In Classical Mathematical Logic, Richard L. Epstein relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. The book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings. These lead to the formalization of the real numbers and Euclidean plane geometry. The scope and limitations of modern logic are made clear in these formalizations.

The book provides detailed...

Now in a new edition --the classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century, while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient formal logic to give a full development of Godel's incompleteness theorems. Part IV considers...

Dina Siegel and Hans Nelen The term 'global organized crime' has been in use in criminology since the mid 1990s. Even more general and abstract than its daughter-terms (transnational or cross-border organized crime), 'global organized crime' seems to embrace the activities of criminal groups and networks all around the planet, leaving no geographical space untouched. The term appears to cover the geographical as well as the historical domain: 'global' has taken on the meaning of 'forever and ever'. Global organized crime is also associatively linked with 'globalisation'. The social...

Propositional Logics presents the history, philosophy, and mathematics of the major systems of propositional logic. Classical logic, modal logics, many-valued logics, intuitionism, paraconsistent logics, and dependent implication are examined in separate chapters. Each begins with a motivation in the originators' own terms, followed by the standard formal semantics, syntax, and completeness theorem. The chapters on the various logics are largely self-contained so that the book can be used as a reference. An appendix summarizes the formal semantics and axiomatizations of the logics. The view...

This series of books presents the fundamentals of logic in a style accessible to both students and scholars. The text of each essay presents a story, the main line of development of the ideas, while the notes and appendices place the research within a larger scholarly context. The essays overlap, forming a unified analysis of logic as the art of reasoning well, yet each essay is designed so that it may be read independently. The question addressed in this volume is how we can justify our beliefs through reasoning. The first essay, "Arguments," investigates what it is that we call true or...