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forall x: An Introduction to Formal Logic

Name: forall x: An Introduction to Formal Logic
Author: P. D. Magnus

P. D. Magnus · 2005

4.5 from 2 reviews · 29 views

Logic & argument Analytic

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What it is

A free, openly licensed textbook for a first course in formal logic. It begins with the notions of argument and validity, then teaches sentential logic: symbolising English sentences, truth tables, and tests for validity and consistency. It moves on to quantified (first-order) logic, covering symbolisation with predicates, quantifiers and identity, and the formal semantics of models. A final part teaches a natural deduction proof system for both sentential and quantified logic. The book includes many exercises and is designed to be adapted: because its licence allows modification, other logicians have produced their own versions, including widely used remixes, so readers will find several editions in circulation. It is written for students with no background in mathematics, and it concentrates on doing logic rather than on the philosophy of logic.

Why read it

It costs nothing and teaches predicate logic properly, step by step, with enough exercises to make the skill stick.

Where to start

Work through the sentential logic chapters with the exercises before moving on to quantifiers.

Reviews

Ana Clara Ferreira Mar 2026

I tutor undergraduates and this is what I use, in one of the remixed versions. The exercises are the point: students cannot fake their way through translating 'every student who passed admires some teacher'. The natural deduction system is clean, and the fact that it is free matters a great deal in a country where textbooks cost a week's rent.

Tomasz Wójcik Dec 2025

A solid, unpretentious textbook. You will find little metatheory here, and readers who want soundness and completeness proved in full should move on afterwards. For learning to symbolise and prove, though, it is hard to beat. I recommend it to anyone teaching themselves.

Ana Clara Ferreira Mar 2026

I tutor undergraduates and this is what I use, in one of the remixed versions. The exercises are the point: students cannot fake their way through translating 'every student who passed admires some teacher'. The natural deduction system is clean, and the fact that it is free matters a great deal in a country where textbooks cost a week's rent.
Tomasz Wójcik Dec 2025

A solid, unpretentious textbook. You will find little metatheory here, and readers who want soundness and completeness proved in full should move on afterwards. For learning to symbolise and prove, though, it is hard to beat. I recommend it to anyone teaching themselves.