Logic and Fixed-Domain Reasoning
Volume 1: An Empirico-Pragmatist Model Theory and Proof Theory
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Beschreibung
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.
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.
This book is open access, which means that you have free and unlimited access Describes, for the first time, two related concepts of logical system over fixed domain Presents a novel approach to logic demarcation questions Develops a substitutional theory of relations over fixed domain
Autor*in
Ralph Gregory Taylor
Themen in »Logic and Fixed-Domain Reasoning«
Open Access Logic over Fixed Domain Logical System Over Fixed Domain Truth-Functional Expansion Game-Theoretic Semantics Substitutional Theory of Relations Over Fixed Domain Permutation-Invariant Operation Over Fixed Domain Generalized Quantifier Over Fixed Domain Krasner-McGee Theorem Three-Valued Logic Over Fixed Domain Description Logic Logic Demarcation Question Peirce's First-Intentional Logic of Relations Zermelo's Systems of Infinitely Long Propositions