Validity
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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.
A tautology, or tautologous formula, is truth functionally valid. Not all valid formulas of quantificational logic are tautologies. See also truth table.
[edit] Example
Consider the following argument form in which the letters P, Q, and S represent unanalyzed or uninterpreted sentences.
- All P are Q
- S is P
- Therefore, S 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 (S is P), then (S is Q).
[edit] See also
