This new text brings the traditional material of introductory logic (critical thinking, informal and modern symbolic logic) to bear on present day issues - terrorism, abortion, the death penalty, ABM treaty, stem cell research - essays and editorials found in the New York Times, USA Today, Miami Herald, and other major newspapers and news magazines from all over the United States. This original format engages students in applying logic and critical thinking to important issues. They learn not only the techniques of introductory logic but will achieve a much deeper understanding of the great controversies that we face.
Symbolic logic may be superior to classical Aristotelian logic for the sciences, but not for the humanities. This text is designed for do-it-yourselfers as well as classrooms.
A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.
Logic is often perceived as having little to do with the rest of philosophy, and even less to do with real life. In this engaging and accessible introduction, Graham Priest shows how wrong that conception is. He explores the philosophical roots of the subject, explaining how modern formal logic deals with issues ranging from the existence of God and the reality of time to paradoxes of probability and decision theory. Along the way, Priest lays out the basics of formal logic in simple, nontechnical terms.
First published in 2000. This is Volume II of eight in the Philosophy of Logic and Mathematics series and focuses on controversy and the principles of dynamic logic and modern reasoning.
Timothy Williamson gives an original and provocative treatment of deep metaphysical questions about existence, contingency, and change, using the latest resources of quantified modal logic. Contrary to the widespread assumption that logic and metaphysics are disjoint, he argues that modal logic provides a structural core for metaphysics.
In this challenging and provocative analysis, Dale Jacquette argues that contemporary philosophy labours under a number of historically inherited delusions about the nature of logic and the philosophical significance of certain formal properties of specific types of logical constructions. Exposing some of the key misconceptions about formal symbolic logic and its relation to thought, language and the world, Jacquette clears the ground of some very well-entrenched philosophical doctrines about the nature of logic, including some of the most fundamental seldom-questioned parts of elementary propositional and predicate-quantificational logic. Having presented difficulties for conventional ways of thinking about truth functionality, the metaphysics of reference and predication, the role of a concept of truth in a theory of meaning, among others, Jacquette proceeds to reshape the network of ideas about traditional logic that philosophy has acquired along with modern logic itself. In so doing Jacquette is able to offer a new perspective on a number of existing problems in logic and philosophy of logic.
