Of course we all know now that mathematics has proved that logic doesn't really make sense, but Etchemendy (philosophy, Stanford Univ.) goes further and challenges the received view of the conceptual underpinnings of modern logic by arguing that Tarski's model-theoretic analysis of logical consequences is wrong. He may have found the soft underbelly of the dead horse. Annotation copyrighted by Book News, Inc., Portland, OR.

Bringing together powerful new tools from set theory and the philosophy of language, this book proposes a solution to one of the few unresolved paradoxes from antiquity, the Paradox of the Liar. Treating truth as a property of propositions, not sentences, the authors model two distinct conceptions of propositions: one based on the standard notion used by Bertrand Russell, among others, and the other based on J.L. Austin's work on truth. Comparing these two accounts, the authors show that while the (...) Russellian conception of the relation between sentences, propositions, and truth is crucially flawed in limiting cases, the Austinian perspective has fruitful applications to the analysis of semantic paradox. In the course of their study of a language admitting circular reference and containing its own truth predicate, Barwise and Etchemendy also develop a wide range of model-theoretic techniques--based on a new set-theoretic tool, Peter Aczel's theory of hypersets--that open up new avenues in logical and formal semantics. (shrink)

Covers first-order language in method appropriate for first and second courses in logic. CD-ROM consists of a new book, 3 programs,and an Internet-based grading service.

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. (shrink)

The Language of First-Order Logic is a complete introduction to first-order symbolic logic, consisting of a computer program and a text. The program, an aid to learning and using symbolic notation, allows one to construct symbolic sentences and possible worlds, and verify that a sentence is well formed. The truth or falsity of a sentence can be determined by playing a deductive game with the computer.

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 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 ; 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 are available for Windows, Macintosh and Linux systems. Instructors do not need to use the programs themselves in order to be able to take advantage of their pedagogical value. More about the software can be found at lpl.stanford.edu. 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. (shrink)

This book is intended, along with the computer program, to introduce the user to some of the most important concepts and tools of logic, including learning a new computer language.

Tarski's World 3.0 is an innovative and enjoyable way to introduce your students to the language of first-order logic. Using this program, students quickly master the meaning of the connectives and quantifiers, and soon become fluent in the symbolic language at the core of modern logic. Tarski's World allows the students to build three-dimensional worlds and describe them in first-order logic. They evaluate the sentences in the constructed worlds, and if their evaluation is incorrect, the program provides them with a (...) game that leads them to understand where they went wrong. The package is intended as a supplement to any standard logic text, or for use by anyone who wants to learn the language. The disk and manual contain over a hundred exercises from very basic to highly sophisticated. (shrink)

Turing's World is a self-contained introduction to Turing machines, one of the fundamental notions of logic and computer science. The text and accompanying diskette allow the user to design, debug, and run sophisticated Turing machines in a graphical environment on the Macintosh. Turning's World introduces users to the key concpets in computability theory through a sequence of over 100 exercises and projects. Within minutes, users learn to build simple Turing machines using a convenient package of graphical functions. Exercises then progress (...) through a significant portion of elementary computability theory, covering such topics as the Halting problem, the Busy Beaver function, recursive functions, and undecidability. Version 3.0 is an extensive revision and enhancement of earlier releases of the program, allowing the construction of one-way and two-way finite state machines (finite automata), as well as nondeterministic Turing and finite-state machines. Special exercises allow users to explore these alternative machines. (shrink)

This text/courseware package presents a new approach to teaching first-order logic. Taking advantage of Tarski's World 4.0, the text skilfully balances the semantic conception of logic with methods of proof. The book contains eleven chapters, in four parts. Part I is about propositional logic, Part II about quantifier logic. Part III contains chapters on set theory and inductive definitions. Part IV contains advanced topics in logic, including topics of importance in applications of logic in computer science. The Language of First-order (...) Logic contains hundreds of problems and exercises for the user to work through. (shrink)

