Traditional logic as a part of philosophy is one of the oldest scientific disciplines. Mathematical logic, however, is a relatively young discipline and arose from the endeavors of Peano, Frege, Russell and others to create a logistic foundation for mathematics. It steadily developed during the 20th century into a broad discipline with several sub-areas and numerous applications in mathematics, informatics, linguistics and philosophy. While there are already several well-known textbooks on mathematical logic, this book is unique in that it is (...) much more concise than most others, and the material is treated in a streamlined fashion which allows the professor to cover many important topics in a one semester course. Although the book is intended for use as a graduate text, the first three chapters could be understood by undergraduates interested in mathematical logic. These initial chapters cover just the material for an introductory course on mathematical logic combined with the necessary material from set theory. This material is of a descriptive nature, providing a view towards decision problems, automated theorem proving, non-standard models and other subjects. The remaining chapters contain material on logic programming for computer scientists, model theory, recursion theory, Godel’s Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text. The author has provided exercises for each chapter, as well as hints to selected exercises. About the German edition: …The book can be useful to the student and lecturer who prepares a mathematical logic course at the university. What a pity that the book is not written in a universal scientific language which mankind has not yet created. - A.Nabebin, Zentralblatt. (shrink)

Was ist Wahrheit? Zufolge welcher Standards erkennt man, was wahr oder falsch ist? Wie lassen sich derartige Kriterien rechtfertigen? Die vornehmlich durch die Wende zur Sprache und die Ausbildung einer Metatheorie der analytischen Wissenschaften geprägte neuere Erörterung dieser Hauptfragen zur Wahrheit führt auf Vorfragen: Von welchen Gebilden sagen wir in welcher Weise, sie seien wahr oder falsch? Was sind und was leisten Definitionen, Kriterien, Regeln, Bedingungen der Wahrheit und Falschheit? Die vorliegende Schrift entfaltet einen systematischen Rahmen, in dem die Vorfragen (...) zur Wahrheit beantwortet und die Hauptfragen in neuer Weise organisiert werden. (shrink)

Intermediate Logic is an ideal text for anyone who has taken a first course in logic and is progressing to further study. It examines logical theory, rather than the applications of logic, and does not assume any specific technical grounding. The author introduces and explains each concept and term, ensuring readers have a firm foundation for study. He provides a broad, deep understanding of logic by adopting and comparing a variety of different methods and approaches.