Chapter 15

GENERAL NAMES AND ALLIED DISTINCTIONS.

To discipline us against the errors we are liable to in receiving knowledge through the medium of words--such is one of the objects of Logic, the main object of what may be called the Logic of Consistency.

Strictly speaking, we may receive knowledge about things through signs or single words, as a nod, a wink, a cry, a call, a command. But an assertory sentence, proposition, or predication, is the unit with which Logic concerns itself--a sentence in which a subject is named and something is said or predicated about it. Let a man once understand the errors incident to this regular mode of communication, and he may safely be left to protect himself against the errors incident to more rudimentary modes.

A proposition, whether long or short, is a unit, but it is an analysable unit. And the key to syllogistic analysis is the General Name. Every proposition, every sentence in which we convey knowledge to another, contains a general name or its equivalent. That is to say, every proposition may be resolved into a form in which the predicate is a general name. A knowledge of the function of this element of speech is the basis of all logical discipline. Therefore, though we must always remember that the proposition is the real unit of speech, and the general name only an analytic element, we take the general name and its allied distinctions in thought and reality first.

How propositions are analysed for syllogistic purposes will be shown by-and-by, but we must first explain various technical terms that logicians have devised to define the features of this cardinal element. The technical terms CLASS, CONCEPT, NOTION, ATTRIBUTE, EXTENSION or DENOTATION, INTENSION or CONNOTATION, GENUS, SPECIES, DIFFERENTIA, SINGULAR NAME, COLLECTIVE NAME, ABSTRACT NAME, all centre round it.

A general name is a name applicable to a number of different things on the ground of some likeness among them, as _man_, _ratepayer_, _man of courage_, _man who fought at Waterloo_.

From the examples it will be seen that a general name logically is not necessarily a single word. Any word or combination of words that serves a certain function is technically a general name. The different ways of making in common speech the equivalent of a general name logically are for the grammarian to consider.

In the definition of a general name attention is called to two distinct considerations, the individual objects to each of which the name is applicable, and the points of resemblance among them, in virtue of which they have a common name. For those distinctions there are technical terms.

CLASS is the technical term for the objects, different yet agreeing, to each of which a general name may be applied.

The points of resemblance are called the common ATTRIBUTES of the class.

A class may be constituted on one attribute or on several. _Ratepayer_, _woman ratepayer_, _unmarried woman ratepayer_; _soldier_, _British soldier_, _British soldier on foreign service_. But every individual to which the general name can be applied must possess the common attribute or attributes.

These common attributes are also called the NOTION of the class, inasmuch as it is these that the mind notes or should note when the general name is applied. CONCEPT is a synonym perhaps in more common use than notion; the rationale of this term (derived from _con_ and _capere_, to take or grasp together) being that it is by means of the points of resemblance that the individuals are grasped or held together by the mind. These common points are the one in the many, the same amidst the different, the identity signified by the common name. The name of an attribute as thought of by itself without reference to any individual or class possessing it, is called an ABSTRACT name. By contradistinction, the name of an individual or a class is CONCRETE.

Technical terms are wanted also to express the relation of the individuals and the attributes to the general name. The individuals jointly are spoken of as the DENOTATION, or EXTENSION or SCOPE of the name; the common attributes as its CONNOTATION, INTENSION, COMPREHENSION, or GROUND. The whole denotation, etc., is the class; the whole connotation, etc., is the concept.[1] The limits of a "class" in Logic are fixed by the common attributes. Any individual object that possesses these is a member. The statement of them is the DEFINITION.

To predicate a general name of any object, as, "This is a cat," "This is a very sad affair," is to refer that object to a class, which is equivalent to saying that it has certain features of resemblance with other objects, that it reminds us of them by its likeness to them. Thus to say that the predicate of every proposition is a general name, expressed or implied, is the same as to say that every predication may be taken as a reference to a class.

Ordinarily our notion or concept of the common features signified by general names is vague and hazy. The business of Logic is to make them clear. It is to this end that the individual objects of the class are summoned before the mind. In ordinary thinking there is no definite array or muster of objects: when we think of "dog" or "cat," "accident," "book," "beggar," "ratepayer," we do not stop to call before the mind a host of representatives of the class, nor do we take precise account of their common attributes. The concept of "house" is what all houses have in common. To make this explicit would be no easy matter, and yet we are constantly referring objects to the class "house". We shall see presently that if we wish to make the connotation or concept clear we must run over the denotation or class, that is to say, the objects to which the general name is applied in common usage. Try, for example, to conceive clearly what is meant by house, tree, dog, walking-stick. You think of individual objects, so-called, and of what they have in common.

A class may be constituted on one property or on many. There are several points common to all houses, enclosing walls, a roof, a means of exit and entrance. For the full concept of the natural kinds, _men_, _dogs_, _mice_, etc., we should have to go to the natural historian.

