DEFINITION.
=1. IMPORTANCE.=
To be clear, cogent, concise and consistent is to be logical.
Reference has been made to a striking tendency on the part of writers
and speakers to use words loosely. It is a noticeable fact that
scholars generally aim to be profound rather than clear, philosophical
rather than pointed.
In the use of text books more or less pedagogical these are the common
complaints: “I don’t understand what he means” or “You have to read so
much to get so little.” This condition gives to the topic of definition
a prominence which cannot be overlooked by those who are seeking the
truth; because the definition is the clearest, briefest and altogether
the most satisfactory way of describing an idea. Likewise the habit
of defining any doubtful term reduces to a minimum the possibility of
misunderstanding.
The subject must appeal strongly to the instructor, as he, above all
others, should make his work stand for clearness, pointedness and
continuity.
=2. THE PREDICABLES.=
_A predicable is a term which can be affirmed or predicated of any
subject._ In the proposition, “A man is a rational animal,” the term
“rational animal” is a predicable, because it can be affirmed of the
subject _man_.
To gain a clear knowledge of the definition it is quite necessary
to understand the _five predicables_ which we shall consider in the
following order:
1. Genus.
2. Species.
3. Differentia (difference).
4. Property.
5. Accident.
(1) _Genus_ and (2) _Species_.
Genus and species are relative terms and can best be defined together.
_A genus is a term which stands for two or more subordinate classes._
_A species is a term which represents one of the subordinate classes._
The genus may be subdivided into species; the species together form the
genus.
To illustrate: The term _man_ stands for five subordinate classes or
species, as white, black, brown, yellow and red. “Man” is, therefore,
a genus, while “white man” and “black man,” etc., are species. The
term “polygon” is a genus with reference to “trigon,” “tetragon,”
“pentagon,” etc., while “trigon” is a species of “polygon.”
Any given genus may be a species of some higher class. That is, “man,”
which is a genus with reference to the kinds of men, is a species
of the higher class “biped,” while “biped” is a species of “animal,”
“animal” a species of “organized being,” “organized being” of “material
being,” “material being” of “being.” But here we stop, as there is no
higher grade to which “being” can be referred. This highest genus takes
the name of _summum genus_.
Similarly any given species may be a genus of some lower class.
“White man,” for example, which is a species of “man,” is a genus of
“American,” “Englishman,” “German,” “Frenchman,” etc. “American” is
a genus of “New Yorker,” “Californian,” etc., while “New Yorker” is
a genus of “Smith of Jamaica.” This last term is an individual and
cannot be subdivided. It represents the lowest possible species and
is referred to in logic as _infima species_.
It is obvious that the highest genus cannot become a species, neither
can the lowest species become a genus.
PROXIMATE GENUS.
The proximate genus is the next class above. To illustrate: “Animal”
is a genus of “man,” but “biped” is the proximate genus of “man.”
“Quadrilateral” is the genus of “square,” but “rectangle” is the
proximate genus. The next class above “trigon” is _polygon_ not
_figure_. Hence “polygon” is the proximate genus of “trigon.”
GENUS AND SPECIES OF NATURAL HISTORY.
In natural history the following terms are used to denote the
various grades of kinship in any scheme of classification: (1) kingdom,
(2) class, (3) order, (4) family, (5) genus, (6) species, (7) variety,
(8) the individual thing. Here “genus” and “species” are absolute not
relative and occupy a _fixed_ place in the scheme, while from a logical
viewpoint any of the grades indicated between the lowest and highest
would be the species of the next higher grade or a genus of the next
lower; e. g., _order_ is a species of “class,” while it is the genus
of “family.”
GENUS, A DOUBLE MEANING.
We recall that any class name or genus has a double use, extensional
and intensional. When considered from the standpoint of its extension,
a genus represents a group of objects or is _mathematical_ in its
application, but when used in an intensional sense it represents a
group of qualities or is _logical_ in its application.
Considered extensionally the genus refers to a larger number of objects
than the species. But when viewed intensionally the species refers to
more qualities than the genus. This was made clear when discussing the
law of variation in the extension and intension of terms.
