Philosophical and Mathematical Logic

Abstract

Having studied mathematics, in particular foundations and philosophy of mathematics, it happened that I was asked to teach logic to the students in the Faculty of Philosophy of the Radboud University Nijmegen. It was there that I discovered that logic is much more than just a mathematical discipline consisting of definitions, theorems and proofs, and that logic can and should be embedded in a philosophical context. After ten years of teaching logic at the Faculty of Philosophy at the Radboud University Nijmegen, thirty years at the Faculty of Philosophy of Tilburg University and nine years at the Faculty of Philosophy of the Erasmus University Rotterdam, I got many ideas how to improve my LOGIC book which was published twenty five years ago in 1993 by Verlag Peter Lang. Although the amount of work was enormous, I felt I should do it. It is like working on a large painting where you put some extra color in one corner, add a little detail at another place, shed some more light on a particular face, etc. This book was written to serve as an introduction to logic, with special emphasis on the interplay between logic and mathematics, philosophy, language and computer science. The reader will not only be provided with an introduction to classical propositional and predicate logic, but to philosophical (modal, deontic, epistemic) and intuitionistic logic as well. Arithmetic and G¨odel’s incompleteness theorems are presented, there is a chapter on the philosophy of language and a chapter with applications: logic programming, relational databases and SQL, and social choice theory. The last chapter is on fallacies and unfair discussion methods.