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.

A collective name may be used as a general name when it is extended on the ground of what is common to all such totalities as it designates. "An excited mob is dangerous;" "An army without discipline is useless." The collective name is then "connotative" of the common characters of the collection.

MATERIAL OR SUBSTANTIAL NAMES. The question has been raised whether names of material, gold, water, snow, coal, are general or collective singular. In the case of pieces or bits of a material, it is true that any predicate made concerning the material, such as "Sugar is sweet," or "Water quenches thirst," applies to any and every portion. But the separate portions are not individuals in the whole signified by a material name as individuals are in a class. Further, the name of material cannot be predicated of a portion as a class name can be of an individual. We cannot say, "This is a sugar". When we say, "This is a piece of sugar," sugar is a collective name for the whole material. There are probably words on the borderland between general names and collective names. In such expressions as "This is a _coal_," "The bonnie _water_ o' Urie," the material name is used as a general name. The real distinction is between the distributive use and the collective use of a name; as a matter of grammatical usage, the same word may be used either way, but logically in any actual proposition it must be either one or the other.

ABSTRACT NAMES are names for the common attributes or concepts on which classes are constituted. A concrete name is a name directly applicable to an individual in all his attributes, that is, as he exists in the concrete. It may be written on a ticket and pinned to him. When we have occasion to speak of the point or points in which a number of individuals resemble one another, we use what is called an abstract name. "Generous man," "clever man," "timid man," are concrete names; "generosity," "cleverness," "timidity," are abstract names.

It is disputed whether abstract names are connotative. The question is a confused one: it is like asking whether the name of a town is municipal. An abstract name is the name of a connotation as a separate object of thought or reference, conceived or spoken of in abstraction from individual accidents. Strictly speaking it is notative rather than _con_notative: it cannot be said to have a connotation because it is itself the symbol of what is called the connotation of a general name.[4]

The distinction between abstract names and concrete names is virtually a grammatical distinction, that is, a distinction in mode of predication. We may use concrete names or abstract names at our pleasure to express the same meaning. To say that "John is a timid man" is the same thing as saying that "Timidity is one of the properties or characteristics or attributes of John". "Pride and cruelty generally go together;" "Proud men are generally cruel men."

General names are predicable of individuals because they possess certain attributes: to predicate the possession of those attributes is the same thing as to predicate the general name.

Abstract forms of predication are employed in common speech quite as frequently as concrete, and are, as we shall see, a great source of ambiguity and confusion.

[Footnote 1: It has been somewhat too hastily assumed on the authority of Mansel (Note to Aldrich, pp. 16, 17) that Mill inverted the scholastic tradition in his use of the word _Connotative_. Mansel puts his statement doubtfully, and admits that there was some licence in the use of the word Connotative, but holds that in Scholastic Logic an adjective was said to "signify _primarily_ the attribute, and to _connote_ or _signify secondarily_ ([Greek: prossemainein]) the subject of inhesion". The truth is that Mansel's view was a theory of usage not a statement of actual usage, and he had good reason for putting it doubtfully.

As a matter of fact, the history of the distinction follows the simple type of increasing precision and complexity, and Mill was in strict accord with standard tradition. By the Nominalist commentators on the _Summulae_ of Petrus Hispanus certain names, adjectives grammatically, are called _Connotativa_ as opposed to _Absoluta_, simply because they have a double function. White is connotative as signifying both a subject, such as Socrates, of whom "whiteness" is an attribute, and an attribute "whiteness": the names "Socrates" and "whiteness" are Absolute, as having but a single signification. Occam himself speaks of the subject as the primary signification, and the attribute as the secondary, because the answer to "What is white?" is "Something informed with whiteness," and the subject is in the nominative case while the attribute is in an oblique case (_Logic_, part I. chap. x.). Later on we find that Tataretus (_Expositio in Summulas_, A.D. 1501), while mentioning (Tract. Sept. _De Appellationibus_) that it is a matter of dispute among Doctores whether a connotative name _connotat_ the subject or the attribute, is perfectly explicit in his own definition, "Terminus connotativus est qui praeter illud pro quo supponit connotat aliquid adjacere vel non adjacere rei pro qua supponit" (Tract. Sept. _De Suppositionibus_). And this remained the standard usage as long as the distinction remained in logical text-books. We find it very clearly expressed by Clichtoveus, a Nominalist, quoted as an authority by Guthutius in his _Gymnasium Speculativum_, Paris, 1607 (_De Terminorum Cognitione_, pp. 78-9). "Terminus absolutus est, qui solum illud pro quo in propositione supponit, significat. Connotativus autem, qui ultra idipsum, aliud importat." Thus _man_ and _animal_ are absolute terms, which simply stand for (supponunt pro) the things they signify. _White_ is a connotative name, because "it stands for (supponit pro) a subject in which it is an accident: and beyond this, still signifies an accident, which is in that subject, and is expressed by an abstract name". Only Clichtoveus drops the verb _connotat_, perhaps as a disputable term, and says simply _ultra importat_.

