Argument Glossary
Definition
An argument is an ordered pair consisting of a set of sentences of a language (its premises) and a single sentence of the same language (its conclusion). A word like 'hence' or 'therefore' is often inserted between the two to show that it records an inference.
Disambiguation: The inputs or parameters of a function are also called its arguments. This usage has nothing to do with the notion of an argument as a piece of reasoning.
Comments
Some authors use the word 'argument' to mean what we call a derivation. It seems better to separate the two notions, so that a sequent can represent an argument form, and the validity of an argument can be assessed without raising the question of whether a particular derivation of it conforms to some rules.
Validity: An argument is valid if it is impossible for its premises to be true and its conclusion at the same time false.
In the same way, a sequent is valid if every interpretation satisfying all of its premises also satisfies its conclusion.
Examples of classically valid arguments
- All logicians are rational; some philosophers are not rational; therefore not all philosophers are logicians.
- All horses are animals; therefore all horses' heads are animals' heads.
- It is neither raining nor not raining; therefore it is Tuesday.