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How to Learn Logic

A structured path through Logic — from first principles to confident mastery. Check off each milestone as you go.

Logic Learning Roadmap

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Estimated: 23 weeks

Foundations of Logical Thinking

1-2 weeks

Begin with the basic concepts of arguments, premises, and conclusions. Learn to distinguish between deductive and inductive reasoning, and understand what it means for an argument to be valid or sound. Practice identifying arguments in everyday language.

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Introduction to Logic by Irving Copi (Chapters 1-3)(free)Khan Academy: Introduction to Logic and Critical Thinking(free)

Propositional Logic Fundamentals

2-3 weeks

Study propositional logic: propositions, logical connectives (NOT, AND, OR, IF-THEN, IF AND ONLY IF), truth tables, and basic equivalences. Learn to translate natural language statements into symbolic form and evaluate compound propositions.

A Concise Introduction to Logic by Patrick Hurley (Part II)(free)Open Logic Project: Propositional Logic (free online textbook)(free)

Logical Equivalences and Normal Forms

1-2 weeks

Master key equivalences including De Morgan's Laws, distribution, contraposition, and double negation. Learn to convert formulas into conjunctive and disjunctive normal forms. Practice simplifying complex logical expressions.

Discrete Mathematics and Its Applications by Kenneth Rosen (Chapter 1)(free)MIT OpenCourseWare: Mathematics for Computer Science(free)

Rules of Inference and Proofs

2-3 weeks

Study the fundamental rules of inference: modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism, and constructive dilemma. Learn proof techniques including direct proof, proof by contradiction, and proof by cases.

Logic: The Laws of Truth by Nicholas Smith (Chapters 4-6)(free)Stanford Encyclopedia of Philosophy: Classical Logic(free)

Predicate Logic and Quantifiers

2-3 weeks

Extend your knowledge to first-order predicate logic. Learn about predicates, variables, the universal and existential quantifiers, and the domain of discourse. Practice translating complex English sentences into predicate logic notation.

Language, Proof and Logic by Jon Barwise and John Etchemendy(free)Coursera: Introduction to Mathematical Thinking by Keith Devlin(free)

Informal Logic and Fallacies

2 weeks

Study informal logic, argumentation theory, and critical thinking. Learn to identify and analyze common logical fallacies such as ad hominem, straw man, red herring, false dilemma, slippery slope, and appeal to authority in real-world arguments.

Asking the Right Questions by Browne and Keeley(free)Logically Fallacious by Bo Bennett (comprehensive fallacy reference)(free)

Metatheory and Advanced Topics

3-4 weeks

Explore the metatheoretical properties of logical systems: soundness, completeness, decidability, and consistency. Study Godel's incompleteness theorems at an introductory level and understand their significance for the foundations of mathematics.

Godel's Proof by Ernest Nagel and James Newman(free)Stanford Encyclopedia of Philosophy: Godel's Incompleteness Theorems(free)

Applied Logic and Extensions

3-4 weeks

Explore how logic is applied in computer science (Boolean algebra, circuit design, programming), philosophy (modal logic, epistemic logic), linguistics (formal semantics), and artificial intelligence (knowledge representation, automated reasoning).

Logic in Computer Science by Michael Huth and Mark Ryan(free)An Introduction to Non-Classical Logic by Graham Priest(free)

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Choose a different way to engage with this topic — no grading, just richer thinking.

Explore your way — choose one:

Explore with AI →
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Logic Learning Roadmap - Study Path | PiqCue