(5) A definition must not be negative, if it can be affirmative.
Briefly, a definition must be adequate (1), terse (2), clear (4); and must not be tautologous (3), or, if it can be avoided, negative (5).
§ 379. It is worth while to notice a slight ambiguity in the term 'definition' itself. Sometimes it is applied to the whole proposition which expounds the meaning of the term; at other times it is confined to the predicate of this proposition. Thus in stating the first four rules we have used the term in the latter sense, and in stating the fifth in the former.
§ 380. We will now illustrate the force of the above rules by giving examples of their violation.
Rule 1. Violations. A triangle is a figure with three equal sides.
A square is a four-sided figure having all its sides equal.
In the first instance the definition is less extensive than the term defined, since it applies only to equilateral triangles. This fault may be amended by decreasing the intension, which we do by eliminating the reference to the equality of the sides.
In the second instance the definition is more extensive than the term defined. We must accordingly increase the intension by adding a new attribute 'and all its angles right angles.'
Rule 2. Violation. A triangle is a figure with three sides and three angles.
One of the chief merits of a definition is to be terse, and this definition is redundant, since what has three sides cannot but have three angles.