A generalization, ‘all F things are G things’, is represented in formal logic by the quantification (∀x )(Fx → Gx ). This has the property that when there are no things that are F, it is true (it means the same as ‘there are no F things that are not G’, which is obviously true when there are no F things at all). In such a case the generalization is said to be vacuously true. A contrasting view of such generalizations is taken in traditional logic: see square of opposition.
Philosophy dictionary. Academic. 2011.