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

Format:

Book

Author/Creator:

Wolff, Michael.

Contributor:

Wolf, Clark.

Language:

English

Subjects (All):

Logic--Philosophy.

Logic.

Physical Description:

1 online resource (418 pages)

Edition:

1st ed.

Other Title:

Essay on the Principles of Logic

Place of Publication:

Berlin/Boston : Walter de Gruyter GmbH, 2023.

Summary:

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.

Contents:

Intro

Preface to the English Edition

Contents

Introduction

I Analytical Part: Analysis of Logical Languages

Section One The Language of the Syllogistic

Section Two The Language of the Calculus of Classes

Section Three The Language of the Logical Calculus of Functions

II Synthetic Part: Construction of the Logical Calculus of Functions from the Elements of the Syllogistic

41 General Preliminary Remark

Section One Rules for Deriving Rules

Section Two Hypothetical and Disjunctive Syllogistic

Section Three Categorical Syllogistic

Section Four Modal Syllogistic

Section Five Contentful Syllogistic Inference

Section Six Derivation of Formulas within the Framework of a System Extended Beyond the Limits of Elementary Deductive Logic

Section Seven Provability and Derivability within the Logical Calculus of Functions

Conclusion

Appendix 1 On the Completeness of a Syllogistic without Logical Conjunction

Appendix 2 Mathematical Induction without Higher-Level Predicate Logic

Appendix 3 Reduction of Truth-Functional Expressions to Non-Truth-Functional Expressions

Appendix 4 Compatibility and Incompatibility

Appendix 5 Modern Non-Syllogistic Systems of Modal Logic in Their Relationship to Modal Syllogistic

Appendix 6 Non-Classical Systems of Logic in Their Relationship to the Logical Calculus of Functions

Appendix 7 The Barcan Formula

Appendix 8 On Bivalence

Appendix 9 Absolute Logical Constants

Index of Symbols Used

Outline of the Rules Used Mainly in the Proofs of Part II

Index of Metalogical Rules Used in the Proofs of Part II

Index of Syllogistic Rules Used Directly in the Validity Proofs of Assertoric Syllogisms (in 56)

Index of Modal-Syllogistic Rules Used Directly in the Validity Proofs of Modal Syllogisms (in 63).

Index of Logical Rules Used Directly for the Derivation of Truth-Functional Rules and Laws (in 74 and 75)

Bibliography

Subject Index

Name Index.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9783110784930

3110784939

OCLC:

1378937906