Validity
From Exampleproblems
- This article discusses validity in logic; for the term in the social sciences see validity (statistics).
In logic, the form of an argument is valid precisely if it cannot lead from true premises to a false conclusion. An argument is said to be valid if, in every model in which all premises are true, the conclusion is true. For example: "All A are B; some A are C; therefore some B are C" is a valid form.
A formula of logic is said to be valid if it is true under every interpretation (also called structure or model). See also model theory or mathematical logic.
The relation between the two notions is expressed by the deduction theorem and the resolution theorem.
A tautology, or tautologous formula, is truth functionally valid. Not all valid formulas of quantificational logic are tautologies. See also the truth table article.
Example
Consider the following argument form in which the letters P, Q, and A represent unanalyzed or uninterpreted sentences.
- All P are Q
- A is P
- Therefore, A is Q
The validity of an actual argument can be determined by translating it into an argument form, and then analyzing the argument form for validity. (The argument form above is valid; see syllogism.)
- If (all P are Q) and (A is P), then (A is Q).
