forallx:Cambridge is a textbook for introductory formal logic. I made it for the first year philosophy formal logic course in Cambridge. 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 . (Please also get in touch if you have spotted a mistake.)

Available downloads

forallx:Cambridge pdf
forallx:Cambridge source code
Solutions booklet pdf
Solutions booklet source code

About the license

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.

More about forallx:Cambridge

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:

  1. Use/Mention. The Cambridge version discusses the distinction between use and mention, and enforces strict quotation rules.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. Metatheory. The textbook 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: ‘I hoped 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.

Version history

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
Fixed minor mistakes

2012
First release; license Creative Commons Attribution-ShareAlike 3.0

Metatheory is an introduction to the metatheory of truth-functional logic, also known as the propositional calculus. It is the textbook for a Cambrige Part IB course on metatheory, and it continues immediately from the textbook for the first-year course in formal logic, .

Given the license, you can print as many copies of this as you like, or use the source code to make derivative works, provided you respect various conditions. But if you do use Metatheory, please let me know! I can be contacted at .

Available downloads

Metatheory pdf
Metatheory LaTeX source code

About the license

Metatheory is released under a Creative Commons license (CC BY 4.0; full details are available 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.

More about Metatheory

Metatheory does not itself contain an account of truth-functional logic, but instead assumes a prior understanding. More specifically, this book assumes a thorough understanding of the syntax, semantics and proof-system for TFL (truth-functional logic) that is presented in . There is nothing very surprising about the syntax or semantics of TFL, and the proof-system is a fairly standard Fitch-style system.

Metatheory does not, though, presuppose any prior understanding of (meta)mathematics. Chapter 1 therefore begins by explaining induction from scratch, first with mathematical examples, and then with metatheoretical examples. Each of the remaining chapters presupposes an understanding of the material in Chapter 1.

Chapter 2 covers results relating to substitution, including Interpolation and Duality. Chapters 3 and 4 cover normal form theorems and expressive adequacy. Chapters 5 and 6 cover soundness and completeness.

One idiosycracy of Metatheory is worth mentioning: it uses no set-theoretic notation. Where I need to talk collectively, I do just that, using plural locutions.

Metatheory is released under a Creative Commons 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.

Version history

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

2017
Main release uses XeLaTeX and Arno Pro fonts
Support for LaTeX and Computer Modern via metatheory-basic.sty
Fixed minor mistakes

2014
Fixed minor mistakes

2013
First release; license Creative Commons Attribution-ShareAlike 3.0

Open Set Theory is a brief introduction to the philosophy of set theory. It is written for students with a little background in logic (such as one might get from ), and some high school mathematics. By the end of this book, students reading it might have a sense of:

  1. why set theory came about;
  2. how to reduce large swathes of mathematics to set theory + arithmetic;
  3. how to embed arithmetic in set theory;
  4. what the cumulative iterative conception of set amounts to;
  5. how one might try to justify the axioms of ZFC.
Chapters 1–3 of this book are taken from Open Logic Text, with only tiny changes. Reciprocally, I am contributing Open Set Theory back to the Open Logic Project.

Given the license, you can print as many copies of this as you like, or use the source code to make derivative works, provided you respect various conditions. But if you do use Open Set Theory, please let me know! I can be contacted at . Equally, and especially since this is a first release, there are guaranteed to be mistakes in this book; if you spot any, please, let me know.

Available downloads

Open Set Theory pdf
Open Set Theory LaTeX source code

About the license

Open Set Theory is released under a Creative Commons license (CC BY 4.0; full details are available 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.

Version history

2019
First release; license Creative Commons BY 4.0

Over the past few years, I have released three Open Education Resources. These are open source electronic textbooks, for use by teachers or for self-study. The links will take you to a page describing the book, and allowing you to download it in various formats.