(3) _Differentia._
_The differentia of a term is that attribute which distinguishes a
given species from all the other species of the genus._
It has been observed that the species refers to more qualities than
the genus. In fact, it represents all the attributes of the genus plus
those which distinguish the particular species from the other species
of the genus. These additional qualities are the differentiæ of the
particular species.
TO ILLUSTRATE:
The attribute which distinguishes man from the other bipeds of the
world is his rationality. That which distinguishes the rectangle from
the other parallelograms is its four right angles. The attributes
_rationality_ and _right angles_ are differentiae.
(4) _Property._
_A property of a term is any attribute which helps to make the term
what it is._ Thus “consciousness” is a property of man, “binding” a
property of book, “angles” a property of triangle. Deprive the terms
of these attributes and their true nature is altered.
A differentia is a property according to the foregoing definition.
However, Jevons defines “property” as “Any quality which is common to
the whole of a class, but is not necessary to mark out the class from
other classes.” This viewpoint excludes “differentia” from the notion
of property. The difference in opinion is of slight importance.
(5) _Accident._
_An accident of a term is any attribute which does not help to make
the term what it is._ It may indifferently belong or not belong to the
term. Deprive a term of an accident and the nature of the term remains
unchanged. Thus, a teacher’s position, a man’s watch, the fact that the
angle is one of 80° are all accidents.
It is obvious that a property is a _constant_ attribute while an
accident is variable. This gives to the former a universal validity
while the latter is more or less shifting and uncertain. All triangles
must have _three angles_ (property) while the _value of each angle in
degrees_ (accident) admits of unlimited variation.
Some logicians divide accidents into separable and inseparable. A man’s
_hat_ would be a separable accident while his _birthplace_ would be an
inseparable accident.
FIVE PREDICABLES ILLUSTRATED.
In the following brief descriptions the five predicables are
designated:
(species) (genus) (differentia)
(1) This ――――――――― is a ――――――――――――― with ―――――――――――――――――
rectangle parallelogram four right angles
(accident)
its longer sides being ――――――――――.
ten inches
(species) (differentia) (prox. genus)
(2) This ――――――――― is a ――――――――――――― ――――――――――――― with the
man rational biped
(property) (accident)
――――――――――――――――――― and a ――――――――――――――――.
power of locomotion ruddy complexion
(species) (genus) (differentia) (property)
(3) A ――――――――― is a ――――――― of ――――――――――――― and ――――――――――――,
trigon polygon three sides three angles
(accident)
―――――――――――――――――――――――――――――――――――――――――――――――――――――.
the sum of the angles being equal to two right angles
=3. THE NATURE OF A DEFINITION.=
It will be remembered that an individual notion is a notion of a single
thing or attribute, while a general notion is a notion of a class of
things or a group of attributes. A term which represents an individual
notion is known as a _singular term_, while a term which stands for a
general notion is referred to as a _general term_.
One may explain the meaning of a singular term which stands
for one thing by enumerating its various attributes. For example,
such attributes as a piercing bark, a yellow color, intelligent,
companionable, a strong liking for sweetmeats, explain the meaning
of the singular term “Fido.” Likewise we may explain the meaning of
a general term by enumerating its attributes. To illustrate: power of
speech, rationality, ability to laugh, etc., explain the meaning of
the general term _man_. The explanation of the singular term fits only
Fido. There is probably no other dog in the world just like Fido. But
the explanation of the general term _man_ may be applied to _all_ men.
A brief enumeration of attributes which may be applied to a _class of
things_ often takes the form of a definition. The word definition comes
from the word _definire_, meaning to limit or fix the bounds of.
A definition, then, consists of the enumeration of such attributes
as distinguish a term from all other terms. In this sense it would
seem that the singular term _Fido_, as well as the general term
_man_, admits of definition, but it is usual for logicians to confine
definition to the _general term_. Singular terms may be _described_;
general terms, _defined_.
A DEFINITION OF DEFINITION.
