This book grew out of lectures. It is intended as an introduction
to classical two-valued predicate logic. The restriction to
classical logic is not meant to imply that this logic is
intrinsically better than other, non-classical logics; however,
classical logic is a good introduction to logic because of its
simplicity, and a good basis for applications because it is the
foundation of classical mathematics, and thus of the exact sciences
which are based on it. The book is meant primarily for mathematics
students who are already acquainted with some of the fundamental
concepts of mathematics, such as that of a group. It should help
the reader to see for himself the advantages of a formalisation.
The step from the everyday language to a formalised language, which
usually creates difficulties, is dis cussed and practised
thoroughly. The analysis of the way in which basic mathematical
structures are approached in mathematics leads in a natural way to
the semantic notion of consequence. One of the substantial
achievements of modern logic has been to show that the notion of
consequence can be replaced by a provably equivalent notion of
derivability which is defined by means of a calculus. Today we know
of many calculi which have this property."
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