Essay on the Principles of Logic: A Defense of Logical Monism

Michael Wolff

Published by De Gruyter 2023

Essay on the Principles of Logic

A Defense of Logical Monism

Michael Wolff
Translated by: W. Clark Wolf

https://doi.org/10.1515/9783110784930

Overview
Contents

About this book

Wolff's book defends the Kantian idea of a "general logic" whose principles underlie special systems of deductive logic. It thus undermines "logical pluralism," which tolerates the co-existence of divergent systems of modern logic without asking for consistent common principles. Part I of Wolff’s book identifies the formal language in which the most general principles of logic must be expressed. This language turns out to be a version of syllogistic language already used by Aristotle. The universal validity of logical principles, as well as the translatability of other logical languages into this language, are shown to depend only on the meanings of its logical vocabulary. Part II of the book answers the metalogical question concerning the deductive relation between general logic and special logical systems, which also have their own (less general) principles. This part identifies the rules according to which logical rules can be derived from principles. The main result of the book is that the highest principles of logic and metalogics are provided by the syllogistic, when properly understood.

Author / Editor information

Michael Wolff, Universität Bielefeld, Bielefeld.

Topics

Frontmatter Publicly Available Download PDF	I
Preface to the English Edition Publicly Available Download PDF	V
Contents Publicly Available Download PDF	XIII
Introduction Publicly Available Download PDF	XIX
I Analytical Part: Analysis of Logical Languages
Section One The Language of the Syllogistic Requires Authentication Unlicensed Licensed Download PDF	1
Section Two The Language of the Calculus of Classes Requires Authentication Unlicensed Licensed Download PDF	41
Section Three The Language of the Logical Calculus of Functions Requires Authentication Unlicensed Licensed Download PDF	72
II Synthetic Part: Construction of the Logical Calculus of Functions from the Elements of the Syllogistic
§ 41 General Preliminary Remark Requires Authentication Unlicensed Licensed Download PDF	143
Section One Rules for Deriving Rules Requires Authentication Unlicensed Licensed Download PDF	149
Section Two Hypothetical and Disjunctive Syllogistic Requires Authentication Unlicensed Licensed Download PDF	158
Section Three Categorical Syllogistic Requires Authentication Unlicensed Licensed Download PDF	178
Section Four Modal Syllogistic Requires Authentication Unlicensed Licensed Download PDF	203
Section Five Contentful Syllogistic Inference Requires Authentication Unlicensed Licensed Download PDF	261
Section Six Derivation of Formulas within the Framework of a System Extended Beyond the Limits of Elementary Deductive Logic Requires Authentication Unlicensed Licensed Download PDF	271
Section Seven Provability and Derivability within the Logical Calculus of Functions Requires Authentication Unlicensed Licensed Download PDF	293
Conclusion Requires Authentication Unlicensed Licensed Download PDF	306
Appendix 1 On the Completeness of a Syllogistic without Logical Conjunction Requires Authentication Unlicensed Licensed Download PDF	315
Appendix 2 Mathematical Induction without Higher-Level Predicate Logic Requires Authentication Unlicensed Licensed Download PDF	321
Appendix 3 Reduction of Truth-Functional Expressions to Non-Truth-Functional Expressions Requires Authentication Unlicensed Licensed Download PDF	329
Appendix 4 Compatibility and Incompatibility Requires Authentication Unlicensed Licensed Download PDF	333
Appendix 5 Modern Non-Syllogistic Systems of Modal Logic in Their Relationship to Modal Syllogistic Requires Authentication Unlicensed Licensed Download PDF	337
Appendix 6 Non-Classical Systems of Logic in Their Relationship to the Logical Calculus of Functions Requires Authentication Unlicensed Licensed Download PDF	351
Appendix 7 The Barcan Formula Requires Authentication Unlicensed Licensed Download PDF	357
Appendix 8 On Bivalence Requires Authentication Unlicensed Licensed Download PDF	359
Appendix 9 Absolute Logical Constants Requires Authentication Unlicensed Licensed Download PDF	365
Index of Symbols Used Requires Authentication Unlicensed Licensed Download PDF	369
Outline of the Rules Used Mainly in the Proofs of Part II Requires Authentication Unlicensed Licensed Download PDF	371
Index of Metalogical Rules Used in the Proofs of Part II Requires Authentication Unlicensed Licensed Download PDF	373
Index of Syllogistic Rules Used Directly in the Validity Proofs of Assertoric Syllogisms (in § 56) Requires Authentication Unlicensed Licensed Download PDF	375
Index of Modal-Syllogistic Rules Used Directly in the Validity Proofs of Modal Syllogisms (in § 63) Requires Authentication Unlicensed Licensed Download PDF	377
Index of Logical Rules Used Directly for the Derivation of Truth-Functional Rules and Laws (in § 74 and § 75) Requires Authentication Unlicensed Licensed Download PDF	379
Bibliography Requires Authentication Unlicensed Licensed Download PDF	381
Subject Index Requires Authentication Unlicensed Licensed Download PDF	387
Name Index Requires Authentication Unlicensed Licensed Download PDF	395

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Scholars/students interested in logic or analytic, classical German, or ancient philosophy, libraries, institutes
Pages
- Front matter: 21
- Main content: 396
Illustrations
- Illustrations: 13
- Tables: 5
Keywords: bivalence principle; paraconsistency; existential import; square of oppositions

eBook

Published: May 22, 2023
ISBN: 9783110784930

Hardcover

Published: May 22, 2023
ISBN: 9783110784862