> [!Definition] Definition (logical validity) > An [[Argument]] is *logically valid* iff there is no possible situation in which its premises are all true and its conclusion false. > > In other words, an argument is logically valid iff it's conclusion is a [[Logical consequence|logical consequence]] of its premises. > > *Negation*. An argument is logically invalid iff it has a [[Counterexample]]. > [!NOTE] Definition (for formal language) > 1. A [[L1P (Propositional Logic)|propositional logic]] argument is ***logically valid*** iff in joint truth table for all its premises and conclusions there is no row in which its premises are all $T$ and its conclusion $F$. > 2. An argument is ***valid in virtue of its truth functional form*** iff it has a [[Sentence#^efade4|truth functional]] form that can be captured by an $L_{1p}$ argument which is ***logically valid***. (We can say that it is TT-valid). > [!info] Note > - Every argument that is valid in virtue of its truth functional form is also valid in the general sense. > - Not every valid argument is valid in virtue of its truth functional form. > # Example > [!Example] > Suppose $P,Q$ are $L_{1p}$ sentences then the following argument is logically valid: >| $P$ >| $\lnot P$ >|---- >| $Q$ > [!Example] Example > | $P \lor Q$ > | $P$ > |--- > | $(Q\lor \lnot Q)$ > >> In general, if the conclusion of an argument is a [[Sentence#^e8f9c8|tautology]], that argument is logically valid.