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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".