# Systems of Formal Logic

• L. H. Hackstaff
Book

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 193-206
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Pages 207-233
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Pages 234-283
9. L. H. Hackstaff
Pages 284-303
10. L. H. Hackstaff
Pages 304-312
11. L. H. Hackstaff
Pages 313-343
12. Back Matter
Pages 344-356

### 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