_A definition of a term is a statement of its meaning by enumerating
its characteristic attributes._
That the enumeration must be in terms of its distinguishing or
characteristic attributes is implied in the derivation of the term
_definition_. The attributes must establish limits or bounds, just as a
line fence limits a land owner’s possessions. To indicate that man is a
creature possessing the power of locomotion, sense of sight and ability
to eat, is surely not a definition, as the marks are not characteristic
of men only. These attributes set no boundary between man and horse,
consequently the statement is a faulty _description_ of man, not
a _definition_. But when the enumeration includes such attributes
as power of speech, rationality and ability to laugh, then does the
description become a definition. To put it differently: A definition is
a description of a term by means of its distinguishing attributes. This
statement may be considered a definition of man, though somewhat faulty:
“A man is a creature who is rational and who possesses the power of
speech and ability to laugh.”
=4. DEFINITION AND DIVISION COMPARED.=
We have learned that general terms when connotative may be used
extensionally or intensionally.
A definition indicates the _intensional_ nature of a term, while a
statement which points out the _extensional_ nature of a term is known
as logical division. More briefly: A definition is an _intensional_
statement of the nature of the term, while logical division is an
_extensional_ statement of the nature of the term.
To illustrate: The following statements are definitions:
(1) A dog is a domesticated quadruped of the genus canis and given
to barking.
(2) A quadrilateral is a rectilinear figure of four sides.
(3) Soil is a substance composed of pulverized rock and decayed
vegetable matter in which plants will grow.
The following represent Logical Division:
(1) Dogs are divided into hounds, terriers, bull, etc.
(2) The kinds of quadrilaterals are trapeziums, trapezoids and
parallelograms.
(3) The various soils are loam, sand, clay, muck, etc.
=5. THE KINDS OF DEFINITIONS.=
Generally speaking there are three kinds of definitions, namely,
(1) Etymological, (2) Descriptive, (3) Logical.[5]
(1) _An etymological definition is one based upon the derivation of the
term._
This kind of a definition, which gives merely the meaning of the
symbol, is sometimes called a _nominal_ or verbal definition; while
a _real_ definition is regarded as one which gives the _meaning
of the notion_ for which the symbol stands. The modern logician is
inclined to ignore this classification on the argument that to make a
distinction between a symbol and the notion it symbolizes is simply to
misunderstand the relation which exists between them. If the definition
does not agree with the thing then it cannot correctly explain the
term which represents the thing. Define correctly the term and one has
defined correctly the notion signified by the term.
The attributes of a term may be separated into three classes:
differentia, property and accident. It would appear possible,
therefore, to define a term by enumerating the accidents only or by
enumerating the properties, or, finally, by stating the differentiae.
But if the enumeration is confined to accidents the chances are that
the statement will be a description, not a definition, as accidents
are seldom sufficiently characteristic to determine the boundaries of
a term. This leaves open two distinct ways of defining a term: First,
by naming the properties or properties and accidents only; second,
by stating the differentiæ only. The former kind is the so-called
descriptive definition, while the latter is the logical.
(2) _A descriptive definition of a term is a description of its nature
by means of its properties and accidents._
(3) _A logical definition of a term is a description of its nature by
means of its differentiæ._
THE THREE KINDS OF DEFINITIONS ILLUSTRATED AND COMPARED.
Etymological Definition of Trigon.
A trigon is a figure of three corners.
Descriptive:
A trigon is a figure which has three sides and three angles, the sum
of the latter being equal to two right angles.
Logical:
A trigon is a polygon of three angles.
It is seen that an etymological definition is simply a root-word
analysis. In the case of _trigon_, the prefix comes from the Greek,
meaning three, while the root-word comes from the Greek meaning corner.
The descriptive definition of trigon names the properties, “three
sides and three angles” (differentiæ) and the accident, “the sum of
the angles of which equals two right angles.”
The logical definition of trigon simply states the proximate genus,
“polygon,” and the differentia, “three angles.”
=6. WHEN THE THREE KINDS OF DEFINITIONS ARE SERVICEABLE.=
The etymological definition is helpful in furnishing a cue for
remembering the descriptive and logical definitions. It also leads
to precision of expression――the right word in the right place. Here
is where the knowledge of a foreign language, particularly Latin, is
helpful.
The descriptive definition is best adapted to the child-mind. Children
think in the large; are not given to hair-splitting discriminations,
and, therefore, _many_ characteristic marks must be mentioned in
order to insure a mastery of the content. With children the logical
definition is often too brief to be clear. For example, it is easy
to see which of the following definitions would be better adapted
to the child-mind. _Logical_: A square is an equilateral rectangle.
