An Introduction to Formal Logic

This text provides a very gentle introduction to formal logic. The chapters are short and punchy, and difficulty rises gradually. I would strongly recommend it as a supplementary text for a student studying formal logic.

It's especially useful for persons who are going to learn logic by self-study. Logic is a very important and fundamental subject. Unfortunately, the supply for this kind of textbooks is not enough in the region I'm living!

Arrived in excellent condition

To be clearer than Peter Smith is simply next to impossible. This book is a beautiful entry-point, a must, in the world of logic. This book now stands in my list of outstanding books on logic : 1. A. Tarski's "Introduction to Logic", a jewel, followed by P. Smith's superb entry-point "An introduction to Formal logic" and the lovely "Logic, a very short introduction" by Graham Priest 2. D. Goldrei's "Propositional and Predicate calculus" 3. Wilfrid Hodges' "Logic", followed by Smullyan's "First-order logic". 4. P. Smith's "An introduction to Gödel's theorems". 5. Kleene's "Introduction to metamathematics" & "Mathematical Logic". 6. G. Priest's " Introduction to non-classical logic". Hence forgetting altogether Van Dalen's indigestible "Logic & Stucture" as well as the even more indigestible Enderton, Mendelson & al...

Great book, but a background in logic would be nice.

Very readable, easy to follow.

This book is terrible. Horribly written. It does have great examples, which is where the stars come from, but written horribly.

If you know little or nothing of modern logic but want to get a thorough grounding in the subject and are prepared to put in a lot of hard work to achieve this, then I strongly recommend this book to you. It will not take you all the way to your goal -- no introductory book of reasonable length could possibly do this -- but it will bring you a good distance towards it, and leave you better prepared to move on to more advanced work than any other introductory book on logic of comparable length that I have ever seen. If you have worked through another elementary book on logic, but still feel uncertain or confused, I would also recommend this book to you. The author starts with some simple basic ideas which are easy to understand and difficult to argue with, and then systematically builds up a complete system of first order predicate logic on the basis of these initial concepts (first order predicate logic is the `bread and butter' logic that underpins nearly all advanced work). The author's style is as clear and readable as one can reasonably hope to find in a serious book on an abstruse and complex subject. The chapters that comprise the book are mostly quite short, and are each well focused on achieving specific learning objectives. Every chapter has a useful summary, and most have exercises as well. The book does not contain any model answers for the exercises, but the author's website fills this gap to a large extent. N.B. although this book presents its subject matter with admirable clarity, it is not a soft option. In order to take full advantage of what it offers you will have to put in a lot of hard work (and do a good proportion of the exercises!). A word of warning -- in spite of its strengths this book will not suit everybody as a first book on logic. If you like to get a good overview of a subject before plunging into the details, including perhaps a bit of history, a discussion of how the subject relates to other disciplines, a sketch map of the main lines of development within the subject, and so on, then you should not choose this as your first book - you will have to look elsewhere for a book that provides such an overview. Another warning - when you move on to more advanced work, you will find that there are a number of different approaches to first order predicate logic `out there'. This book provides a very good grounding in an approach that is usually referred to as `Logic by Trees', but was originally called the `Semantic Tableau method'. This approach is as powerful as any other and is easy to learn, but you will need to acquire a working knowledge of at least one additional approach in order to equip yourself to proceed further. Some authors have tried to overcome this problem by covering two or even more forms of logic in a single book, but Smith has, rightly in my view, decided not to do this. What you get for your money is a very thorough and clear account of his preferred approach, which, if studied carefully, will leave you well prepared to get to grips with additional approaches when you need to. An aspect of the book, which will disappoint some readers, is that there are no references to other books or journal articles in the text. I understand that the author has omitted references in order to keep the book uncluttered, which is a laudable objective, but there are a fair number of places in the text where the author touches on issues which he (rightly in my view) considers too advanced to cover in an introductory book. Readers will certainly want to follow up on some of these issues and will be frustrated by the absence of references. There is a short "further reading" section at the end of the book which picks up a few of the issues that I noticed, but that is no real substitute for `in line' references. However, there is some useful extra material on the author's website, which he hopes to add to in the future. The book has been through 4 printings. If you decide to buy it, try to avoid the first printing if you can. The author took advantage of the second printing to correct errors reported by users. However if you cannot avoid the first printing you will find the corrections on the author's website.

To be clearer than Peter Smith is simply next to impossible. This book is a beautiful entry-point, a must, in the world of logic. This book now stands in my list of outstanding books on logic : 1. A. Tarski's "Introduction to Logic", a jewel, followed by P. Smith's superb entry-point "An introduction to Formal logic" and the lovely "Logic, a very short introduction" by Graham Priest 2. D. Goldrei's "Propositional and Predicate calculus" 3. Wilfrid Hodges' "Logic", followed by Smullyan's "First-order logic". 4. P. Smith's "An introduction to Gödel's theorems". 5. Kleene's "Introduction to metamathematics" & "Mathematical Logic". 6. G. Priest's " Introduction to non-classical logic". Hence forgetting altogether Van Dalen's indigestible "Logic & Stucture" as well as the even more indigestible Enderton, Mendelson & al...

Prof. Smith’s Introduction to Formal Logic is a very good and solid book, but maybe not the best book available for a beginner. The main problem is the prose: sometimes the passages are very boring and the strategy chosen to present some topics seems to be more complicated than required. If you are a beginner, studying logic for the first time, a better book would be Stan Baronett’s Logic (Third edition), published by OUP. Baronett’s book is more objective and presents the topics in a very, very clear way. Smith would be a second book on the topic. Another option is Nicholas Smith’s Logic: the laws of truth. It’s a very clear, easy to read book (and covering much more topics) ranging from beginners to intermediate levels. Peter Smith decided to present propositional and predicate logic using trees, although I think natural deduction is a better choice, but this is a matter of preference. He introduces valuation and truth tables in a way I found a bit confusing for an introduction. Pros: definitions and technical vocabulary are precise and rigorous; chapters are short; the book presents a detailed discussion of extensionality, identity and functions, preparing for further reading. Cons: the prose is sometimes boring, as another reviewer has mentioned; chapters are short and so topics are introduced slowly: probably, the intention was to adopt a slow pace and let the reader reason along the process; however, I think a straightforward and direct approach suits better in some cases (for truth tables, valuation and validity for example); the book uses trees, instead of picking natural deduction as proof style. Important facts: there’s a second edition coming and the author dropped trees and introduced natural deduction methods. Smith has also written a guide called Teach Yourself Logic and curiously, TYL is much more agreeable to read than Formal Logic (the guide is also superbly informative).