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First-Order Logic: An Introduction
This teaching book is designed to help its readers to reason systematically, reliably, and to some extent self-consciously, in the course of their ordinary pursuits-primarily in inquiry and in decision making. The principles and techniques recommended are explained and justified - not just stated; the aim is to teach orderly thinking, not the manipulation of symbols.
Paperback, 343 pages
Published October 13th 1998 by Walter de Gruyter
(first published October 1998)
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My second-favorite introductory logic book. Most everyone that I know used Mates for their Advanced Symbolic logic text. Cauman, I admit, is less rigorous in her exposition of proof-theoretic methods (her * notation system is unusual). However, she does discuss, in great detail, the metaphysical consequences of illicit existential instantiation and universal generalization.