Logic

What it takes for a conclusion to follow, why that depends on the shape of an argument rather than its subject, and why a valid argument can still be worthless.

Five connectives with fixed meanings, brackets that fix scope, and the ordinary English words that refuse to fit.

Every possible situation in {{2}}^{{n}} rows, which turns validity into something you can check by hand and then defeats you by doubling.

Why {P}{\to }{Q} counts as true whenever {P} is false, what that costs, and the two invalid forms that share its table with the valid ones.

When two formulas have the same column they are interchangeable, which turns logic into calculation and lets any formula be rewritten into a standard shape.

Deriving a conclusion line by line, with one rule to introduce each connective and one to take it apart, every rule justified by its truth table.

Supposing something in order to discharge it, which is what proves a conditional, a negation and a disjunction of cases, and completes the system.

Breaking sentences into predicates, names and variables so that "all" and "some" become visible, with the two translations everything else depends on.

Predicates with two places let quantifiers stack, and the order they stack in decides what is being claimed.

An interpretation is a domain plus an extension for each predicate, and one small interpretation is enough to refute an argument for good.

Four rules for {\forall } and {\exists }, two of them carrying restrictions, and what goes wrong the moment a restriction is dropped.

One predicate with a fixed meaning in every model, which is what it takes to say "at least two", "exactly one" and "the".

The methods a working proof uses, each one an instance of a rule already established, and the one method that is not a rule of logic at all.

Where the machinery stops: formalisation is a judgement, valid arguments can be worthless, and the fallacies that matter most are not failures of form.