_Descriptive_: A square is a figure of four equal sides and four right
angles.
The logical definition may be introduced to the student of the
secondary school.
Few exercises are better adapted to the development of powers of
discrimination and precision than practice in defining logically the
common terms of every-day life. For example: “A book is a pack of
paper-sheets bound together.” “A chair is a piece of furniture with
back and seat, designed for the seating of one person.” “A lead pencil
is a cylindrical writing implement with lead through the center.”
“A door is an obstacle designed to swing in and out to open and close
an entrance.” “An eraser is an implement made to rub out written or
printed characters.”
These definitions, coming from training school students, are not above
criticism, yet they illustrate the point in hand.
=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._
species genus differentia
(1) A ――――――― is a ――――― with ―――――――――――.
bird biped feathers
species genus differentia
(2) A ――――――― is a ―――――― ―――――――――――――――――――――――――――.
mascot person supposed to bring good luck
species genus differentia
(3) ―――――――― is a ―――――― of ―――――――――――――――――.
Religion system faith and worship
species genus differentia
(4) A ―――――――― is a ―――――――――――― ―――――――――――――.
moonbeam ray of light 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.
=8. TERMS WHICH CANNOT BE DEFINED LOGICALLY.=
A logical definition insists upon a proximate genus and differentia.
But as there is no genus higher than the highest genus (_summum genus_)
then surely such cannot be defined logically. The words _being_ and
_thing_ illustrate terms of this class. Moreover, it is impossible
to give a satisfactory definition of an individual (_infima species_)
as no attributes can be mentioned which will distinguish definitely
and permanently the individual from others of the class. We may
perceive the attributes but not those that are possessed solely
by the individual. To say that Abraham Lincoln was a man who was
simple and honest is not a definition, as other men have had the
same characteristics.
Again there are a few terms such as life, death, time and space which
cannot be defined satisfactorily. These terms seem to be in a class by
themselves or of their own genus (_sui generis_).
Since a definition of a term is a brief explanation of it by means of
its attributes, it follows that collective terms and terms standing for
a single attribute are incapable of definition. Such terms as group,
pain, attribute, belong to this class.
We may say, then, that there are some terms too high, some too low and
some too peculiar to come within the province of logical definition.
In short, “_summum genus_,” “_infima species_” and “_sui generis_” are
incapable of definition.
=9. DEFINITIONS OF COMMON EDUCATIONAL TERMS.=
(1) _Development_ is the process whereby the latent possibilities
of an individual are unfolded or the invisible conditions of a
situation are made apparent.
Development means expansion according to principle, while
unfolding may or may not involve a principle.
(2) _Education_ is the process employed in developing systematically,
symmetrically and progressively all of the capabilities of a
single life; or
(3) _Education_ is the process of modifying experience in order to
make the life as valuable as it ought to be.
(4) _Teaching_ is the art of occasioning those activities which
result in knowledge, power and skill.
It is the duty of the true teacher to inspire the child to
activity along right lines. Through his own activity the child
shapes his inner world which is sometimes termed _character_.
Knowledge is anything known, power is ability to act, skill is a
readiness of action.
(5) _Instruction_ is the art of occasioning those activities which
result in knowledge.
Instruction develops the understanding; teaching develops
character.
(6) _Training_ is the occasioning of those activities which, by means
of directed exercise, result in power and skill.
Training and education are not interchangeable. Training implies
an outside authority, while education, which involves inner
development, may proceed without supervision.
(7) _Knowledge_ is anything acquired by the act of knowing.
(8) _Learning_ is the act of acquiring knowledge or skill.
(9) Instruction, training, teaching, learning and education all
involve activity.
Instruction arouses activity which results in knowledge;
training directs activity which produces power and skill;
teaching includes both instruction and training. Learning is an
activity which results in knowledge and skill, while education
is a developing process which involves all the others.
(10) A _science_ is knowledge classified for the purpose of
discovering general truths.
(11) _An art_ is a skillful application of knowledge and power to
practice.
