Language, Proof and Logic

This textbook/software package covers first-order language in a method appropriate for first and second courses in logic. The unique on-line grading services instantly grades solutions to hundred of computer exercises. It is specially devised to be used by philosophy instructors in a way that is useful to undergraduates of philosophy, computer science, mathematics, and linguistics. The book is a completely rewritten and much improved version of The Language of First-order Logic. Introductory material is presented in a more systematic and accessible fashion. Advanced chapters include proofs of soundness and completeness for propositional and predicate logic, as well as an accessible sketch of Godel's first incompleteness theorem. The book is appropriate for a wide range of courses, from first logic courses for undergraduates (philosophy, mathematics, and computer science) to a first graduate logic course. The package includes four pieces of software: Tarski's World 5.0, a new version of the popular program that teaches the basic first-order language and its semantics; Fitch, a natural deduction proof environment for giving and checking first-order proofs;Boole, a program that facilitates the construction and checking of truth tables and related notions (tautology, tautological consequence, etc.);Submit, a program that allows students to submit exercises done with the above programs to the Grade Grinder, the automatic grading service.Grade reports are returned to the student and, if requested, to the student's instructor, eliminating the need for tedious checking of homework. All programs will be available on both Windows and Macintosh OS. Instructors do not need to use the programs themselves in order to be able to take advantage of their pedagogical value.The price of a new text/software package includes one Registration ID, which must be used each time work is submitted to the grading service. Once activated, the Registration ID is not transferable.

Jon Barwise (1942-2000) was a mathematician, philosopher and logician. He taught at the Universities of Yale and Wisconsin before becoming the first director of the Center for the Study of Language and Information at Stanford University. From 1990 until his death he was professor of philosophy at Indiana University. John Etchemendy has been professor of philosophy at Stanford since 1983. In 2000 he became Provost of Stanford University.

Acknowledgements
Introduction	p. 1
Propositional Logic	p. 17
Atomic Sentences	p. 19
The Logic of Atomic Sentences	p. 41
The Boolean Connectives	p. 67
The Logic of Boolean Connectives	p. 93
Methods of Proof for Boolean Logic	p. 127
Formal Proofs and Boolean Logic	p. 142
Conditionals	p. 176
The Logic of Conditionals	p. 198
Quantifiers	p. 225
Introduction to Quantification	p. 227
The Logic of Quantifiers	p. 257
Multiple Quantifiers	p. 289
Methods of Proof for Quantifiers	p. 319
Formal Proofs and Quantifiers	p. 342
More about Quantification (optional)	p. 364
Applications and Metatheory	p. 403
First-order Set Theory	p. 405
Mathematical Induction	p. 442
Advanced Topics in Propositional Logic	p. 468
Advanced Topics in FOL	p. 495
Completeness and Incompleteness	p. 526
Summary of Formal Proof Rules	p. 557
Glossary	p. 562
General Index	p. 573
Exercise Files Index	p. 585
Table of Contents provided by Blackwell. All Rights Reserved.

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