as to their means of communication. It is well known that Leibniz proposed to put the practice of mathematical communication and mathematical reasoning on a firm base; it was, however, not before the nineteenth century that those enterprises were (more) successfully undertaken by G. Frege and G. Peano. No matter how ingeniously and rigorously Frege, Russell, Hilbert, Bernays and others developed mathematical logic, it was only in the second half of this century that logic and its language showed any features of interest to the general mathematician. The sophisticated results of Gödel were of course immediately appreciated, but they remained for a long time technical highlights without practical use. Even Tarski's result on the decidability of elementary algebra and geometry had to bide its time before any applications turned up.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2004). Introduction. In: Logic and Structure. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85108-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-85108-0_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20879-2
Online ISBN: 978-3-540-85108-0
eBook Packages: Springer Book Archive