ABSTRACT
In a loose sense a proposition contradicts its contraries, since it entails (see IMPLICATION) their contradictories. ‘X is black’ contradicts ‘X is white’, if it entails ‘X is not white’.
. In a categorical proposition of traditional formal logic, replacement of a proposition by another (its contrapositive) which follows logically from it and is got by negating the subject and predicate and interchanging them. The contrapositive of ‘All cats are animals’ is ‘All non-animals are non-cats’. Contraposition can be validly carried out on only some of the traditional types of proposition. Contraposition of a conditional or hypothetical proposition negates its antecedent and its consequent and interchanges them. ‘If grass is green, snow is white’ has as contrapositive ‘If snow is not white, grass is not green’. This latter process is occasionally called transposition.
