Blackwell Reference Online

Extract

L ogic If a statement B can be validly inferred or deduced from the premises A 1 , A 2 , … A n , in such a way that it is impossible that all the premises A 1 , A 2 , … A n can be true while B is false, then B is a logical consequence of these premises. Every consequence of true propositions must be true . The deductive relation that holds between premises and the conclusion is independent of the subject-matter of the words contained in premises and conclusion. Logical consequence is generally symbolized by a double turnstile ¦. That B is the logical consequence of 1 , A 2 , … A n , can be written “A 1 , A 2 , … A n ¦ B.” Logical consequence is a synonym of logical implication. It indicates that there is a necessary relationship between premises and conclusion. The inference is necessary, leading invariably to true conclusions from true premises. “We can define the concept of logical consequence as follows: The sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X.” Tarski, Logic, Semantics and Metamathematics ... log in or subscribe to read full text