A Precis of Mathematical Logic
The work of which this is an English translation appeared originally in French as Precis de logique mathematique. In 1954 Dr. Albert Menne brought out a revised and somewhat enlarged edition in German (Grund riss der Logistik, F. Schoningh, Paderborn). I
- PDF / 17,022,586 Bytes
- 109 Pages / 430.916 x 649.204 pts Page_size
- 10 Downloads / 201 Views
SYNTHESE LIBRARY A SERIES OF MONOGRAPHS ON THE RECENT DEVELOPMENT OF SYMBOLIC LOGIC, SIGNIFICS, SOCIOLOGY OF LANGUAGE, SOCIOLOGY OF SCIENCE AND OF KNOWLEDGE, STATISTICS OF LANGUAGE AND RELATED FIELDS
Editors: B. H. KAZEMIER / D. VUYSJE
J. M. BOCHENSKI
A PRECIS OF MATHEMATICAL LOGIC Translated from the French and German editions by Otto Bird
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
ISBN 978-90-481-8329-6 ISBN 978-94-017-0592-9 (eBook) DOI 10.1007/978-94-017-0592-9 Copyright 1959 by Springer Science+Business Media Dordrecht Originally published by D. Reidel Publishing Company, Dordrecht, Holland in 1959 No part of this book may be reproduced in any form, by print, photoprint, microfilm, or any other means without permission from the publisher.
CONTENTS
TRANSLATOR'S PREFACE
I
GENERAL PRINCIPLES
§ 0 Introduction 0.1 Notion and history / 0.2 Logic and mathematics /0.3 Applications
1
§ 1 Fundamental Expressions and Operations 1.1 Expression, constant, variable / 1.2 Substitution, syntactical category / 1.3 Sentence, name, functor / 1.4 Classification of variables and functors / 1.5 Definition
3
§ 2 Rules of Writing 2.1 Supposition / 2.2 The placing of functors / 2.3 Parentheses / 2.4 Dots
6
II
THE LOGIC OF SENTENCES
§ 3 Truth Functors 3.1 Truth values / 3.2 Negation / 3.3 Dyadic truth functors / 3.4 Alternation / 3.5 Material implication / 3.6 Disjunction / 3.7 Conjunction /3.8 Equivalence /3.9 Gonseth's graphical representation; terminology § 4 Evaluation 4.1 Definitions / 4.2 The technique of evaluation
9
16
§ 5 Equivalences 19 5.1 Laws in which all the variables are equiform / 5.2 Laws of alternation / 5.3 Laws of implication / 5.4 Laws of disjunction / 5.5 Laws of conjunction / 5.6 Laws of equivalence / 5.7 Rules of transformation
CONTENTS
§ 6 'First Principles' and implications 6.1 'First principles' / 6.2 Characteristic laws of implication / 6.3 Laws of the syllogism / 6.4 Modes of the hypothetical syllogism / 6.5 Modes of the disjunctive and copulative syllogism / 6.6 Laws of composition and dilemmas
23
§ 7 Axiomatic system 7.1 Definition / 7.2 Terms and definitions / 7.3 Sentences and rules of formation / 7.4 Laws and deduction / 7.5 Formalism / 7.6 Consistency /7.7 Completeness and independence /7.8 Rules
26
§ 8 A System of the logic of sentences 8.1 Primitive terms, rule of definition and rules of formation / 8.2 Definitions / 8.3 Rules of deduction /8.4 Axioms / 8.5 Deduction
30
§ 9 A System of the rules of deduction 34 9.1 Definitions / 9.2 Names of the expressions 8 / 9.3 Rules of translation /9.4 Examples of rules 9 /9.5 The schematic notation and method of Gentzen
III
THE LOGIC OF PREDICATES AND CLASSES
A.
The Logic of Terms
§ 10 Syllogistic 10.0 Primitive terms and rules / 10.1 Definitions and axioms / 10.2-4 Logical square and conversion / 10.5-7 The moods of the syllogism B
37
The Logic of Predicates
§ 11 Monadic predicates 11.1 Definitions /11.2 Quantifiers /11.3 Free and bound variables
43
46 § 12 Laws of monadic predicates 12.1 Methodological principle / 12.2
Data Loading...
