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forall x: Calgary: An Introduction to Formal Logic
An introduction to formal logic, covering truth-functional (propositional) and first-order (predicate) logic. It deals with logical notions such as entailment and satisfiablity, symbolization of English sentences using connectives and quantifiers (including identity, e.g., definite descriptions), the semantics of TFL (truth tables) and FOL (first-order interpretations), and proofs (using and natural deduction). Advanced topics discussed are the truth-functional adequacy of propositional logic, normal forms, the soundness of the proof system, and the basics of modal logic. Available for free download at forallx.openlogicproject.org.
398 pages, Paperback
Published September 3, 2019
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Displaying 1 - 8 of 8 reviews
April 3, 2024
Paul Tomassi kan ta seg en bolle
August 11, 2020
Forallx: Calgary is a free, incredibly well-written, and succinct introduction to formal logic, including Truth-Functional Logic, First Order Logic, and even a small amount of Modal Logic. The pages are colorfully designed in a pleasing hot pink, important terms are highlighted, and almost every section is followed by a series of exercises to help the reader better internalize the topics. As an autodidact, I found the book's contents rigorous without requiring any supplementation, which is a huge plus. All-in-all, this book does its job super well, and I can't wait to read more books from The Open Logic Project!
June 22, 2021
I've read this just as a primer for Gödel Escher Bach, but I see that I'd have enjoyed it even if it weren't for that. I only skipped reading on semantics for systems T, S4 and S5 but the book remains accessible all the way.
June 22, 2025
For All X
This book is a great introduction to logic. The authors seem more motivated by retelling the history of logic to make the arbitrariness of these systems feel more real, rather than rewriting the history and presenting concepts in the most natural way. This approach makes some chapters harder to follow, but it's a reasonable choice.
Expected Learning
I learned about a lot of things I expected to learn about, and now feel like I am capable of defining them: Classical propositional logic, Classical first-order logic, Modal logic, and Soundness & Completeness.
Unexpected Insights
Meta-languages and Object-languages
To have almost any formal understanding of logical systems, it is required to have an understanding of meta-languages and object-languages. Metalinguistic symbols appear constantly. Metalinguistics is required to understand something as simple as the difference between implication and 'therefore' to separate out conclusions - in other words, the difference between an argument and a statement. We can't interpret the three dots through TFL semantics, only English semantics (see: What the Tortoise Said to Achilles). Likewise, entering a subproof can't be understood through TFL semantics. Again, the strict-subproof in modal logic is metalinguistic, even though the same symbol can be used as an operator through object-level semantics.
Modal Logic's Expressiveness
Modal logic is much more formal, flexible, and expressive than I had imagined, and has many graph-theoretic notions. I find it fascinating that Modal logic is just a lightweight functional framework which can have its semantics map onto whatever it is trying to model by enforcing additional constraints on the assignment function. To model 'believes', we may not want reflexivity of the accessibility function, but to model 'physically possible', we want reflexivity. To model 'mathematical necessity' (under mathematical platonism), we may want what's necessary to be necessarily so, and thus we want both reflexivity and transitivity. To model 'metaphysically possible', we want equivalence. The formal structure of the assignment function gave me a new epistemological formal spin on interpretation of metaphysics, as it cannot speak of what is outside of our equivalence class.
Linguistic and Conceptual Reframing
More abstractly, I gained a more functional connotation for words such as 'interpretation', 'expressive', etc. I also gained a lot more respect for 'On What There Is' and 'Naming and Necessity'.
This book is a great introduction to logic. The authors seem more motivated by retelling the history of logic to make the arbitrariness of these systems feel more real, rather than rewriting the history and presenting concepts in the most natural way. This approach makes some chapters harder to follow, but it's a reasonable choice.
Expected Learning
I learned about a lot of things I expected to learn about, and now feel like I am capable of defining them: Classical propositional logic, Classical first-order logic, Modal logic, and Soundness & Completeness.
Unexpected Insights
Meta-languages and Object-languages
To have almost any formal understanding of logical systems, it is required to have an understanding of meta-languages and object-languages. Metalinguistic symbols appear constantly. Metalinguistics is required to understand something as simple as the difference between implication and 'therefore' to separate out conclusions - in other words, the difference between an argument and a statement. We can't interpret the three dots through TFL semantics, only English semantics (see: What the Tortoise Said to Achilles). Likewise, entering a subproof can't be understood through TFL semantics. Again, the strict-subproof in modal logic is metalinguistic, even though the same symbol can be used as an operator through object-level semantics.
Modal Logic's Expressiveness
Modal logic is much more formal, flexible, and expressive than I had imagined, and has many graph-theoretic notions. I find it fascinating that Modal logic is just a lightweight functional framework which can have its semantics map onto whatever it is trying to model by enforcing additional constraints on the assignment function. To model 'believes', we may not want reflexivity of the accessibility function, but to model 'physically possible', we want reflexivity. To model 'mathematical necessity' (under mathematical platonism), we may want what's necessary to be necessarily so, and thus we want both reflexivity and transitivity. To model 'metaphysically possible', we want equivalence. The formal structure of the assignment function gave me a new epistemological formal spin on interpretation of metaphysics, as it cannot speak of what is outside of our equivalence class.
Linguistic and Conceptual Reframing
More abstractly, I gained a more functional connotation for words such as 'interpretation', 'expressive', etc. I also gained a lot more respect for 'On What There Is' and 'Naming and Necessity'.
July 20, 2020
This book delivers exactly what the title promises - an excellent introduction to formal logic. The explanations are understandable (even for a relative beginner like me), the definitions marked clearly for easy reference, and each chapter contains a ton of example exercises.
I have to admit that I only made it to the end of Part 3, but even just that gave me an excellent idea of what it is all about - and an equally clear understanding that this topic is not for me. At least not the way it was being taught in the course using this textbook. But I am glad I explored it!
I have to admit that I only made it to the end of Part 3, but even just that gave me an excellent idea of what it is all about - and an equally clear understanding that this topic is not for me. At least not the way it was being taught in the course using this textbook. But I am glad I explored it!
January 2, 2025
Helpful and Readable:
If you are looking for a brief but readable introduction to formal logic, read this book. It is well written and can be found for free online.. This book is used in some logic courses, (including schools like Cambridge) and is much better than your standard textbook.
If you are looking for a brief but readable introduction to formal logic, read this book. It is well written and can be found for free online.. This book is used in some logic courses, (including schools like Cambridge) and is much better than your standard textbook.
March 18, 2025
Average book about symbolic logic, not my favorite. The way it explained certain things was over-complicated
November 7, 2025
Easy to understand, good examples
Displaying 1 - 8 of 8 reviews