ABSTRACT

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.

chapter 1|10 pages

The Transmutation of Logic

chapter 2|11 pages

Correctness of Arguments

chapter 3|13 pages

Languages of Logic

chapter 4|11 pages

Basic Sentential Operators

chapter 5|13 pages

Gentzenian Logical Calculi

chapter 6|9 pages

Hilbertian Logical Calculi

chapter 7|6 pages

Properties of Calculi

chapter 8|13 pages

Calculi of Propositional Logic

chapter 9|13 pages

Quantification

chapter 10|17 pages

Calculi of Predicate Logic

chapter 11|6 pages

From Calculi to Formal Semantics

chapter 12|10 pages

Truth-Functional Semantics

chapter 13|14 pages

Extensional Denotational Semantics

chapter 14|14 pages

Denotations Beyond Extensions

chapter 16|13 pages

Through the Looking Glass …

chapter 17|2 pages

Conclusion

Philosophical Problems of Logical Systems