An Introduction to Formal Logic

I was expecting to read a book about Formal Logic - this book is about Formal Logic unfortunately it contains a bit more- The Author, Peter Smith, can''t seem to help himself from advocating for his apparent favored metaphysical worldview of reality, which via an inductive argument would lead me to suspect is atheistic naturalism. It is annoying enough that the author uses confusing Lewis Carroll examples as he attempts to explain logical inference; he needs to take little jabs at theism at several points throughout the book. I made it only as far as Chapter 4 when the Darwin advocacy drove me over the edge. If I want to read a book that advocates for militant atheism I will read something by Richard Dawkins or Christopher Hitchens.Hey Peter Smith, if you are going to make examples of what you consider to be """quantifier shift fallacies """" using pathetic watered down strawmen of theistic arguments for God, why don't you balance it out a little bit and lay out some arguments that demonstrate what a bunk worldview naturalism is?--- at least the reader would come away with the common sense notion that you were trying to play it fair and balanced.In Chapter 1 Mr. Smith uses an "intelligent design" example and asks the reader to evaluate it for deductively validity, of course the author is quick to indicate that "entire books have been written about it but it is not deductively valid""He also uses the conceivability argument from Descartes but does not make any conclusions about the deductive validity of this argument - interesting.I figured maybe he would throw something in about the question begging nature of certain materialistic explanations of reality, yet these were strangely absent in the comparative sense.In Chapter 4, Smith can't help but bash Aristotle, quote "Did Aristotle really use the terrible argument""? Smith apparently thinks he did. Smith continues his advocacy for materialism by preaching at the end of Chapter 4, where Smith states, ""It is perhaps worth noting that a number of SUPPOSED arguments for the existence of God commit the same quantifier shift fallacy."" Peter Smith then begins to erect the strawmenE" (1) Every causal chain has an uncaused first link C: God uncaused cause at the first linkThen Smith throws in a strawman argument for designE"" (1) Every ecological system has a designer, C: God made every ecological systemSmith explains that its wrong to reach the conclusion that a single God caused the each thing to exist or that a single master designer built all ecological systems, there could after all be many designers ----- Duh, yeah, if you set the argument up that way, sure Smith -- I don't know many theists that use arguments like these, though. Why do I need to read about this in your book?Lastly, Peter Smith can't help himself again after using erecting the strawman argument for design, stating """THOUGH THAT IS A PREMISE WHICH DARWIN EXPLODED"" -- -really, Peter Smith?It would have been a different story had the author used some horrible arguments for naturalism that are frequently used by militant atheists like Dawkins, but for some strange reason Peter Smith couldn't seem to present a fair and balanced approach remaining content to focus on theism.If you are going to read a book on formal logic and are a theist, I would choose another --- if you are a militant atheist, this is definitely the book for you as you and the author would appear to share a commonality.Peter Smith should have used an example like the KCA instead of the garbage he pedaled off as being representative of arguments used by theists.KCA ---Everything that begins to exist, has a causeTHE UNIVERSE (not everything Pete), began to exist,Therefore, the universe has a causeIn the future, I would suggest Mr. Smith re-evaluate titles of books he authors if he intends to advocate for a particular metanarrative of reality. For example, this book would best be titled "Formal Logic In The Setting Of Metaphysical Naturalism." At least this way, readers would know what they are getting into before buying the book.

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!

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

Very readable, easy to follow.

Arrived in excellent condition

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.

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

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 Priest2. 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 asthe even more indigestible Enderton, Mendelson & al...

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.

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).

Smiths 'Formal Logic' nimmt sich viel Zeit um die Grundlagen der Aussagen- und Prädikatenlogik (erster Stufe) in einer sehr klaren und nachvollziehbaren (englischen) Sprache nahezulegen. Dementsprechend braucht Smith auch fast ganze 350 Seiten dafür. Aber immer den philosophischen Leser im Blick gelingt Smith es gut die, vorallem gegen Ende des Buches, schwieriger werdenden Themen verständlich zu machen.Was Smith ebenfalls besonders gelingt ist erworbenes Wissen graduell aufeinander aufbauen zu lassen, sodass jeder nächster Schritt intuitiv und leicht nachvollziehbar wirkt. Andere Autoren vermengen gerne, was eigentlich ein eigenes Thema sein sollte, inmitten essentieller Erklärungen zum Grundverständnis der Thematik selbst und verwirren neue Leser nur (vgl. die populäre Einführung von Hoyningen-Huene, der zB zu Beginn der Erklärung der prädikatenlogischen Syntax sofort versucht das Identitätssymbol einzuführen. Smith hat ein komplett eigenes Kapitel dafür eingerichtet, und das auch erst nachdem die Grundlagen gelegt wurden).Das Buch ist außerdem verwendbar als ein Nachschlagewerk. So hat Smith alle wichtigen Definitionen immer leicht erkennbar in großen Kästen eingerahmt, schnell wieder auffindbar.Ebenfalls nett sind Smiths Anstrengungen an der Kritik an das sehr wichtige aussagenlogische Konditional (oder der Implikation). Die klassische (problematische) Auffassung des Konditionals ist zwar durchaus wissenschaftlich gebräuchlich und daher relevant für jeden wissenschaftlich interessierten Philosophen, aber häufig wird die Problematik nicht erklärt. Smith hat dem Konditional ein ganzes Kapitel gewidmet und macht sehr deutlich, worin die Schwierigkeit der Implikation liegt.Ein weiteres großes Plus sind die Aufgaben nach jedem Kapitel. Eine große Menge an Aufgaben mit Lösungen, die im Internet einsehbar sind (obwohl einige wenige Lösungen fehlen). Auch mit verschiedenem Schwierigkeitsgrad. Allerdings können einige der schwierigeren Aufgaben frustrieren, wenn man nicht weiß wie man informelle Beweise verfasst.Meine einzigen Kritikpunkte sind Smiths Umgang mit den vorgestellten Beweissystemen. Die anfängliche 'Counter-example technique' ist noch unproblematisch. Kurz darauf allerdings taucht Smith schnell informell in die 'Natural deduction' (Systeme des natürlichen Schließens nach Jaśkowski Notation) ein, um nie wieder ein Wort über dieses System zu verlieren. Daraufhin wendet er sich semantischen Tableux (in Baumform) zu, die ich persönlich weniger ausdrucksstark als Jaśkowskis oder Gentzens Systeme finde.Fazit: Sehr gut zum Selbststudium geeignet, sehr verständlich und trotzdem Tiefe. Keine Vorkenntnis benötigt (aber trotzdem sehr willkommen). Vielleicht nicht das preiswerteste Buch, aber das Preisleistungsverhältnis stimmt.

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 Priest2. 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 asthe even more indigestible Enderton, Mendelson & al...