_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 program allows students to build three-dimensional worlds and then describe them in first-order logic. The program, compatible with Macintosh and PC formats, also contains a unique and effective corrective tool in the form of a game, (...) which methodically leads students back through their errors if they wrongly evaluate the sentences in the constructed worlds. A brand new feature in this revised and expanded edition is student access to Grade Grinder, an innovative Internet-based grading service that provides accurate and timely feedback to students whenever they need it. Students can submit solutions for the program’s more than 100 exercises to the Grade Grinder for assessment, and the results are returned quickly to the students and optionally to the teacher as well. A web-based interface also allows instructors to manage assignments and grades for their classes. Intended as a supplement to a standard logic text, _Tarski’s World_ is an essential tool for helping students learn the language of logic. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:“Garrulus sum et loquax et expedire nescio. Diu te tenui in istis, sed de cetero procedam.” These are the words of Richard Rufus of Cornwall, a thirteenth-century Scholastic and lecturer at the Universities of Paris and Oxford. Rufus is apologizing to his readers: “I am garrulous and loquacious, and I don’t know how to be efficient. I have detained you with these things a long while, but let me (...) now proceed to another topic.” This apology introduces the third part of the Speculum animae, a preliminary modern edition of which we publish here. In this short treatise, Rufus presents a unique Aristotelian theory of perception, describes what is and is not intelligible, and finally proves to his own satisfaction the immortality of the rational soul. To us this would hardly seem the place to apologize for being long-winded; indeed, we might wonder how Rufus could accomplish such an ambitious task in such a short treatise. We would certainly not accuse him of excessive verbosity. But Rufus was a man of exceptional humility, who once referred to himself as the least of the lesser thinkers of his time.1Despite Rufus’s humility, he was no minor figure in the development of Scholastic philosophy. A teacher at the Universities of Paris and Oxford ,2 he is the author of the earliest known, surviving lectures on several of Aristotle’s major texts, including the Metaphysics, the Physics, De generatione et corruptione, and De anima3 . In fact, Rufus was one of the very first lecturers to teach the libri naturales at Paris after a ban on such instruction was effectively lifted in 1231 A.D. His works were influential not only among his contemporaries, but also among later authors, particularly John Duns Scotus. Roger Bacon, though a harsh critic of Rufus, acknowledged Rufus’s influence and fame decades after his death, albeit among what Bacon termed the “vulgar multitude.”4The Speculum animae is one of Rufus’s later works. He begins the treatise by posing the following question: “In what way is the soul all things?” This refers, of course, to a familiar doctrine Aristotle establishes in the De anima—that the soul is, in some way, all things —and Rufus is here seeking to clarify it. But this is, in fact, only the first of five questions addressed in the Speculum. The five questions Rufus posits and answers in this treatise are, in order:1. In what manner is the soul all things?2. In what manner do a sensible and the sense, or an intelligible and the possible intellect, become one?3. What is predicated and of what is it predicated?4. What is intelligible?5. What is the cause of the immortality of the soul?In this short work, therefore, Rufus addresses apparently diverse topics including perception, understanding, logic, and the nature of the soul. But, in fact, the Speculum is principally a summary of Rufus’s theory of human perception and understanding. Like other medieval theories of perception and understanding, Rufus’s theory centers around the notion of species, a kind of form that is received in the soul when a person senses something or grasps something intellectually.5 In this, and in other aspects of the theory, Rufus was heavily dependent on Aristotle and St. Augustine. Rufus was working in a philosophical tradition based on Aristotle’s categories that had been accepted for centuries in the West. But in his lifetime, the Aristotelian corpus was enlarged to include Aristotle’s psychology and more generally his natural philosophy and metaphysics, together with the commentaries of Averroës . As is well known, this philosophical tradition was respected and continued not just by Rufus but by many authors after his time.So what makes Rufus’s theory.. (shrink)

Some criticisms are offered of Barwise and Etchemendy's theory of truth, the principal one being that it violates a feature of truth called “supervenience”.

In a series of publications beginning in the 1980s, John Etchemendy has argued that the standard semantical account of logical consequence, due in its essentials to Alfred Tarski, is fundamentally mistaken. He argues that, while Tarski's definition requires us to classify the terms of a language as logical or non-logical, no such division is guaranteed to deliver the correct extension of our pre-theoretical or intuitive consequence relation. In addition, and perhaps more importantly, Tarski's account is claimed to be (...) incapable of explaining an essential modal/epistemological feature of consequence, namely, its necessity and apriority. Bernard Bolzano (1781-1848) is widely recognized as having anticipated Tarski's definition in his Wissenschaftslehre (or Theory of Science ) of 1837. Because of the similarities between his account and Tarski's, Etchemendy's arguments have also been extended to cover Bolzano. The purpose of this article is to consider Bolzano's theory in the light of these criticisms. We argue that, due to important differences between Bolzano's and Tarski's theories, Etchemendy's objections do not apply immediately to Bolzano's account of consequence. Moreover, Bolzano's writings contain the elements of a detailed philosophical response to Etchemendy. (shrink)

John Etchemendy (1990) has argued that Tarski's definition of logical consequence fails as an adequate philosophical analysis. Since then, Greg Ray (1996) has defended Tarski's analysis against Etchemendy's criticisms. Here, I'll argue that--even given Ray's defense of Tarski's definition--we may nevertheless lay claim to the conditional conclusion that 'if' Tarski intended a conceptual analysis of logical consequence, 'then' it fails as such. Secondly, I'll give some reasons to think that Tarski 'did' intend a conceptual analysis of logical (...) consequence. (shrink)

John Etchemendy argumenta que, dado el fracaso del análisis tarskianode la noción intuitiva de consecuencia lógica, no hay razones para considerara la formalidad una condición necesaria para dicha relación. En el presentetrabajo critico este argumento. Primeramente, busco mostrar que la crítica deEtchemendy al análisis tarskiano asume dos requisitos de éxito elucidatorio queno es razonable adoptar conjuntamente. En segundo lugar muestro que, rechazadala anterior asunción, dos argumentos a favor de la adecuación extensionalde dicho análisis confieren apoyo al formalismo. Finalmente, (...) menciono algunasconocidas consideraciones de índole pragmática en favor del formalismo. (shrink)

Though the revised edition of A Theory of Justice, published in 1999, is the definitive statement of Rawls's view, so much of the extensive literature on Rawls's theory refers to the first edition. This reissue makes the first edition once again available for scholars and serious students of Rawls's work.