- The book and how to get it
- Exercises and worked answers
- On truth trees
- Other supplementary materials
- Other books
The book and how to get it
An Introduction to Formal Logic was originally published by Cambridge University Press (2003, 2020). It began life as lecture notes for a course for first-year philosophers which I taught for many years.
A corrected version of the second edition is now available as a freely downloadable PDF. 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 book 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. Note that since this reprint isn’t coming from a publisher with a marketing department, you will need to ask your university librarian to order a printed copy for the library. 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:
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
- Diagrammatic summary of PL natural deduction rules used in IFL2
- Diagrammatic summary of QL natural deduction rules used in IFL2
In lieu of podcasts introducing chapters or pairs of chapters (it’s 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)
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
Current corrections count: 0 major, 1 minor. (Printed and PDF versions of the book will be intermittently updated as corrections accrue.)
The exercises, and worked answers
There is a (fairly modest) set of exercises at the end of most chapters. I am somewhat more than halfway through the task of putting stand-alone versions of the exercises here too, along with (often very detailed) worked answers.
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]
Other supplementary materials of various kinds
- Greek alphabet, and symbol sheet
- 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.
Here too are some legacy handouts that might still prove useful:
- 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.
See Chapter 3 of the TYL Study Guide for some suggestions for parallel reading at an introductory level. Later chapters of the Guide give reading suggestions for going further in logic.