Logic and Fixed-Domain Reasoning
Volume 1: An Empirico-Pragmatist Model Theory and Proof Theory
Series: Trends in Logic; 67;
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Product details:
- Publisher Springer Nature Switzerland
- Date of Publication 20 July 2026
- Number of Volumes 1 pieces, Book
- ISBN 9783031981883
- Binding Hardback
- No. of pages369 pages
- Size 235x155 mm
- Language English
- Illustrations XXXIX, 369 p. 32 illus., 5 illus. in color. Illustrations, black & white 700
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Long description:
The author develops, incrementally over the course of several chapters, related concepts of logical system over fixed domain, both classical and nonclassical, by means of pragmatism-inspired translations into paradigmatic, infinitary, quantifier-free languages having rigidly designating constants for all elements of a fixed domain. Each concept fully accommodates both the descriptive (model-theoretic) and deductive (proof-theoretic) tasks of any logic. Chapters 1 through 7 concern first-order logics over fixed domain. Final Chapter 8 takes up second-order logics whereby standard names for each and every boolean-valued function are now introduced. Along the way, substitutional theories of first-, alternatively, second-order relations are presented following Russell. Clarification of classification questions (What is a logical vs. mathematical term? A logical law? A logical operation?) is achieved, for logics over fixed domain, in a manner that may be unattainable in the case of variable-domain logics. The author adopts a nonstandard view according to which the fixed-domain logics of Peirce, Zermelo, and Carnap are no mere stepping stones on the path to variable-domain logics but, rather, constitute an alternative conception having certain clarificatory advantages. Consequently, the book should be of interest to both logicians and philosophers of logic.
MoreTable of Contents:
Chapter 1: A Paradigmatic Family of First-Order Logics over Fixed Domain.- Chapter 2: Deduction Calculi for First-Order Logics over Fixed Domain.- Chapter 3: A Substitutional Theory of First-Order Relations.- Chapter 4: Invariance under Domain Permutations.- Chapter 5: Infinitary First-Order Quantificational Logics.- Chapter 6: First-Order Logics with Generalized Quantification.- Chapter 7: The Province of Fixed-Domain Reasoning.- Chapter 8: Higher-Order Logics over Fixed Domain.
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