Deductive Logic

Deductive Logic: The branch of logic that studies the principles of entailment — the situation that occurs when one proposition follows necessarily from another, or others. This happens when it is impossible for the premises of the argument to be true and the conclusion false. This relationship is sometimes also called implication. Entailment (implication) instantiates the property that has come to be known in logic as validity. An argument where it is impossible for the premises to be true and the conclusion false is said to be “valid,” in the logician’s restricted technical sense of ‘validity’: Usually deductive logic is considered to be a formal inquiry/science. That is, whether an argument is valid depends on its logical form, not on its content. The following example has been used to illustrate:” All men are mortal; Socrates is a man; therefore Socrates is mortal. ”This argument is technically valid even if it should turn out to be the case that there was no such person as Socrates, because the conclusion follows necessarily from the premises. This also illustrates the point that validity is not sufficient for a good argument, “All men are rich; all who are rich are mortal, therefore all men are mortal.” This argument is valid but most would reject it because the first premise is false. So in addition to being valid, the argument must have true premises. (See “Soundness”)

Source: ‘What is Good? What is Bad? The Value of All Values across Time, Place and Theories’ by John McMurtry, Philosophy and World Problems, Volume I-III, UNESCO in partnership with Encyclopedia of Life Support Systems: Oxford, 2004-11.