Validity
From Freepedia
- This article discusses validity in logic, for the term in the social sciences see validity (statistics).
In a logical argument, the term validity is used to determine whether a form of an argument meets a certain set of standards to be deemed valid. An argument is said to be valid if, for every model (m), all premises are true in (m), then the conclusion is true in (m).
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#technical reference.
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).
Formal Validity - Definition
Informal Validity - Definition
