SECOND RULE.
A logical definition should be exactly equivalent to the species defined.
This means that the species must equal the genus plus the differentia or the subject and predicate of the definition must be co-extensive—of the same bigness. The subject must refer to the same number of objects as the predicate.
A man upon the witness stand makes the declaration that he will testify to the truth, the whole truth and nothing but the truth. A logical definition must contain the species, the whole species and nothing but the species. If the definition does not include all the species, it is too narrow; while on the other hand, if it includes other species of the genus it is too broad.
An excellent test of this second requirement is to interchange subject and predicate. If the interchanged proposition means the same as the original then the conditions have been met. To illustrate: Original—A trigon is a polygon of three angles. Interchanged—A polygon of three angles is a trigon.
The very best way of making the definition conform to this rule is to put to oneself these three questions: 1. Does it include all of the species? 2. Does it exclude all other species of the genus? 3. Has it any unnecessary marks?
To exemplify: Let us ask the three questions relative to the following logical definitions:
(1) A parallelogram is a quadrilateral whose opposite sides are parallel.
(2) A bird is a biped with feathers.
Questions: