Logic With Trees: An Introduction to Symbolic Logic

Logic With Trees is a new and original introduction to modern formal logic. Unlike most texts, it also contains discussions on more philosophical issues such as truth, conditionals and modal logic. It presents the formal material with clarity, preferring informal explanations and arguments to intimidatingly rigorous development. Worked examples and excercises enable the readers to check their progress. Logic With Trees equips students with * a complete and clear account of the truth-tree system for first order logic * the importance of logic and its relevance to many different disciplines * the skills to grasp sophisticated formal reasoning techniques necessary to explore complex metalogic * the ability to contest claims that `ordinary' reasoning is well represented by formal first order logic The issues covered include a thorough discussion of truth-functional and full first order logic, using the truth-tree or semantic tableau approach. Completeness and Soundness proofs are given for both truth-functional and first order trees. Much use is made of induction, which is presented in a clear and consistent manner. There is also discussion of alternative deductive systems, an introduction to transfinite numbers and categoricity, the Lowenhein-Skolem theories and the celebrated findings of Godel and Church. The book concludes with an account of Kripke's attempted solution of the liar paradox and a discussion of the weakness of truth-functional account of conditionals. Particularly useful to those who favour critical accounts of formal reasoning, it will be of interest to students of philosophy at first level and beyond and also students of mathematics and computer science.

"[Howson's] explanations are admirably clear, and directed to points that students find difficult ... [B]ooks in the middle ground, where one wants to cover non-trivial mathematical results in classical logic, but at a level that does not entirely alienate non-mathematics students, are fairly hard to find ... Howson's book ... fills this slot admirably."
-Graham Priest, University of Queensland
"Howson takes his readers on a fascinating tour of basic symbolic logic propelled with rigor and incisiveness ...[T]his book is a very useful volume ... [T]he author's enthusiasm for his subject matter shines through."
-"Teaching Philosophy

Colin Howson is Reader in Logic at the London School of Economics and Political Science.