Abstract

A clear, compact, technical presentation of the traditional topics of symbolic logic. The propositional calculus, which Lorenzen develops for ten truth functions, is formulated in six axioms to enable comparison with intuitionism. An important part of the book is Lorenzen's "establishment" of the axioms of Brouwer's intuitionistic calculus by proving their universal admissibility for any calculus. If the and's and if's of these axioms are interpreted as metalinguistic terms used in stating inference rules for object calculi, then no matter what calculus the axioms are added to, no new theorems become provable. In the process of this "establishment" of what he calls "effective logic," Lorenzen makes use of nine different kinds of implication.-J. B. B.