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Systems of Formal Logic

  • L. H. Hackstaff

Table of contents

  1. Front Matter
    Pages I-XI
  2. L. H. Hackstaff
    Pages 1-47
  3. L. H. Hackstaff
    Pages 48-93
  4. L. H. Hackstaff
    Pages 94-129
  5. L. H. Hackstaff
    Pages 130-192
  6. L. H. Hackstaff
    Pages 207-233
  7. L. H. Hackstaff
    Pages 234-283
  8. L. H. Hackstaff
    Pages 304-312
  9. L. H. Hackstaff
    Pages 313-343
  10. Back Matter
    Pages 344-356

About this book

Introduction

The present work constitutes an effort to approach the subject of symbol­ ic logic at the elementary to intermediate level in a novel way. The book is a study of a number of systems, their methods, their rela­ tions, their differences. In pursuit of this goal, a chapter explaining basic concepts of modern logic together with the truth-table techniques of definition and proof is first set out. In Chapter 2 a kind of ur-Iogic is built up and deductions are made on the basis of its axioms and rules. This axiom system, resembling a propositional system of Hilbert and Ber­ nays, is called P +, since it is a positive logic, i. e. , a logic devoid of nega­ tion. This system serves as a basis upon which a variety of further sys­ tems are constructed, including, among others, a full classical proposi­ tional calculus, an intuitionistic system, a minimum propositional calcu­ lus, a system equivalent to that of F. B. Fitch (Chapters 3 and 6). These are developed as axiomatic systems. By means of adding independent axioms to the basic system P +, the notions of independence both for primitive functors and for axiom sets are discussed, the axiom sets for a number of such systems, e. g. , Frege's propositional calculus, being shown to be non-independent. Equivalence and non-equivalence of systems are discussed in the same context. The deduction theorem is proved in Chapter 3 for all the axiomatic propositional calculi in the book.

Keywords

formal logic logic propositional calculus symbolic logic

Authors and affiliations

  • L. H. Hackstaff
    • 1
  1. 1.Wabash CollegeCrawfordsvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-010-3547-7
  • Copyright Information Springer Science+Business Media B.V. 1966
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-3549-1
  • Online ISBN 978-94-010-3547-7
  • Buy this book on publisher's site