Logic: The Laws of Truth

by Nicholas J.J. Smith

Logic is essential to correct reasoning and also has important theoretical applications in philosophy, computer science, linguistics, and mathematics. This book provides an exceptionally clear introduction to classical logic, with a unique approach that emphasizes both the hows and whys of logic. Here Nicholas Smith thoroughly covers the formal tools and techniques of logic while also imparting a deeper understanding of their underlying rationales and broader philosophical significance. In addition, this is the only introduction to logic available today that presents all the major forms of proof--trees, natural deduction in all its major variants, axiomatic proofs, and sequent calculus. The book also features numerous exercises, with solutions available on an accompanying website.

Logic is the ideal textbook for undergraduates and graduate students seeking a comprehensive and accessible introduction to the subject.

Genres: Philosophy, Logic, Mathematics, Nonfiction, Science

544 pages, Hardcover

First published January 1, 2012

Reviews

[Ajam]

I was doing all fine and dandy, until the second chapter 'The language of Propositional Logic' started introducing a glossary with all kinds of symbols pitched as "a language in which the ways of forming complex formulas from simpler components directly mirror the ways in which compound propositions can be formed from simpler propositions.". I then skimmed through the rest and found out, it actually builds upon every preceding established foundations and gets more and more complicated. That's when I lost my interest and closed it.
Now from what I have read, the book is fine with a brutally rigorous walkthrough of Classical Logic, so maybe I will attempt this again when I am older and wiser, or maybe not.
The main reason I was even reading this was because I saw a 4chan chart which had this book at the top on its guide to 'A Foundational Approach to Mathematics'. I guess I overestimated my intellectually inferior monke brain because this clearly is not meant for me -someone who is already severely lacking in even the most basic concepts about this area of study and just wanted something to prepare myself and gradually build my skills before I tackle the big bois like P=NP or Poly-Dimensional Topology all because I read too much Egan, clearly this wasn't the place to begin.
If anything I am all demotivated and frustrated now, welp, time to go cry myself to sleep again and introspect my utter lack of adequacy.

[Tasneem · Rating 4 out of 5]

I didn't expect to write a review for this book at all, mainly because I didn't expect that I would even end up opening the cover.

This is probably the best university textbook I've come across in the past five years.

It is very well written and translates some fairly abstract and arcane concepts with clarity and purpose. The explanations are impressively detailed and step you through even the most obvious logical abstractions so that you never feel bored or overwhelmed.

The best achievement of this book is the colloquial style in which Smith writes; it is easy to understand (which, for a book dealing with logic, is fairly unusual).

The included exercises are relevant and do a good job of testing your conceptual understanding of the content. More detailed answers to these exercises would've been appreciated.

A must read for anyone interested in or studying classical logic.

[Alyssia Dean · Rating 5 out of 5]

Great text for introductory logic.

[Matias · Rating 5 out of 5]

This is a brilliant introduction to mathematical logic, the book is full of very interesting philosophical remarks about logic.

[Mitch Flitcroft · Rating 4 out of 5]

A good introduction to classical logic. Part one covers propositional logic, part two covers predicate logic with identity, and part three covers metatheory, alternative systems of proof, and some set theory. Part one and two are sufficient for most introductory logic courses.

It is comprehensive, and the online solutions to the problems sets are helpful. On the downside, the writing can become confusingly repetitive—often stating a single idea in 6 different ways. Overall, it makes for a good intro logic textbook.

[Yvan Moses Levy · Rating 5 out of 5]

Comprehensive and rigorous

This book is comprehensive, very well written, really rigorous. Chapters 14 and 15 need to be read two times.
The author knows to explain simply and clearly. This book is more than a beginner book, he pushes you to an intermediate level. It's surely one of the bests.

[Richi · Rating 3 out of 5]

A well explained introduction to formal logic. One could teach themselves an entire university subject by just reading the book and completing the excersises.

[Qingyang · Rating 4 out of 5]

Clear concise textbook on basics of logic, although I’m not sure I had the energy and brain power to fully appreciate it. Very long as well with useful exercises.

[Ahmed Khaled]

It wasn't what I'm looking for

[Holden · Rating 5 out of 5]

A rigorous introduction to classical logic. Be sure to read the preface for the core material of the book for a more accessible approach.
The exercises are the best part in my opinion, perfect quarantine material to immerse oneself.

[Neuw Zqsl · Rating 1 out of 5]

Too long-winded.