conversion, in syllogistic, or traditional, logic, interchanging the subject and predicate of a categorical proposition (q.v.), or statement. Conversion yields an equivalent proposition (and is hence a valid inference) in general only with so-called E and I propositions (universal negatives and particular affirmatives). For example, the converse of the E proposition “No men are immortal” is “No immortals are men” and that of the I proposition “Some man is mortal” is “Some mortal is man.”
In mathematics the term converse is used for the proposition obtained by the transformation of AB implies C into AC implies B, rendered symbolically as AB ⊃ C into AC ⊃ B. This operation may in some instances be reduced to the simple converse of an A proposition (universal affirmative) in the sense of traditional logic—for example: “Every equilateral triangle is equiangular,” and, conversely, “Every equiangular triangle is equilateral.” But such a reduction often becomes either impossible or very artificial. In this sense of conversion, the passage from a proposition to its converse is not, in general, a valid inference; and though often a mathematical proposition and its converse may both hold, separate proofs must be given for each case.