Nature of Mathematics

This book explains exactly what human knowledge is. The key concepts in this book are structures and algorithms, i.e., what the readers “see” and how they make use of what they see. Thus in comparison with some other books on the philosophy (or methodology) of science, which employ a syntactic approach, the author’s approach is model theoretic or structural.

The historical and epistemological reflection on the applications of mathematical techniques to the Sciences of Nature - physics, biology, chemistry, and geology - today generates attention and interest because of the increasing use of mathematical models in all sciences and their high level of sophistication.

Mathematics didn't spring spontaneously to life, rules and definitions set in stone for all time. Its progress story has rich connections with measurement and money that have often shaped its development and driven its progress, a process that continues to this day.

Wittgenstein's remarks on mathematics have not received the recogni­ tion they deserve; they have for the most part been either ignored, or dismissed as unworthy of the author of the Tractatus and the Investiga­tions.