John Etchemendy

The Logical Reasoning with Diagrams and Sentences courseware package teaches the principles of analytical reasoning and proof construction using a carefully crafted combination of textbook, desktop, and online materials. This package is sure to be an essential resource in a range of courses incorporating logical reasoning, including formal linguistics, philosophy, mathematics, and computer science. Unlike traditional formal treatments of reasoning, this package uses both graphical and sentential representations to reflect common situations in everyday reasoning where information is expressed in many forms, such as finding your way to a location using a map and an address. It also teaches students how to construct and check the logical validity of a variety of proofs of consequence and non-consequence, consistency and inconsistency, and independence using an intuitive proof system which extends standard proof treatments with sentential, graphical, and heterogeneous inference rules, allowing students to focus on proof content rather than syntactic structure. Building upon the widely used Tarski's World and Language, Proof and Logic courseware packages, Logical Reasoning with Diagrams and Sentences contains more than three hundred exercises, most of which can be assessed by the Grade Grinder online assessment service; is supported by an extensive website through which students and instructors can access online video lectures by the authors; and allows instructors to create their own exercises and assess their students' work.Logical Reasoning with Diagrams and Sentences is an expanded revision of the Hyperproof courseware package.

This textbook/software package covers first-order language in a method 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 accompanying online grading service instantly grades solutions to hundreds of computer exercises. The second edition of "Language, Proof and Logic" represents a major expansion and revision of the original package and includes applications for mobile devices, additional exercises, a dedicated website, and increased software compatibility and support.

"Tarski's World" is an innovative and exciting method of introducing students to the language of first-order logic. Using the courseware package, students quickly master the meanings of connectives and qualifiers and soon become fluent in the symbolic language at the core of modern logic. The accompanying CD-ROM, compatible with both Macintosh and PC formats, includes a unique and effective corrective tool in the form of a game that methodically leads students back through any errors in sentences they have constructed, as well as a program for submitting homework to an automated grader. Intended as a supplement to a standard logic text, "Tarski's World" is an essential resource for helping students learn the language of logic.

Band II: Anwendungen und Metatheorie Dieser Band kn pft sowohl inhaltlich als auch methodisch nahtlos an den ersten Band von Sprache, Beweis und Logik an. Dabei f hrt Band II weit ber die blichen Einf hrungen hinaus und eignet sich als Textgrundlage f r einen Fortsetzungskurs zur blichen Logikeinf hrung. Zusammen ergeben beide B nde somit eine homogene Einf hrung in die Logik, f r die bislang Texte verschiedener Autoren erforderlich waren. Zu den behandelten Themenbereichen z hlen: Theorie der generalisierten Quantoren, numerische Aussagen, Russells Kennzeichnungstheorie vs. Pr suppositionen, naive Mengentheorie und ZFC, mathematische Induktion, induktive Korrektheitsbeweise von Programmen, Hornformeln, Resolutionsverfahren, Skolemisierung, Unifikation, Beweise von Korrektheit, Vollst ndigkeit und Kompaktheit f r Aussagen- und Pr dikatenlogik, das Theorem von L wenheim und Skolem, Skolems 'Paradox', Nichtstandardmodelle der Arithmetik, G dels Unvollst ndigkeitstheorem. Die im Buch erw hnte Software ist vergriffen und nicht mehr erh ltlich.

Band I: Aussagen- und Pr dikatenlogik Mit Sprache, Beweis und Logik liegt nun die auf zwei B nde angelegte deutsche bersetzung des erfolgreichen Lehrbuchs Language, Proof and Logic vor. Band I f hrt in die klassische Aussagen- und Pr dikatenlogik ein und bertrifft dabei andere Logikeinf hrungen an Ausf hrlichkeit und Praxisn he bei weitem. Den Text zeichnen u.a. die folgenden Punkte aus: Der Text zeigt zahlreiche interdisziplin re Ankn pfungspunkte zu Philosophie, Sprachwissenschaft, Mathematik und Informatik auf. Es handelt sich um ein vielerprobtes Standardwerk, dessen hervorragende didaktische Qualit t sich oftmals unter Beweis gestellt hat. Der vorgestellte Kalk l des nat rlichen Schliessens ist praxisnah und verst ndlich. Er wird aufbauend auf informelle Argumentationsmuster eingef hrt, die den Studierenden implizit bereits vertraut sind. Begleitend zum Text gibt es eine umfangreiche Software-Unterst tzung, die sehr zur Veranschaulichung des Stoffes beitr gt. Studierende k nnen so selbst ndig mit den Beweistechniken experimentieren und erhalten unmittelbares Feedback f r viele bungen. "It's as if the teaching of logic moved from black-and-white to Technicolor." - Tom Burke, University of South Carolina

The intuitive concept of consequence, the notion that one sentence follows logically from another, has driven the study of logic for more than two thousand years. But logic has moved forward dramatically in the past century - largely as a result of bringing mathematics to bear on the field. The infusion of mathematically precise definitions and techniques has turned a field dominated by homely admonitions into one characterized by illuminating theorems. The aim of this book is to correct a common misunderstanding of one of the most widely used techniques of mathematical logic. Central to the received view is Tarski's model-theoretic analysis of logical consequence, which Etchemendy argues is fundamentally mistaken. Save indirectly, by those who question classical principles, this standard analysis has gone unchallenged for half a century, with the result that it has come to seem a piece of common knowledge. Etchemendy's critique will shatter the complacency.

Hyperproof is a system for learning the principles of analytical reasoning and proof construction, consisting of a text and a Macintosh software program. Unlike traditional treatments of first-order logic, Hyperproof combines graphical and sentential information, presenting a set of logical rules for integrating these different forms of information. This strategy allows students to focus on the information content of proofs, rather than the syntactic structure of sentences. Using Hyperproof the student learns to construct proofs of both consequence and nonconsequence using an intuitive proof system that extends the standard set of sentential rules to incorporate information represented graphically. Hyperproof is compatible with various natural-deduction-style proof systems, including the system used in the authors' Language of First-Order Logic.

This monograph purports to provide a solution to semantical paradoxes like the Liar. The authors base this solution on J. L. Austin's idea of truth, which is fundamental to situation semantics. They compare two models of language, propositions and truth, one based on Russell and the other on Austin, as they bear on the Liar Paradox. In Russell's view, a sentence expresses a proposition, which is true or not. According to Austin, however, there is always a contextual parameter - the situation the sentence is about - that comes between the sentence and proposition. The Austinian perspective proves to have fruitful applications to the analysis of semantic paradox. The authors show that, on this account, the liar is a genuine diagonal argument. This argument can be shown to have profound consequences for our understanding of some of the most basic semantical mechanisms at work in our language. Jon Barwise is, with John Perry, a co-founder of the Centre for the Study of Language and Information at Stanford.