Abstract

In this textbook on elementary logic the authors present a rigorous treatment of first the propositional, and then the predicate calculi. The first two chapters deal with the former topic exclusively: there is much emphasis on translation of ordinary-language sentences into logic and testing their validity; also a proof notation consisting of nested boxes, similar to the Fitch subproof technique, is introduced and used. The third and fourth chapters are concerned with quantification theory in application to language analysis; the next chapter discusses more theoretical topics including a proof procedure for formulae in prenex normal form and decision procedures for restricted classes of such formulae. Identity is treated next, with the following chapter on definite descriptions. The eighth chapter is more formal in approach and has as its subject the abstract approach to logical systems: the notion of the extension of a theory is introduced at this stage; two examples of formal theories—the theory of commutative ordered fields, and that of real numbers—are presented and come under extensive elaboration. The last chapter discusses variable-binding operations and presents the theory of convergence of series as an example of such a theory with these operations. Each chapter has numerous exercises, and most have historical remarks and lists of theorems of that chapter.—P. J. M.