“A science teaches us to know, an art to do.”
(12) A _fact_ is a single, individual, particular thing made or done.
A _truth_ is general knowledge which exactly conforms to the
facts.
A truth may be a definition, rule, law, or principle.
(13) A _fact_ as opposed to hypothesis is an occurrence which is true
beyond doubt.
An _hypothesis_ is a supposition advanced to explain an
occurrence or a group of occurrences.
A _theory_ is a general hypothesis which has been partly verified.
(14) _Theory_ as opposed to practice means _general knowledge_, while
practice involves the putting into operation one’s theories.
(15) A _fact_ as opposed to phenomenon is something accomplished.
A phenomenon is something shown.
(16) A _method-whole_ is any subdivision of the matter for instruction
which leads to a generalization.
(17) _Method_ is an orderly procedure according to a recognized system
of rules and principles.
As the term is commonly used it includes not only the arrangement
of the subject matter for instruction but the mode of presenting
the same to the mind.
(18) _Induction_ is the process of proceeding from the less general to
the more general.
_Deduction_ is the process of proceeding from the more general to
the less general.
(19) The terms induction and deduction may have reference to forms of
reasoning or to methods of teaching.
The _inductive method_ is the method of deriving a general truth
from individual instances.
The _deductive method_ is the method of applying a general truth
to individual instances.
The inductive method is objective, while the deductive method is
subjective. Induction is the method of discovery; deduction is
the method of instruction.
(20) _Analysis_ is the process of separating a whole into its related
parts.
_Synthesis_ is the process of uniting the related parts to form
the whole.
(21) The _analytic method_ is the method of proceeding from the whole
to the related parts.
The _synthetic method_ is the method of proceeding from the
related parts to the completed whole.
(22) Analysis and synthesis deal with _single things_, while induction
and deduction are concerned with _classes of things_.
(23) The _complete method_ consists of three elements: (1) induction,
(2) deduction, (3) verification or proof.
When the emphasis is placed on the inductive phase, the complete
method is sometimes termed the development method.
=10. OUTLINE.=
DEFINITION.
(1) Importance.
(2) The Predicables.
Genus――species――summum genus――infima species.
Proximate Genus.
Genus and Species of Natural History.
Genus, Double meaning of
Differentia.
Property.
Accident.
Separable, Inseparable.
(3) Nature of Definition.
(4) Definition and Division Compared.
(5) The Kinds of Definitions.
(1) Etymological.
(2) Descriptive.
(3) Logical.
THREE KINDS ILLUSTRATED AND COMPARED.
(6) When the Three Kinds are Serviceable.
(7) The Rules of Logical Definition.
(1) _Essentials._
(2) Same _size_.
(3) Do not _repeat_.
(4) _Unambiguous._
(5) _Language_ affirmative.
(8) Terms Which Cannot be Defined Logically.
Summum genus.
Infima species.
Sui generis.
Collective terms.
A single attribute.
=11. SUMMARY.=
(1) To be logical one must acquire the habit of accurate definition.
This topic ought to appeal strongly to the school teacher, who should
above all others make his work stand for clearness, pointedness and
continuity.
(2) A predicable is a term which can be affirmed or predicated of any
subject.
The five predicables are Genus, Species, Differentia, Property and
Accident.
(1) A Genus is a term which stands for two or more subordinate
classes.
(2) A Species is a term which represents one of the subordinate
classes.
The _proximate genus_ of a species is the next class above the
species, while the _summum genus_ is the highest possible class
in any graded series of terms. The lowest class is the _infima
species_ of that series. The lowest class may be individual.
In natural history genus and species are not relative terms, but
absolute, having a fixed place in the series of gradations.
The term genus possesses a double meaning: it may be used to
represent objects (extensionally) or qualities (intensionally).
(3) The differentia is that attribute which distinguishes a given
species from all the other species of the genus.
(4) A property of a term is any attribute which helps to make that
term what it is.
Differentia is a property according to definition. Some logicians
would not include the differentia in the content of the term
property.
(5) An accident of a term is any attribute which does not help
to make it what it is. Some authorities divide accidents into
separable and inseparable.
(3) A definition of a term is a statement of its meaning by enumerating
its characteristic attributes.
