An Introduction to Formal Logic

The book and how to get it

An Introduction to Formal Logic was originally published by Cambridge University Press (1st edition 2003; 2nd edition 2020). It began life as lecture notes for a course for first-year philosophers which I taught for many years.

As a small contribution to students in these tough times, a corrected version of the second edition is now available as a freely downloadable PDF. (And it is good to see that it is now steadily downloaded about 1300 times a month.)

Many people, however, prefer if possible to work from a physical book. And you can now get a print-on-demand copy of IFL as an inexpensive large-format paperback from Amazon. UK link; US link. Find on your local Amazon by using the ASIN identifier B08GB4BDPG in their search field. (You don’t get the original pretty cover; but otherwise the quality of the printing and paper is very acceptable, especially given the comparatively very low price. Apologies that this is Amazon only, but this is the way to keep the price right down.)

There is also a nicer but still inexpensive hardback version intended for libraries, available from bookshops and library suppliers as well as from online sellers, with the ISBN 978-1916906327. Note that since this reprint isn’t coming from a publisher with a marketing department, you will need to actually ask your university librarian to order a printed copy for the library. Please, please do so!

This second edition has been very extensively revised and rewritten, and one particular difference from the first edition should be highlighted here. The book now focuses on a natural deduction proof system done Fitch-style, while the previously edition introduced so-called truth trees (tableaux). However, revised versions of the old chapters on truth trees for propositional and for predicate logic are still available, but now as (freely available) online supplements; so those teaching a tree-based course based on the first edition aren’t being cut adrift.

If you want to get an idea of the way the book proceeds without skimming the whole PDF, then the section-by-section table of contents should give you a good indication:

Section-by-section table of contents for IFL2

If you want to know about the particular natural deduction system adopted — since no two books seem to use exactly the same ND system — you’ll get a good idea from

Logic bites and snippets

In lieu of podcasts introducing chapters or pairs of chapters (it’s too difficult to handle symbols in an audio format!), here’s a series of bitesized informal written introductions giving some orientation in a reasonably relaxed way:

Logicbites (first twenty now online)

Over the years, I have answered a lot of logic-related questions on the exceedingly useful math.stackexchange site. Here are some of my efforts:

Logical snippets: over a hundred short answers to queries on elementary logic — apart from the sections on arithmetic and on Gödel’s theorem, mostly accessible to (near) beginners.

Corrections!

Inevitably — it is a law of book-writing! — there will be typos (and possibly thinkos too) which need correction. They will be listed on the following

IFL2 corrections page

There are currently about twenty typos which need correction of which only two or three are likely to cause puzzlement. (Printed and PDF versions of the book will be intermittently updated when enough corrections accrue.)

The exercises, and worked answers

There is a (fairly modest) set of exercises at the end of most chapters. There are standalone versions for most of the question sets and (often very detailed) worked answers here:

End-of chapter exercises from IFL2, and their solutions.

If you are looking for answers to the exercises in the first edition, then go to this page.

On truth trees

Ideally beginners should end up knowing about both ND and truth trees (tableaux); different teachers will make different choices of which to do first. If you want to use the book for a tree-based course, or want to find out about trees later, here are some more chapters! (Relevant exercises will follow.)

Trees for propositional logic [Considerably revised from IFL1]
Trees for quantificational logic [Temporary version soon to be revised]

The first edition

For corrections to the first edition and answers to the exercises, then go to this page.

Other legacy supplementary materials of various kinds

Greek alphabet, and symbol sheet
Sets, relations and functions. In IFL we really play down the use of set-theoretic notation. In parallel reading, you may well encounter such notation being put to use. This old handout might help to explain.
Proof systems It is hinted in IFL2 that natural deduction can be done in other styles than Fitch’s. For something on this, and on other proof systems, see another legacy handout.
‘If” and ‘⊃’ says more about Grice’s theory of conditionals.
How to read Dummett on Quantifiers.
Intentional Contexts expands on some themes briefly skirted around in the book.
Russell’s Theory of Descriptions expands on some themes in the book’s chapter.

Other books?

There are many other first introductions to logic at a similar level to IFL, some terrible, some mediocre, and a few very good. For a short freely downloadable text, see versions of forall X such as this one. I think the best traditional book alternative is my namesake Nick Smith’s excellent Logic: The Laws of Truth (Princeton UP).

See my Study Guide for some suggestions for going further in logic.

Quick links