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Learn Logic

Learn exactly when a conclusion follows and when it only seems to.

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Logic is the study of valid reasoning: when a conclusion really follows from its premises. Formal logic makes this precise with symbols. Propositional logic handles statements joined by and, or, not and if-then, using truth tables and proof rules like modus ponens. Predicate logic adds quantifiers, "for all" and "there exists," which lets you express claims about every or some object. Along the way you learn the difference between validity and soundness, and how to spot common formal and informal fallacies. Learnr builds a personalized logic course and teaches it in short interactive lessons with lots of translation and proof practice.

How to learn Logic, step by step

Learn what makes an argument valid. An argument is valid if the conclusion must be true whenever the premises are true, and sound if it is valid with true premises. Practice judging short arguments before using any symbols.
Translate English into symbols. Turn sentences into propositional logic with ¬, ∧, ∨, → and ↔, paying special attention to "only if," "unless" and "neither nor." Translation is where most beginner errors happen.
Use truth tables to test claims. Build truth tables for compound statements and check validity, tautologies and equivalences such as De Morgan's laws and the contrapositive. Notice that a conditional is false only when the antecedent is true and the consequent false.
Practice natural deduction proofs. Learn modus ponens, modus tollens, conjunction, disjunction elimination and conditional proof, then prove conclusions step by step. A few proofs a day in Learnr builds the pattern recognition proofs depend on.
Add quantifiers with predicate logic. Express statements like "every student passed some exam" with ∀ and ∃, pay attention to quantifier order, and learn that negating "for all" gives "there exists something not."
Apply logic to real arguments. Analyze arguments in articles and debates, identify formal fallacies like affirming the consequent and informal ones like straw man and false dilemma, and rewrite weak arguments in valid form.

What you'll learn

Translate English sentences into propositional and predicate logic
Use truth tables to test validity and logical equivalence
Build natural deduction proofs with standard inference rules
Work with quantifiers, including negating quantified statements
Distinguish valid from sound arguments and identify common fallacies

What's inside your Logic course

A sample path Learnr builds for Logic. Your real course adapts to your goal and level.

1. Arguments, validity and soundness
2. Propositional logic and connectives
3. Truth tables and logical equivalence
4. Natural deduction proofs
5. Predicate logic and quantifiers
6. Fallacies and logic in everyday reasoning

How long does it take to learn Logic?

An introductory formal logic course covering propositional and predicate logic takes about 2 to 4 months at 3 to 5 hours a week. Truth tables come quickly, while proofs and quantifier translation take the most practice.

What you need before you start

Nothing beyond careful reading and patience with symbols. No prior math is required, though comfort with algebraic notation makes the symbols feel familiar sooner.

Common mistakes to avoid

Treating "if P then Q" as also meaning "if Q then P," which is the fallacy of affirming the consequent.
Confusing validity with truth. A valid argument can have a false conclusion if a premise is false.
Swapping the order of quantifiers, which changes "everyone loves someone" into "someone is loved by everyone."

How Learnr builds your course

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Logic questions, answered

Is logic math or philosophy?

Both. Formal logic is taught in philosophy departments as the study of reasoning and in math and computer science departments as the foundation for proofs, programming and circuit design. The core material overlaps heavily.

Will learning logic help with the LSAT?

The LSAT reasoning sections reward careful reading of conditionals, quantifiers and argument structure, which formal logic trains. Logic is not test prep, though, so pair it with practice on the test's own question types.