Philosophy of Logical Systems
This book addresses the hasty development of modern logic, especially its introducing and embracing various kinds of artificial languages and moving from the study of natural languages to that of artificial ones. This shift seemed extremely helpful and managed to elevate logic to a new level of rigor and clarity. However, the change that logic underwent in this way was in no way insignificant, and it is also far from an insignificant matter to determine to what extent the "new logic" only engaged new and more powerful instruments to answer the questions posed by the "old" one, and to what extent it replaced these questions with new ones.
Hence, this movement has generated brand new kinds of philosophical problems that have still not been dealt with systematically. Philosophy of Logical Systems addresses these new kinds of philosophical problems that are intertwined with the development of modern logic. Jaroslav Peregrin analyzes the rationale behind the introduction of the artificial languages of logic; classifies the various tools which were adopted to build such languages; gives an overview of the various kinds of languages introduced in the course of modern logic and the motifs of their employment; discusses what can actually be achieved by relocating the problems of logic from natural language into them; and reaches certain conclusions with respect to the possibilities and limitations of this "formal turn" of logic.
This book is both an important scholarly contribution to the philosophy of logic and a systematic survey of the standard (and not so standard) logical systems that were established during the short history of modern logic.
1. The Transmutation of Logic
2. Correctness of Arguments
3. Languages of Logic
4. Basic Sentential Operators
5. Gentzenian Logical Calculi
6. Hilbertian Logical Calculi
7. Properties of Calculi
8. Calculi of Propositional Logic
10. Calculi of Predicate Logic
11. From Calculi to Formal Semantics
12. Truth-Functional Semantics
13. Extensional Denotational Semantics
14. Denotations Beyond Extensions
15. Matching Calculi and Systems of Formal Semantics
16. Through the Looking Glass
17. 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