Logic & Proof
What makes an argument binding?
Before anything can be proved, something has to settle what counts as a proof. This subject builds that machinery from ordinary language: what a statement is, what a quantifier really claims, and why four or five argument shapes turn out to be enough for all of mathematics.
Statements
When is a sentence the kind of thing that can be true?
What a proof is for
Two people can agree on every fact and still disagree, which is a clue that argument is doing something beyond stating facts. The film finds the gap; the document formalises it.
Truth tables were not obvious
Implication as usually defined says that a false statement implies anything, which offends everybody the first time they meet it. The film shows why every alternative is worse.
Quantifiers
How much does swapping two words change?
For all, there exists, and the order of the words
Swapping two quantifiers turns a true statement into a false one, and the film builds a case where the difference is the difference between a theorem and nonsense.
Negation, done mechanically
Negating a statement with three nested quantifiers is a procedure, not an insight — but only once you have watched the procedure fail when applied carelessly.
Methods of proof
Why does assuming the opposite ever work?
Contradiction, and why it feels like cheating
Proving something by assuming its opposite looks like sleight of hand until you see it as the only tool available for a negative claim. Irrationality is the case study.
Induction is not about dominoes
The domino picture explains the mechanism and hides the axiom. What induction actually rests on is a property of the natural numbers that has to be assumed.
Formal systems
What if the rules themselves are the object of study?
Logic & Proof, as one volume
Every document in this subject is a chapter of the same book, compiled from one source with live cross-references and continuous numbering. Download the whole thing, or take chapters as you go — the page numbers and theorem references agree either way.
Download Volume I ↓