Pros, cons and fuzz

Logic is a large subject that covers a range of thinking and topics. The analysis and evaluation of arguments, the construction of systems that are intended to represent particular areas of reasoning and the philosophical problems raised by such representation would all be counted as part of logic. These books try to cram in this diversity while ensuring that they are accessible.

Royce Jones's Foundations of Critical Thinking is concerned with practical everyday reasoning. Jones begins by introducing the basic vocabulary of "argument", "implication" and "inference" and proceeds to examine issues such as the ambiguity and emotive force of words. Five chapters on "grounds of inference" follow, covering facts and hypotheses, generalisations, analogy, causation and criteria. Discussions of the nature of disputes and resolutions are followed by an analysis of the different tactics that may be deployed in arguments. Traditional logic and the evaluation of syllogisms by Venn diagram are covered before proceeding to propositional logic and truth tables.

Four useful appendices cover essay writing, definitions, fallacies and exercises in examining texts. Helpfully, Jones gives answers to selected exercises, and the book is supported by a website. Well written, attractively packaged and containing some good cartoons, Foundations of Critical Thinking is a helpful addition to the literature.

Understanding Arguments , by Robert Fogelin and Walter Sinnott-Armstrong, is also concerned with informal logic and looking at arguments in their context and setting. It is a standard text now in its sixth edition. This covers much the same material as Critical Thinking but goes much further: quantification logic is introduced as well as induction and probability. The second part of the book concerns areas of argumentation with real examples of cases from the law, ethics, science and philosophy presented and discussed. Clearly written, containing interesting exercises and discussion questions, Understanding Arguments is warmly recommended. In choosing between this and Critical Thinking , the choice is one of deciding between a deep or a brief introduction: the teacher or student on a short course would probably be better with Jones, the material in Fogelin and Sinnott-Armstrong would probably take a whole year to cover.

Turning from critical thinking and informal logic, Mark Sainsbury's Logical Forms is an introduction to philosophical logic, that is the problems that are raised by formalising English in formal logical languages. Starting with a discussion of validity and related notions that involves areas such as possibility and necessity, inconsistency, the difference between sentences and propositions, and the purpose of formalisation, Sainsbury then proceeds to truth functionality and the relationship between a truth-functional language and English. Sections are devoted to the important question of reading material implication as the English "if", and this is a good place to see Paul Grice's conversational implicature employed to defend such a reading. Conditionals and probability are then discussed in a chapter that is a complete rewrite of the first edition and one of the major changes.

Quantification, with all of the standard problems covered, including names and descriptions and the relationship between them, identity and numerical quantifiers. There are also interesting sections on second-order logic and free logic. Issues arising from necessity occupy the next chapter with a discussion of the de dicto / de re distinction and the metaphysical issues that come out of the concept of a possible world. The book concludes with an extended analysis of the project of formalisation. Logical Forms is written in a way that makes the dry, abstract problems of philosophical logic accessible, but that is not to say that it makes them easy - no book could do that.

While written for a student who has completed a first course on formal logic, it could be read by those who have less experience. It could be used either as a supplementary text on a formal logic course to discuss philosophical issues as they arise - which is how I have used the first edition - or as a core text for a philosophical logic course. It is one of the best books of its kind and is thoroughly recommended.

An Introduction to Non-Classical Logic by Graham Priest is a book that does require a first course in formal logic. It assumes the background of classical logic and is an exploration of the systems that have been devised by those who argue that classical logic either licenses inferences that are not valid and so goes too far, or that it does not go far enough. After a brief survey of classical logic with a tableaux-deductive system, Priest introduces tableaux systems for modal logics - both normal and non-normal - conditional logics and intuitionist logic. There then follow introductions to many-valued logics, relevant logics and, finally, fuzzy logic.

Throughout all of this, Priest always raises the philosophical problems that have led logicians to propose these new systems as challenges to the classical system and also the philosophical issues that follow from their introduction. This is not an easy book and, as the exercises are vital to understanding, solutions to at least some of them would have been helpful. But for anyone who wants to explore the non-classical systems, it is the only book of its kind and could not be more highly recommended.

Francis Moorcroft is lecturer in philosophy, University of Hull.