Learning language of logic

Paul Tomassi's Logic provides a useful addition to the many introductory logic textbooks available. Chapter one discusses validity, logical form and the value of studying logic. In chapters two and three, Tomassi introduces a syntactic system for demonstrating the validity of arguments in propositional logic (PL). This is a natural deduction system that is easy to use, although perhaps not austere enough for some logicians.

Only in chapter four are we introduced to semantics for PL via the truth tables. However, no teacher or student using Tomassi would have a problem in reversing the order of topics. This chapter also gives a truth-tree method for showing validity.

Chapter five presents a language for predicate logic (QL). Here we are shown the expressive power of such a language and introduced to Bertrand Russell on names, descriptions and existence. A natural deduction system for proving validity in QL is given in chapter six, while chapter seven develops the truth-tree method for demonstrating invalidity in QL.

Throughout there is a discussion of soundness, completeness and decidability. All of these topics have further reading indicated.

Tomassi's writing is easy and clear: he admits that the style is "deliberately slow" but students will be able to move at their own pace. There are many exercises for practice and summary boxes provide a useful revision aid.

I would recommend Logic to students who require a supplement to their set book and to teachers who have not yet found just the right text.

Francis Moorcroft teaches at the Centre for Lifelong Learning, University of Hull.