Philosophy of Logical Systems

Jaroslav Peregrin is the research professor at the Department of Logic of the Institute of Philosophy of the Czech Academy of Sciences and a professor at the Faculty of Philosophy of the University of Hradec Králové, Czechia. He is the author of Doing Worlds with Words (1995), Meaning and Structure (Ashgate, 2001), Inferentialism (2014) and Reflective Equilibrium and the Principles of Logical Analysis (together with V. Svoboda; Routledge, 2017). His current research focuses on logical and philosophical aspects of inferentialism and on more general questions of normativity.

• Preface1. The Transmutation of Logic2. Correctness of Arguments3. Languages of Logic4. Basic Sentential Operators5. Gentzenian Logical Calculi6. Hilbertian Logical Calculi7. Properties of Calculi8. Calculi of Propositional Logic9. Quantification10. Calculi of Predicate Logic11. From Calculi to Formal Semantics12. Truth-Functional Semantics 13. Extensional Denotational Semantics14. Denotations Beyond Extensions15. Matching Calculi and Systems of Formal Semantics16. Through the Looking Glass17. Conclusion: Philosophical Problems of Logical Systems

"The book is well written and accessible; it introduces, and offers a philosophical commentary on, the main formal tools developed by logicians over the past 140 years or so. In doing so, it covers philosophically important topics such as the interpretation of variables, higher-order logics, universal algebra, and the correspondence between valuations and deductive calculi in propositional logic." – Notre Dame Philosophical Reviews"In a tour-de-force survey of logical systems, Peregrin addresses the fundamental question of how logical systems relate to natural langue argumentation. The book develops the view that logical systems are models and challenges widespread assumptions about the nature of logical semantics." – Georg Brun, University of Bern"For the general student of philosophy or linguistics it is hard to understand why to do formal logics at all. By using a rule-theoretical access, Peregrin’s book shows step by step how ideal models are necessary tools for understanding the form of valid reasoning, but no first results in a meliorating project of replacing natural by formal languages." – Pirmin Stekeler-Weithofer, University of Leipzig