What an argument is
Some statements are given, and a conclusion is drawn from them. When does the conclusion really have to follow?
Where you are 4 inside
What this area is about
An argument is a list of statements taken as given, the premises, followed by a conclusion drawn from them. Whether the conclusion is forced depends only on the argument’s shape, not on what its statements are about. A few shapes always work, a few look almost the same and never do, and this area teaches you to tell them apart.
How these fit together
The idea. Valid and sound arguments names the two questions: does the conclusion follow, and are the premises true?
Two valid forms, each with its fallacy. Modus ponens, chaining, and a common fallacy goes from p \to q and p to q, and chains p \to q and q \to r into p \to r (hypothetical syllogism). Its fallacy, affirming the consequent, goes from p \to q and q to p. Modus tollens, ruling out, and a common fallacy goes from p \to q and \neg q to \neg p, and from p \lor q and \neg p to q (disjunctive syllogism). Its fallacy, denying the antecedent, goes from p \to q and \neg p to \neg q. Each fallacy uses the right conditional from the wrong end.
Method. Testing an argument with a truth table checks any argument built from whole statements for a row where every premise is true and the conclusion false.
A path through it
Valid and sound first, then modus ponens, then modus tollens, each with its fallacy. Then the truth-table test, which confirms each valid form and breaks each fallacy.
These forms are the steps every proof is made of, so the area leads to direct proof, proof by contraposition and proof in geometry.