(4) Definitions explain a term intensionally, while logical division
explains a term extensionally.
(5) There are three kinds of definitions: (1) etymological,
(2) descriptive, (3) logical.
An etymological definition is based upon the derivation of the term;
a descriptive definition states the characteristic properties and
accidents of a term, while a logical definition is simply a statement
of the differentia of a term.
(6) The etymological definition leads to precision of expression, the
descriptive definition is best adapted to the child-mind, while the
logical definition belongs to the realm of secondary education.
(7) Five rules summarize the requirements to which a logical definition
must conform. In a word or two these five rules are: Every logical
definition must (1) state the genus and differentia, (2) be equivalent
to the species defined, (3) not repeat the name to be defined, (4) not
be expressed in obscure language, (5) commonly be affirmative.
(8) Some terms are too high (summum genus), some too low (infima
species), some too peculiar (sui generis) to come within the province
of logical definition.
=12. ILLUSTRATIVE EXERCISES.=
1a. The italicized words in the following propositions are predicables
because they are affirmed of the subject:
(1) “This man weighs _one hundred fifty pounds_.”
(2) “A bird is a _feathered biped_.”
(3) “The earnest teacher is an _indefatigable worker_.”
(4) “Walking is the _most beneficial outdoor exercise_.”
1b. Underscore the predicables in the following:
(1) “All men are rational.”
(2) “Teachers must be just.”
(3) “Every form of unhappiness springs from a wrong condition of the
mind.”
(4) “Calmness of mind is one of the beautiful jewels of wisdom.”
2a. To clarify our ideas it is an excellent plan to select a group
of words belonging to the same genus with a view of defining them as
simply and expeditiously as possible. As an illustration _building_
may be selected as a genus. The word _kind_ will suggest to us the
species, such as dwelling, church, theatre, school, barn, bird-house,
granary and smoke-house. Next it is necessary to discover the basis of
distinction. This seems to be the use to which the building is put. Now
we are ready for the definitions:
_Species_ _Genus_ _Differentia_
A dwelling is a building where people live.
A church is a building where people worship.
A theatre is a building where people act.
A school is a building where children are taught.
A barn is a building where domestic animals, hay and
grain are kept.
A bird-house is a building designed for birds.
A granary is a building where grain is stored.
A smoke-house is a building where meat is smoked.
2b. By selecting _man_ as the genus, define the terms Caucasian,
Mongolian, Ethiopian, Malay and American Indian. Treat the term _chair_
in the same manner.
3a. One may easily distinguish a property from an accident by asking
himself the question, “Would subtracting the attribute from the term
alter its identity”? For example in the following, I find that the
words italicized are properties because subtracting each from the term
changes its identity:
_Term_ _Attributes_
man age, _rationality_, possessions.
book _binding_, _leaves_, size, color, contents.
radium _emits intense light and heat_, costs a million dollars
a pound.
snail _air-breathing mollusk_, moves slowly.
slush _soft mud and snow_, six inches deep.
3b. Indicate the common attributes of the following terms, underscoring
the properties: Tree, teacher, garden, house, river.
4. The rules summarize well the essentials of the subject matter of the
logical definition. Therefore, it is highly important for the student
to have these rules at the “tip of the tongue.” With this in view a
device of this nature may be helpful. Make each letter of the word
rules stand for the initial letter of a suggestive word in each of the
five _rules_. For example: r (repeat), u (unambiguous), l (language
affirmative), e (essential), s (same size).
With a little study “r and repeat,” “u and unambiguous,” “l and
language affirmative,” “e and essential,” “s and same size” may be
firmly linked together in the memory. _Repeat_ suggests the third
rule, do not repeat the name, etc.; _unambiguous_, the fourth rule,
not ambiguous language, etc.; _language affirmative_, the fifth rule;
_essentials_, the first rule; _same size_, the second rule, subject
and predicate must be of same size. The fact that the rules are not
recalled in order of treatment is inconsequential.
It is the writer’s experience that fifteen minutes of concentrated
study upon this device or one similar to it will indelibly stamp upon
the mind these troublesome rules.
The student may be able to devise a more helpful keyword.
