7. THE RULES OF LOGICAL DEFINITION.
Five rules summarize the requirements to which a logical definition must conform.
FIRST RULE.
A logical definition should state the essential attributes of the species defined.
This means that a logical definition should contain the species, the proximate genus and the differentia. As the terms species, genus and differentia have been explained, it will be sufficient to briefly illustrate this rule.
Logical According to the First Rule.
(1) A species
bird is a genus
biped with differentia
feathers.
(2) A species
mascot is a genus
person differentia
supposed to bring good luck.
(3) species
Religion is a genus
system of differentia
faith and worship.
(4) A species
moonbeam is a genus
ray of light differentia
from the moon.
Illogical According to the First Rule.
(1) A man is a rational animal.
(“Biped” is the proximate genus, not “animal.”)
(2) A Connotative term always denotes both an object and an attribute.
(No genus.)
(3) A trigon is a polygon.
(No differentia.)
(4) It is a term which denotes an indefinite number of objects or attributes.
(No species.)
The Foregoing Illogical Definitions Made Logical.
(1) A man is a rational biped.
(2) A Connotative term is a term which denotes both an object and an attribute.
(3) A trigon is a polygon of three angles.
(4) A general term is a term which denotes an indefinite number of objects or attributes.
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:
(1) Does the definition include all the parallelograms? Yes. Does it exclude all other quadrilaterals? Yes. Are there any unnecessary marks? No.
(2) Does it include all birds? Yes. Does it exclude all other bipeds? Yes. Any unnecessary marks? No.
Illogical According to the Second Rule.
(1) A man is a vertebrate animal.
(Too broad. Does not exclude other species of the genus, such as horses, dogs, etc.)
(2) A barn is a building where horses are kept.
(Too narrow. Does not include all of the species, such as cow barn.)
(3) An equilateral triangle is a triangle all of whose sides and angles are equal.
(Equal angles is an unnecessary mark.)
The Foregoing Definitions Made Logical.
(1) A man is a rational biped. (Proximate genus.)
(2) A barn is a building where horses and cattle are kept and hay and grain are stored.
(3) An equilateral triangle is a triangle all of whose sides are equal.
THIRD RULE.
A definition must not repeat the name to be defined nor contain any synonym of it.
A violation of this rule is known as “a circle in defining” (circulus in definiendo).
There are some exceptions to this rule, as in the case of compound words and a species which takes its name from its proximate genus. To say that a hobby-horse is a horse, or that an equilateral triangle is a triangle, is not only allowable but necessary, that the proximate genus may be used.
The following definitions are illogical according to the third rule:
(1) A teacher is one who teaches.
(2) Life is the sum of the vital functions.
(3) A sensation is that which comes to the mind through the senses.
FOURTH RULE.
A definition must not be expressed in obscure, figurative or ambiguous language.
A violation of this rule is referred to in logic as “defining the unknown by the still more unknown” (ignotum per ignotius).
It is known that the purpose of definition is to make clear some obscure term, consequently unless every word used is understood the chief aim of the definition has been defeated.
From this it must not be inferred that all definitions should be free from technical terms. Such a restriction would make the defining of many terms unsatisfactory and in a few cases practically impossible. To the student of evolution the following definition by Spencer is intelligible while to the uninitiated it would appear obscure: “Evolution is a continuous change from an indefinite, incoherent homogeneity to a definite coherent heterogeneity through successive differentiations and integrations.”
This rule insists upon simple language when it is possible to use such in giving an accurate and comprehensive meaning to the term defined.
Illogical Definitions According to the Fourth Rule.
(1) “A net is something which is reticulated and decussated, with interstices between the intersections.” Dr. Johnson.
(2) “Thought is only a cognition of the necessary relations of our concepts.”
(3) “The soul is the entelechy, or first form of an organized body which has potential life.” Aristotle.
FIFTH RULE.
When possible the definition must be affirmative rather than negative.
The fact that there are a considerable number of terms which admit of a negative definition only, takes from the force of this rule. Such terms as deafness, inexpressible, infidel and the like can best be defined negatively.
It likewise happens that when words are used in pairs it is expedient to define one affirmatively and the other negatively. Recall, for example, the definitions of relative and absolute terms: “A relative term is one which needs another term to make its meaning clear.” “An absolute term is one which does not need another term to make its meaning clear.”
Illogical Definitions According to the Fifth Rule.
(1) A gentleman is a man who is not rude.
(2) An element is a substance which is not a compound.
(3) An univocal term is a term which does not have more than one meaning.