Formal Logic

This surveys and unifies the major systems of propositional logics, answering the question “If logic is the right way to reason, why are there so many logics?” It is the standard reference in the subject, as well as providing a clear and easy way to learn the subject from scratch.

This presents the basic syntax and semantics of predicate logic motivated by attempting to formalize ordinary language reasoning. It is the only textbook that takes formalization as a serious motive for the subject and a serious constraint on the formalism. It make it clear why predicate logic is worth studying. It provides a basis for all predicate logics.

This develops classical mathematical logic, viewing it as motivated by attempts to formalize mathematics. The scope and limitations of the formal system are explored: formalizations of theories of linear orders, arithmetic, groups, rings, fields, one- and two-dimensional Euclidean geometry, and second-order logic are all presented. It is the only place to see axiomatic geometry formulated in first-order logic where the syntax and semantics are clearly separated.

Intended for a course for beginning students in philosophy, mathematics, linguistics, or computer science.

Many applications of the formal systems to formalizing ordinary language propositions and inferences clarify better the assumptions we make in reasoning taking account of time and space by making those precise in the formal systems.  Appendices on events, branching times, intentions, and descriptive names add to the scope of the work.

The classic presentation of the theory of computable functions in the context of the foundations of mathematics.

The acclaimed 18” x 28” (45.7 cm x 71.1 cm) poster now in a new edition.