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

• Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2023 Part 1
• VerfasserIn: Wolff, Michael,
• MitwirkendeR: Wolf, W. Clark,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2023]; ©2023
• Year of Publication: 2023
• Language: English
• Physical Description: 1 online resource (XXI, 396 p.)

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.

Table of Contents

Frontmatter -- 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