This book shows how the main set-theoretic and semantic paradoxes can be solved in a systematic way, which is conceptualized independently of the paradoxes themselves.
Universal Logic conceptualizes a new logic, where the main inference connective is understood as 'meaning containment'. Classical logic plays a restricted role, applying to 'classical sentences', while the new logic is studied in depth with chapters on semantics, proof theory, and properties. Based on this logic, simple consistency is proved for naive class theory, also in conjunction with 'classical theories' such as a Z-F-style set theory. This book shows how the main set-theoretic and semantic paradoxes can be solved in a systematic way, which is conceptualized independently of the paradoxes themselves.
Throughout the twentieth century, the classical logic of Frege and Russell dominated the field of formal logic. But, as Ross Brady argues, a new type of weak relevant logic may prove to be better equipped to present new solutions to persistent paradoxes. Universal Logic begins with an overview of classical and relevant logic and discusses the limitations of both in analyzing certain paradoxes. It is the first text to demonstrate how the main set-theoretic and semantic paradoxes can be solved in a systematic way and as such will be of great interest to both scholars and students of logic.
The classical logic of Frege and Russell has dominated formal logic in the 20th century. But a new type of weak relevant logic may prove itself to be better equipped to present new solutions to persisting paradoxes.
Universal Logic conceptualizes a new weak quantified relevant logic where the main inference connective is understood as 'meaning containment.' This logic is intended to analyze naive set/class theories. The volume begins with an overview of classical logic and relevant logic, and discusses the limitations of both types of logic in analyzing certain paradoxes. A summary on the history of logic segues into the author's introduction of his new logic modeled on the properties of set-theoretic containment. This book is the first to demonstrate how the main set-theoretic and semantic paradoxes can be solved in a systematic way, which is conceptualized independently of the paradoxes themselves.
