Logic
For kids. English first. Symbols at the end.
Every lesson opens with a sentence a kid would actually say, names the logical structure already inside it, and ends with a small interactive widget for testing the truth-question. Logic isn't being introduced — it's being named.
If you're trying to figure out where to start or where to stop, the Course Map lays out the five levels of understanding and what each one unlocks.
Course Map
Pick your stopping point. What each module unlocks, and which level fits which goal.
1.1 — AND
Both halves true. The whole sentence stands or falls on both parts. AND is picky.
1.2 — OR
At least one half true. Logic uses inclusive OR; English overloads the word. The ambiguity untangled.
1.3 — NOT
Flips the truth value. TRUE becomes FALSE; FALSE becomes TRUE. The simplest of the four words.
1.4 — IF
Sets up a consequence. When can your parents be accused of lying? Only one row of the truth table makes it true.
Module 1 — Drills
Ten mixed AND / OR / NOT / IF problems. Pick TRUE or FALSE, see the reasoning.
2.1 — Combining
Stack the four words. Parens decide which piece evaluates first. Work a compound sentence down to a single truth value, step by step.
2.2 — NOT Distributes
NOT in front of a parenthesized AND or OR moves inside and flips the operator. De Morgan's Law in English. The negative version is often easier to think about.
2.3 — IF Inside Other Things
IF doesn't just stand alone. It can be a piece inside bigger sentences, combined with AND, OR, NOT. Evaluate each IF, then combine. Plus the key NOT-IF flip.
2.4 — Translating Ambiguous English
English is sloppy; logic is precise. Spot the ambiguity, pick the right translation. Inclusive vs exclusive OR, hidden NOTs, IF that's really IFF, truth-relationship vs cause.
Module 2 — Drills
Ten problems on compounds: parens, NOT distribution, IFs inside, and the English-ambiguity traps from 2.4.
4.1 — Premises and Conclusions
An argument has premises (the givens) and a conclusion (what they support). Signal words like 'therefore' mark the conclusion. Watch for implicit premises.
4.2 — Valid vs True
The most important distinction in logic. TRUE is about sentences matching reality. VALID is about conclusions following from premises. SOUND = both at once.
4.3 — Modus Ponens
The most common valid argument shape in the world. IF X THEN Y, plus X, gives you Y. You use it constantly without naming it.
4.4 — Modus Tollens
Modus Ponens's twin. IF X THEN Y, plus NOT Y, gives you NOT X. The detective move: the evidence isn't there, so the trigger didn't happen.
Module 4 — Drills
Ten problems on arguments: spot the conclusion, identify MP vs MT, valid vs sound, fill in the implicit premise.
5.1 — Affirming the Consequent
The most common logical fallacy. Looks like Modus Ponens but runs backward through the IF-THEN. Confirming the consequent doesn't prove the antecedent.
5.2 — Denying the Antecedent
The second classic fallacy. Looks like Modus Tollens but denies the IF part instead of the THEN part. The THEN part can still hold for other reasons.
5.3 — The Slippery OR
Presenting two options as if they're the only options. Also called false dichotomy. Real choices are often more than two — watch for the rhetorical trick.
5.4 — IF vs IFF Confusion
Most everyday 'if' statements really mean 'iff.' That hidden shift is what fuels the fallacies in 5.1 and 5.2. Spot which one the speaker means.
Module 5 — Drills
Ten problems on telling valid arguments from fallacies. Affirming the consequent, denying the antecedent, slippery OR, IF vs IFF.
6.1 — Why Shorthand
Why mathematicians use symbols (∧ ∨ ¬ → ↔). Brevity and universality. Symbols don't add anything — they package familiar ideas more compactly.
6.2 — The Symbols
Nine symbols cover all of sentential logic: ∧ ∨ ¬ → ↔ ⊕ ⊤ ⊥ ∴. Each is a label for an idea you already know. Variables, parens, order of operations.
6.3 — Translation Drills
The only way to get fast at symbols is practice. English to symbols, symbols to English, argument shape identification.
7.1 — What's a Proof?
A proof is the path from premises to conclusion, written so anyone can walk it. Each step earns its place. 'I think' becomes 'I can show.'
7.2 — Direct Proof
Chain inferences from premises to conclusion. Each step uses MP, MT, or another rule applied to earlier lines. The most common proof shape.
7.3 — Proof by Contradiction
Assume the opposite of what you want to prove. Derive a contradiction. Conclude the original. The classic indirect-proof technique.
7.4 — Proof by Cases
When an OR appears in the premises, prove the conclusion in each branch separately. If it holds in both cases, it holds overall.
Module 7 — Drills
Ten problems on the three proof techniques: spot direct vs contradiction vs cases, fill in the next step, judge whether a proof is complete.
8.1 — Objects and Properties
Pedro is happy. There's a thing we're talking about (Pedro) and something we're saying about it (happy). That's the predicate move.
8.2 — All
All dogs bark. Every single one. The claim covers the whole group — one exception kills it.
8.3 — Some
Some kids play piano. At least one. Just one match is enough to make the claim true.
8.4 — NOT-all and NOT-some
The flip-and-swap rule. Not all dogs bark = some dog doesn't bark. NOT moves through ALL and SOME by swapping them.
Module 8 — Drills
Ten problems on objects, properties, all, some, and the flip-and-swap rule. No scoring — just practice.
9.1 — Must and Might
Modal words. Must, might, could, has to. They don't talk about what IS — they talk about what MUST or COULD be.
9.2 — Necessary
It must be raining. Necessarily true. The claim holds in every possible situation — one alternative kills it.
9.3 — Possible
It could be raining. The claim holds in at least one possible situation — one example is enough.
9.4 — NOT-must and NOT-could
The modal flip-and-swap rule. Not necessarily = possibly not. Not possible = necessarily not. Same trick as the quantifier flip.
Module 9 — Drills
Ten problems on must/might, necessity and possibility, and the modal flip-and-swap rule. No scoring — just practice.