=13. REVIEW QUESTIONS.=
(1) Why should the subject of definition appeal strongly to the
school teacher?
(2) Define a predicable.
(3) Name in order the five predicables.
(4) Define and illustrate the terms genus and species.
(5) Explain the terms summum genus, infima species, sui generis.
(6) Illustrate proximate genus.
(7) Explain the terms genus and species as used in natural history.
(8) Exemplify the double meaning of the genus man.
(9) Define and illustrate differentia.
(10) In what sense is the species a richer term than the genus?
(11) Distinguish between property and accident.
(12) Illustrate separable and inseparable accidents.
(13) Give descriptive definitions of the following, indicating the
five predicables: logic, general term, non-connotative term,
obversion.
(14) Define definition; illustrate.
(15) Distinguish between definition and division.
(16) Name, define and illustrate the three kinds of definitions.
(17) Distinguish between real and verbal definitions.
(18) Define in three ways the following: king, government, city, metal.
(19) State the rules of logical definition.
(20) What words may be used as _cues_ to aid in recalling the rules
for logical definition?
(21) Under what circumstances will the wise teacher make use of each
of three kinds of definitions?
(22) Relative to the second rule for logical definition what are the
_three_ questions that one should ask himself?
(23) Explain the exceptions to the third rule.
(24) In connection with the fourth rule what may be said as to the use
of technical terms?
(25) What facts take from the force of the fifth rule?
(26) What classes of words do not admit of logical definition?
Illustrate.
(27) Define education, teaching, instruction, training.
(28) Distinguish by illustration between induction and synthesis;
deduction and analysis.
=14. QUESTIONS FOR ORIGINAL THOUGHT
AND INVESTIGATION.=
(1) Why should the _scholar_ be tempted to speak and write
illogically?
(2) Name the parts of speech that may be classed as predicables.
(3) Explain the ten categories as given by Aristotle.
(4) Show that genus and species are relative terms.
(5) Why should the definition be needed most in the abstract sciences,
such as theology, ethics, political economy, juris-prudence and
psychology?
(6) Define sin, life, wrong, personality, habit, character.
(7) From the viewpoint of natural history find the species in the
series of terms of which _polygon_ is a member.
(8) What is the plural of differentia?
(9) Why should logic insist upon the proximate genus?
(10) (a) Man is a rational animal.
(b) Man is a rational biped (proximate genus).
In the case of the immature mind the first definition would be
clearer. Why?
(11) “A property of a term is any mark or characteristic which belongs
to that term.” Is this definition logical? Give reasons.
(12) What is the difference between the logical and the popular
conception of _property_?
(13) Is there any difference between the logical and popular
conception of accidents?
(14) “The term _conferentia_ might be used to stand for the essence of
the genus, as the term differentia represents the essence of the
species.”[6] Explain this.
(15) John Stuart Mill affirms that there is no such thing as a real
definition. Discuss this.
(16) In your opinion, of the five rules of logical definition what one
is violated most by the average teacher? Give reasons.
(17) Distinguish between symbol and content.
(18) Why are descriptive definitions best for young children? What
educational principle is involved?
(19) From the standpoint of the five rules for logical definition
criticise the following:
(1) A man is a reasonable vertebrate.
(2) A gentleman is a man with no visible means of support.
(3) A man is an organized entity whose cognitive powers function
rationally.
(4) A metal is an element with a metallic luster.
(5) A triangle is a figure of three sides.
(6) A teacher is one who imparts knowledge.
(7) Education is the process of drawing out all that is beautiful
in the body and noble in the soul.
(8) A democrat is a man who believes in free trade.
(9) A government is a commonwealth controlled by direct vote of
the people.
(20) Write the foregoing definitions in logical form.
(21) Since man is the only animal given to laughter, why is not the
following a logical definition: “Man is a laughing animal.”
(22) “A logical definition should contain the species, the genus and
the appropriate differentia.” Is there any reason for using the
term appropriate?
(23) In connection with genus and species explain subaltern.
(24) Is laughter a property of human being or an accident?
(25) Show how a pedagogue may be an instructor but not a teacher.
(26) Illustrate the complete method.
(27) Show that induction may consist of a series of analyses; also a
series of syntheses.