An argument is a sequence of statements called the premises aimed at demonstrating the truth of an statment called the conclusion. Typically, the symbol "
An argument is said to be "valid" if the conclusion necessarily follows from or is a consequence of the premises, in other words it takes a form that makes it impossible for the premises to be true but the conclusion to be false.
An argument is said to be conceptually "valid" if it is valid for the specific sentences used.
If an argument is formally valid the individual sentences should be able to be replaced and the argument will still remain valid. This is unlike conceptual validity which depends only on the specific sentences used.
TODO: Finish formal validity with rules of inference
true is called a critical row. If there is a critical row in which the conclusion is false, then it is possible for an argument of the given form to have true premises and a false conclusion, and so the argument form is invalid. If the conclusion in every critical row is true, then the argument form is valid.Test whether or not the following argument is valid
| Premises | Conclusion | |||||||
|---|---|---|---|---|---|---|---|---|
| F | F | F | T | T | F | T | T | T |
| F | F | T | F | F | F | T | T | T |
| F | T | F | T | T | F | T | F | |
| F | T | T | F | T | F | T | F | |
| T | F | F | T | T | F | T | T | F |
| T | F | T | F | F | T | F | T | |
| T | T | F | T | T | F | T | F | |
| T | T | T | F | T | T | T | T | T |
Critical rows are shown in bold
This argument is invalid as the premises are both true in third critical row (row 6, when true, false, and false) but the conclusion is false.
An argument is said the be sound if it is both valid and all the premises are true, for example we can consider the following example:
Despite the argument being valid the conclusion makes no sense. This argument is not sound as we know Oranges are fruits making the premise "Oranges are not fruit" false.
Conversely, just because all the premises are true and the conclusion is true, the argument is not necessarily sound, for example:
If Paris were to declare independence from the rest of France, then the conclusion would no longer be true, even though both of the premises would remain true. Therefore since we can suppose a situation where the premises are true but the conclusion is not true, the argument is still invalid and thus unsound even though factually the premises and conclusion of this argument are all true.