DEGREES OF GENERALITY. One class is said to be of higher generality than another when it includes that other and more. Thus animal includes man, dog, horse, etc.; man includes Aryan, Semite, etc.; Aryan includes Hindoo, Teuton, Celt, etc.

The technical names for higher and lower classes are GENUS and SPECIES. These terms are not fixed as in Natural History to certain grades, but are purely relative one to another, and movable up and down a scale of generality. A class may be a species relatively to one class, which is above it, and a genus relatively to one below it. Thus Aryan is a species of the genus man, Teuton a species of the genus Aryan.

In the graded divisions of Natural History genus and species are fixed names for certain grades. Thus: Vertebrates form a "division"; the next subdivision, _e.g._, Mammals, Birds, Reptiles, etc., is called a "class"; the next, _e.g_., Rodents, Carnivora, Ruminants, an "order"; the next, _e.g._, Rats, Squirrels, Beavers, a "genus"; the next, _e.g._, Brown rats, Mice, a "species".

Vertebrates (division).

Mammals, Birds, Reptiles, etc. (class).

Rodents, Ruminants, Carnivors, etc. (order).

Rats, Squirrels, Beavers, etc. (genus).

Brown rats, Mice, etc. (species).

If we subdivide a large class into smaller classes, and, again, subdivide these subdivisions, we come at last to single objects.

Men ------------ Europeans, Asiatics, etc.

------------- Englishmen, Frenchmen, etc.

--------------------- John Doe, Richard Roe, etc.

A table of higher and lower classes arranged in order has been known from of old as a _tree_ of division or classification. The following is Porphyry's "tree":--

Being / Corporeal Incorporeal / (Body) / Animate Inanimate / (Living Being) / Sensible Insensible / (Animal) / Rational Irrational / (Man) --------------------------------------- Socrates, Plato, and other individuals.

The single objects are called INDIVIDUALS, because the division cannot be carried farther. The highest class is technically the SUMMUM GENUS, or _Genus generalissimum_; the next highest class to any species is the PROXIMUM GENUS; the lowest group before you descend to individuals is the INFIMA SPECIES, or _Species specialissima_.

The attribute or attributes whereby a species is distinguished from other species of the same genus, is called its DIFFERENTIA or DIFFERENTIae. The various species of houses are differentiated by their several uses, dwelling-house, town-house, ware-house, public-house.

Poetry is a species of Fine Art, its differentia being the use of metrical language as its instrument.

A lower class, indicated by the name of its higher class qualified by adjectives or adjective phrases expressing its differential property or properties, is said to be described PER GENUS ET DIFFERENTIAM.

Examples: "Black-bird," "note-book," "clever man," "man of Kent,"

"eminent British painter of marine subjects". By giving a combination of attributes common to him with nobody else, we may narrow down the application of a name to an individual: "The Commander-in-Chief of the British forces at the battle of Waterloo".

Other attributes of classes as divided and defined, have received technical names.

An attribute common to all the individuals of a class, found in that class only, and following from the essential or defining attributes, though not included among them, is called a PROPRIUM.

An attribute that belongs to some, but not to all, or that belongs to all, but is not a necessary consequence of the essential attributes, is called an ACCIDENT.

The clearest examples of Propria are found in mathematical figures.

Thus, the defining property of an equilateral triangle is the equality of the sides: the equality of the angles is a proprium. That the three angles of a triangle are together equal to two right angles is a proprium, true of all triangles, and deducible from the essential properties of a triangle.

Outside Mathematics, it is not easy to find _propria_ that satisfy the three conditions of the definition. It is a useful exercise of the wits to try for such. Educability--an example of the proprium in mediaeval text-books--is common to men, and results from man's essential constitution; but it is not peculiar; other animals are educable. That man cooks his food is probably a genuine proprium.

That horses run wild in Thibet: that gold is found in California: that clergymen wear white ties, are examples of Accidents. Learning is an accident in man, though educability is a proprium.

What is known technically as an INSEPARABLE ACCIDENT, such as the black colour of the crow or the Ethiopian, is not easy to distinguish from the Proprium. It is distinguished only by the third character, deducibility from the essence.[2]

Accidents that are both common and peculiar are often useful for distinguishing members of a class. Distinctive dresses or badges, such as the gown of a student, the hood of a D.D., are accidents, but mark the class of the individual wearer. So with the colours of flowers.

_Genus_, _Species_, _Differentia_, _Proprium_, and _Accidens_ have been known since the time of Porphyry as the FIVE PREDICABLES. They are really only terms used in dividing and defining. We shall return to them and endeavour to show that they have no significance except with reference to fixed schemes, scientific or popular, of Division or Classification.

Given such a fixed scheme, very nice questions may be raised as to whether a particular attribute is a defining attribute, or a proprium, or an accident, or an inseparable accident. Such questions afford great scope for the exercise of the analytic intellect.

We shall deal more particularly with degrees of generality when we come to Definition. This much has been necessary to explain an unimportant but much discussed point in Logic, what is known as the inverse variation of Connotation and Denotation.

Connotation and Denotation are often said to vary inversely in quantity. The larger the connotation the smaller the denotation, and _vice versa_. With certain qualifications the statement is correct enough, but it is a rough compendious way of expressing the facts and it needs qualification.

