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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.
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.
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.
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.
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.
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.
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