Tim Button

*forallx: Cambridge* is a textbook for introductory formal logic. We use it in Cambridge for the first year philosophy formal logic course. It covers both truth-functional logic and first-order logic, introducing students to semantics and to a Fitch-style natural deduction system. The textbook contains numerous exercises, for which there is a complete solutions booklet.

Given the license, you can print as many copies as you like, or make derivative works. But if you do use the book, please let P.D. Magnus and me know! I can be contacted at *tecb2* at *cam* dot *ac* dot *uk*. (Please also get in touch if you have spotted a mistake!)

*forallx: Cambridge* pdf

*forallx: Cambridge* source code

Solutions booklet pdf

Solutions booklet source code

*forallx:Cambridge* is based upon P.D. Magnus’s *forallx*, available at fecundity.com/logic. Both texts are released under a Creative Commons license (CC BY 4.0; full details are available at here). The following is a human-readable summary of (and not a substitute for) that license. You are free to:

*Share*: copy and redistribute the material in any medium or format

*Adapt*: remix, transform, and build upon the material for any purpose, even commercially.

Under the following terms:

*Attribution*: You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.

The book is based upon P.D. Magnus’s *forallx*.
Magnus very generously released his book under a Creative Commons license. This licenses derivative work, and the
text was altered for the Cambridge Course. *forallx: Cambridge*
is now released under the
same license. In brief, this means that you can
use the texts free of charge. But you can also download the source
files, make changes to them, and make a version of the textbook
suitable for your own requirements.

It might help to explain, quickly, the main differences Magnus’s original text, and the Cambridge version. There are substantive differences in the order in which material is presented. There are also points at which the material differs, in particular:

**Use/Mention**. The Cambridge version discusses the distinction between use and mention, and enforces strict quotation rules.**Semantics**. Magnus has a chapter discussing formal set-theoretic semantics for both TFL and FOL. This has been removed from the Cambridge version, and replaced with something a little bit lighter.**Proof system**. Both books use a Fitch-style natural deduction system. However, the system for the Cambridge version has rules governing ‘⊥’, and is designed so that deleting a single rule yields intuitionistic logic. This makes it easier for students to explore non-classical logics, later in life. The Cambridge version also has an appendix, discussing different but equivalent natural deduction systems.**Plurals**. The Cambridge version eschews all talk of sets in favour of plural-locutions. So we say that some sentences are*jointly inconsistent*, rather than saying that a*set*of sentences is inconsistent.**Solutions**. The Cambridge version comes with a solutions booklet for all the practice exercises in the book. This allow for students to mark their own work.**Metatheory**. The textbook*Metatheory*continues on from the Cambridge version. This explores the metatheory of the truth-functional systems presented in the Cambridge version of*forallx*.

Moreover, since I adapted Magnus’s book for Cambridge, plenty of other versions of *forallx* have sprung up. They are maintained at the Open Logic Project. If you want to teach with *forallx*, in any version, you should visit their site!

I would like to repeat my thanks to P.D. Magnus. He has been extraordinarily generous, in making *forallx* available to everyone. When I first made this page, in 2012, I wrote that I hope that other logic teachers will be inspired by his generosity, and will continue to build upon this foundation. I am really delighted that this is happening.

**2018**

License changed to CC BY 4.0

Main release uses Libertinus fonts (open source and available here)

Two rules renamed: ⊥I as ¬E, and ⊥E as X

Definitions added for ⊭ and ⊬

FOL symbolisation keys use new conventions (see §16.2)

Explanation added concerning superscripts on predicates (see §19.5)

Explanation of ∴ improved (see §7.4)

Minor rephrasings throughout

**2017**

Main release uses XeLaTeX and Arno Pro fonts

Support for LaTeX and Computer Modern via forallx-basic.sty

Fixed minor mistakes

**2014**

Fixed minor mistakes

**2013**

All parts relating to metatheory were removed

These were re-released in *Metatheory*

Fixed minor mistakes

**2012**

First release; license Creative Commons Attribution-ShareAlike 3.0

Last modified 31 Oct 2018