The main fact to be expressed is that the more general a name is, the thinner is its meaning. The wider the scope, the shallower the ground.

As you rise in the scale of generality, your classes are wider but the number of common attributes is less. Inversely, the name of a species has a smaller denotation than the name of its genus, but a richer connotation. _Fruit-tree_ applies to fewer objects than _tree_, but the objects denoted have more in common: so with _apple_ and _fruit-tree_, _Ribston Pippin_ and _apple_.

Again, as a rule, if you increase the connotation you contract the area within which the name is applicable. Take any group of things having certain attributes in common, say, _men of ability_: add _courage_, _beauty_, _height of six feet_, _chest measurement of 40 inches_, and with each addition fewer individuals are to be found possessing all the common attributes.

This is obvious enough, and yet the expression inverse variation is open to objection. For the denotation may be increased in a sense without affecting the connotation. The birth of an animal may be said to increase the denotation: every year thousands of new houses are built: there are swarms of flies in a hot summer and few in a cold.

But all the time the connotation of _animal_, _house_, or _fly_ remains the same: the word does not change its meaning.

It is obviously wrong to say that they vary in inverse proportion.

Double or treble the number of attributes, and you do not necessarily reduce the denotation by one-half or one-third.

It is, in short, the meaning or connotation that is the main thing.

This determines the application of a word. As a rule if you increase meaning, you restrict scope. Let your idea, notion, or concept of _culture_ be a knowledge of Mathematics, Latin and Greek: your _men of culture_ will be more numerous than if you require from each of them these qualifications _plus_ a modern language, an acquaintance with the Fine Arts, urbanity of manners, etc.

It is just possible to increase the connotation without decreasing the denotation, to thicken or deepen the concept without diminishing the class. This is possible only when two properties are exactly co-extensive, as equilaterality and equiangularity in triangles.

SINGULAR and PROPER NAMES. A Proper or Singular name is a name used to designate an individual. Its function, as distinguished from that of the general name, is to be used purely for the purpose of distinctive reference.

A man is not called Tom or Dick because he is like in certain respects to other Toms or other Dicks. The Toms or the Dicks do not form a logical class. The names are given purely for purposes of distinction, to single out an individual subject. The Arabic equivalent for a Proper name, _alam_, "a mark," "a sign-post," is a recognition of this.

In the expressions "a Napoleon," "a Hotspur," "a Harry," the names are not singular names logically, but general names logically, used to signify the possession of certain attributes.

A man may be nicknamed on a ground, but if the name sticks and is often used, the original meaning is forgotten. If it suggests the individual in any one of his qualities, any point in which he resembles other individuals, it is no longer a Proper or Singular name logically, that is, in logical function. That function is fulfilled when it has called to mind the individual intended.

To ask, as is sometimes done, whether Proper names are connotative or denotative, is merely a confusion of language. The distinction between connotation and denotation, extension and intension, applies only to general names. Unless a name is general, it has neither extension nor intension:[3] a Proper or Singular name is essentially the opposite of a general name and has neither the one nor the other.

A nice distinction may be drawn between Proper and Singular names, though they are strict synonyms for the same logical function. It is not essential to the discharge of that function that the name should be strictly appropriated to one object. There are many Toms and many Dicks. It is enough that the word indicates the individual without confusion in the particular circumstances.

This function may be discharged by words and combinations of words that are not Proper in the grammatical sense. "This man," "the cover of this book," "the Prime Minister of England," "the seer of Chelsea,"

may be Singular names as much as Honolulu or Lord Tennyson.

In common speech Singular names are often manufactured _ad hoc_ by taking a general name and narrowing it down by successive qualifications till it applies only to one individual, as "The leading subject of the Sovereign of England at the present time". If it so happens that an individual has some attribute or combination peculiar to himself, he may be suggested by the mention of that attribute or combination:--"the inventor of the steam-engine," "the author of Hudibras".

Have such names a connotation? The student may exercise his wits on the question. It is a nice one, an excellent subject of debate.

Briefly, if we keep rigid hold of the meaning of connotation, this Singular name has none. The combination is a singular name only when it is the subject of a predication or an attribution, as in the sentences, "The position of the leading subject of etc., is a difficult one," or "The leading subject of etc., wears an eyeglass".

In such a sentence as "So-and-so is the leading subject of etc.," the combined name has a connotation, but then it is a general and not a singular name.

COLLECTIVE NAMES, as distinguished from General Names. A collective name is a name for a number of similar units taken as a whole--a name for a totality of similar units, as army, regiment, mob, mankind, patrimony, personal estate.

A group or collection designated by a collective name is so far like a class that the individual objects have something in common: they are not heterogeneous but homogeneous. A mob is a collection of human beings; a regiment of soldiers; a library of books.

The distinction lies in this, that whatever is said of a collective name is said about the collection as a whole, and does not apply to each individual; whatever is said of a general name applies to each individual. Further, the collective name can be predicated only of the whole group, as a whole; the general name is predicable of each, distributively. "Mankind has been in existence for thousands of years;" "The mob passed through the streets." In such expressions as "An honest man's the noblest work of God," the subject is functionally a collective name.