So in the Port Royal Logic (1662), from which possibly Mill took the distinction: "Les noms qui signifient les choses comme modifiees, marquant premierement et directement la chose, quoique plus confusement, et indirectement le mode, quoique plus distinctement, sont appeles _adjectifs_ ou _connotatifs_; comme rond, dur, juste, prudent" (part i. chap ii.).

What Mill did was not to invert Scholastic usage but to revive the distinction, and extend the word connotative to general names on the ground that they also imported the possession of attributes. The word has been as fruitful of meticulous discussion as it was in the Renaissance of Logic, though the ground has changed. The point of Mill's innovation was, premising that general names are not absolute but are applied in virtue of a meaning, to put emphasis on this meaning as the cardinal consideration. What he called the connotation had dropped out of sight as not being required in the Syllogistic Forms. This was as it were the point at which he put in his horn to toss the prevalent conception of Logic as Syllogistic.

The real drift of Mill's innovation has been obscured by the fact that it was introduced among the preliminaries of Syllogism, whereas its real usefulness and significance belongs not to Syllogism in the strict sense but to Definition. He added to the confusion by trying to devise forms of Syllogism based on connotation, and by discussing the Axiom of the Syllogism from this point of view. For syllogistic purposes, as we shall see, Aristotle's forms are perfect, and his conception of the proposition in extension the only correct conception. Whether the centre of gravity in Consistency Logic should not be shifted back from Syllogism to Definition, the latter being the true centre of consistency, is another question. The tendency of Mill's polemic was to make this change. And possibly the secret of the support it has recently received from Mr. Bradley and Mr. Bosanquet is that they, following Hegel, are moving in the same direction.

In effect, Mill's doctrine of Connotation helped to fix a conception of the general name first dimly suggested by Aristotle when he recognised that names of genera and species signify Quality, in showing what sort a thing is. Occam carried this a step farther towards clear light by including among Connotative Terms such general names as "monk," name of classes that at once suggest a definite attribute. The third step was made by Mill in extending the term Connotation to such words as "man," "horse," the _Infimae Species_ of the Schoolmen, the Species of modern science.

Whether connotation was the best term to use for this purpose, rather than extension, may be questioned: but at least it was in the line of tradition through Occam.]

[Footnote 2: The history of the definition of the _Proprium_ is an example of the tendency of distinctions to become more minute and at the same time more purposeless. Aristotle's [Greek: idion] was an attribute, such as the laugh of the man or the bark of the dog, common to all of a class and peculiar to the class (_quod convenit omni soli et semper_) yet not comprised in the definition of the class. Porphyry recognised three varieties of [Greek: idia] besides this, four in all, as follows:--(1) an attribute peculiar to a species but not possessed by all, as knowledge of medicine or geometry; (2) possessed by a whole species but not peculiar to it, as being a biped in man; (3) peculiar to a species, and possessed by all at a certain time, as turning grey in old age; (4) Aristotle's "proprium," peculiar and possessed by all, as risibility. The idea of the Proprium as deducible from or consequent on the essence would seem to have originated in the desire to find something common to all Poryphyry's four varieties.]

[Footnote 3: It is a plausible contention that in the case of the Singular name the extension is at a minimum and the intension at a maximum, the extension being one individual, and the intension the totality of his attributes. But this is an inexact and confused use of words. A name does not _extend_ beyond the individual except when it is used to signify one or more of his prominent qualities, that is, is used with the function of a general name. The _ex_tension of a Singular name is zero: it has no extension. On the other hand, it suggests, in its function as a Singular name, no properties or qualities; it suggests only a subject; _i.e._, it has no intension. The ambiguity of the term Denotation helps the confusion in the case of Singular names. "Denote" in common speech means to indicate, to distinguish. But when in Logic we say that a general name denotes individuals, we have no thought of indicating or distinguishing: we mean only that it is applicable to any one, without respect of individuals, either in predication or epithetic description.]

[Footnote 4: Strictly speaking, as I have tried to indicate all along, the words Connotation and Denotation, or Extension and Intension, apply only to general names. Outside general names, they have no significance. An adjective with its noun is a general name, of which the adjective gives part of the Connotation. If we apply the word connotation to signify merely the suggestion of an attribute in whatever grammatical connexion, then an abstract name is undoubtedly as much connotative as an adjective. The word _Sweetness_ has the same meaning as _Sweet_: it indicates or signifies, conveys to the mind of the reader the same attribute: the only difference is that it does not at the same time indicate a subject in which the attribute is found, as _sweet apple_. The meaning is not _con_noted.]