This is a complete and open textbook for formal logic. Formal logic, as a field, is a subdiscipline within Philosophy which studies the relationship between assumptions (premises) and conclusions. It is ‘formal’ in the sense that it concerns the form or shape of the assumptions/conclusions on an abstract level so the same logical structure can be used in many different unrelated contexts with the same level of certainty. This textbook covers the key concepts such as entailment, validity, symbolization, and proofs, as well as some more advanced topics like Modal Logic. Using a Fitch-style proof system, the formal languages covered are Propositional Logic, Quantified Logic, and Modal Logics.
There are many other versions/editions of forallx out there, this one is unique in that:
- It provides biographies for various logicians and philosophers important to the history and development of formal logic.
- It reimagines the modal logic system to be both sound and complete.
- It redefines the inference rule Dilemma in order to retain the spirit while being more practically useful.
- It includes an additional equivalency rule (TAUT) which simplifies many proofs.
- It returns to P.D. Magnus' original Disjunction Elimination, Negation Introduction, and Negation Elimination inference rules.
There are 10 modules (sections or parts) covering a different aspect of logic. These are:
- Arguments and Logic
- Symbolization
- Truth Tables
- Natural Deduction I
- Natural Deduction II
- Quantified Logic
- Validity in QL
- Natural Deduction in QL I
- Natural Deduction in QL II
- Modal Logic
This work is under perpetual development and may change with time. As it sits now, it is a fully functional textbook which is being used at Pierce College and other colleges and universities around the globe.
This book was designed for a quarter-long (10 weeks) introduction to formal logic. In my classes, I (Davis A. Smith) cover all modules, spending 1 week per module. The CC BY license gives you the right to download and distribute the book yourself. In order to ensure that all your students have the same version of the book throughout the term you’re using it, you should upload the PDF you decide to use to your LMS rather than merely give your students a link to the source. You are also free to have the PDFs printed by your bookstore.
The syntax and proof systems are supported by Graham Leach-Krouse’s free, online logic teaching software application Carnap.io. I recommend that this be included in your course as a course companion. It allows for submission and automated marking of exercises such as symbolization, truth tables, and natural deduction proofs.
Davis Smith earned his Master’s Degree in Philosophy from Arizona State University and is an adjunct Philosophy professor at three colleges, Pierce College, Bellevue College, and Olympic College, all in Washington, USA. He specializes in teaching introductory level courses. One of his goals in teaching is to make Philosophy accessible to all people. The cost and quality of textbooks are under-discussed obstacles to accessibility which Mr. Smith seeks to remove. His other textbooks are:
- Questions We Have An Introduction to Philosophy
- Who Should I Be? What Should I Do? An Introduction to Ethics
Outside of his OER textbooks, his current projects relate to the plausibility of libertarian free will, the philosophy of rhyme, and the philosophy of profanity.
You can download PDFs of the most current version under development here:
- forallxd.pdf This is the default, basic edition.
- Additional explanations for symbolization.
- More glossary entries and definitions will be added.
- Brief content for informal logic will be added.
- Improved and refined content for Modal Logic will be added.
- Proof theories for Temporal Logic and Deontic Logic will be added.
forallx: R3 by Davis A. Smith is a revision and expansion of forallx: Calgary, by Aaron Thomas-Bolduc and Richard Zach, used under a CC BY 4.0 license, which was based on forallx: Cambridge, by Tim Button (University College London), used under a CC BY 4.0 license, which was based, in turn, on forallx, by P.D. Magnus (University at Albany, State University of New York), used under a CC BY 4.0 license. It includes additional material from forallx by P.D. Magnus and Metatheory by Tim Button, used under a CC BY 4.0 license, and from forallx: Lorain County Remix, by Cathal Woods and J. Robert Loftis as well as original material by Davis A. Smith. Biographies for Alan Turing, Bertrand Russell, and Kurt Gödel were provided by The Open Logic Project and used under a CC BY 4.0 license. The biography for William of Ockham was provided by Andrew Jeffery and used with his permission. The image used in the biography of William of Ockham was taken by John Salmon and used under a CC BY 2.0 license.
This work is licensed under a Creative Commons Attribution 4.0 license. You are free to copy and redistribute the material in any medium or format, and remix, transform, and build upon the material for any purpose, even commercially, under the following terms:
- 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.
- You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
The production of this work was made possible by Professional Development funds provided by Pierce College's Employee Learning and Development (ELAD).