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man race.

GENERAL OR ABSTRACT IDEAS.

which it is necessary to form ideas and fabricate names are not very numerous, being limited chiefly to the huIt was much more necessary to assign ideas and names to the individuals of this class, than to assign ideas and names to all the individuals of all the classes in nature, while the expedient of giving a general name is equally convenient for the purposes of communication.*

This power of forming an idea of a class of objects, is called abstraction, for the following reason: The idea of a class contains only those parts or qualities which are common to all the individuals of the class; while the qualities peculiar to any individual are left out, or abstracted from those which constitute the general idea of the class.

The general or abstract idea, for example, of the class of vegetables called trees, contains the following parts: a plant of considerable height, which sets out large branches, is clothed with bark, and in summer bears leaves and seeds. All the plants that can be called trees have these qualities; and in forming an idea of these qualities, the mind abstracts its attention from all the qualities which are peculiar to any particular tree, such as the size and direction of the branches, the nature of the wood, the color, surface, and shape of the bark, and of the leaves, and the nature and properties of the seeds, such as berries, acorns, apples, pears, &c. Again, the general idea of a horse contains the idea of a large and beautiful quadruped, of cylindrical body, high-set neck, taper limbs, swift, strong, useful, docile; but it includes not the ideas of shape, color, size, pleasure, or utility, which distinguish individuals, the race-horse, the hunter, the war-horse, or the horse of the plough.

[*The notions formed in the mind from things offered to it, are either of single objects, as of "this pain, that man, Westminster Abbey ;" or of many objects gathered into one, as "pain, man, abbey." Notions of single objects are called intuitions, as being such as the mind receives when it simply attends to or inspects (intuetur) the object. Notions formed from several objects are called conceptions, as being produced by the power which the mind possesses of taking several things together (concipere, i. e., capere hoc cum illo). They are also called general notions. -Thomson.]

CLASSES OF OBJECTS.

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The mind is not satisfied with forming one grade of classes, which may comprehend individuals. It generalizes much further, with the same view of simplifying and facilitating the means of communication and knowledge, and of abridging the number of ideas and words. It constitutes classes above classes. Accordingly, it

forms a second class, containing the properties which one first class has in common with other first classes, so that the first class is now considered as making only one of the constituent parts of the second class.

The class of creatures called men, for example, comprehends what qualities are common to all its individuals, Romulus, Alexander, Julius Cæsar. But the class of men has many common qualities with other classes of living creatures, horses, dogs, sheep, fishes, fowls, &c., namely, life, motion, shape, color; and hence, of these common properties is framed a higher class, called that of animals, which contains the qualities common to all living creatures.*

The mind sometimes ascends higher, and forms another class more general, of all the properties which this second class has in common with other classes in nature. For example, animals have several properties in common with vegetables, as shape, color, growth, decay, circulation of juices; of these is formed a third class, called animated nature. We may proceed further still to form a fourth class, which will contain all things,

[* By observing John, Thomas, and Peter, and abstracting from their accidents the essential marks, we get the notion of man; but again, by comparing the conception man with other conceptions, cow, sheep, wolf, whale, and observing the mark common to all, that they suckle their young, we form the wider conception mammalia,-wider, because it includes man and many other conceptions. We may carry the process further still; and, with writers on Natural History, compare the mammalia with aves, amphibia, pisces, insectæ, and vermes, when we shall discover that all these, however different, agree in having life and sensation, from which marks we gain the new conception animal, wider than any of the former, as including them all,-higher, as requiring a second step in the abstractive process to reach it.-Thomson.]

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STEPS OF GENERALIZING.

animate and inanimate. The properties, however, of it are very few, and scarcely amount to more than existence and figure.

Though all these steps of generalizing are sometimes necessary or useful, yet knowledge and language seldom require attention to more than three of them; namely, the individual, the first class, and the second. The first class is called the species, the second the genus. Thus, Alexander is the individual, man is the species, and animal is the genus; the royal oak is the individ-ual, tree is the species, and vegetable is the genus; St. James's is the individual, dwelling-house is the species, edifice is the genus. The third and fourth classes are also denominated genera. The second class, or the one immediately above the species, is called the proximate genus, the third and fourth classes are called transcendent genera. The proximate genus of the species man is animal; existence is the transcendent genus. The proximate genus of tree is vegetable; the transcendent may be animated nature, or existence.*

It is to be observed, though general or abstract ideas are more comprehensive, or extend to more objects, than particular ideas, yet that they are less complex, or contain fewer parts, and that the more general they are, the less complex they are, or contain fewer parts in pro

[The same class which is a genus with reference to the sub-classes or species included in it, may be itself a species with reference to a more comprehensive, or superior, genus. Man is a species with reference to animal, but a genus with reference to the species, mathematician. Animal is a genus, divided into two species, man and brute; but animal is also a species, which, with another species, vegetable, makes up the genus, organized being. Biped is a genus with reference to man and bird, but a species with respect to the superior genus, animal. Taste is a genus, of which, sweet taste, sour taste, &c., are species; but taste is a species of the genus, sensation. Virtue, a genus with reference to justice, temperance, &c., is one of the species of the genus, mental quality.-Mills' Logic, p. 82.]

EXTENSION AND INTENSION.

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portion. The reason is exceedingly obvious. A genus contains only the few properties which are common to the several species which it includes, and which are not nearly so numerous as those that belong to each species. The species, again, contains the properties which are common to all the individuals it includes, and which are not so numerous as those that pertain to each individual. The genus animal, for instance, includes few properties, life, shape, color, motion, growth, decay. The species man contains all these properties of the genus, besides those of the species, namely, power of speech, thinking, acting with design, and many others. The individual contains all these qualities I have enumerated, both of the genus and of the species, together with those peculiar to the individual, wise or prudent, knowing or ignorant, rich, poor, fortunate, unfortunate,— all these qualities, however variable, and in a particular degree corresponding to the nature or character of the individual.*

[*Extension and Intension. When we compare a vague and general conception with a narrower and more definite one, we find that the former contains far more objects in it than the latter. Comparing plant with geranium, for example, we see that plant includes ten thousand times more objects, since the oak, and fir, and lichen, and rose, and countless others, including geranium itself, are implied in it. This capacity of a conception we call its extension. The extension of plant is greater than that of geranium, because it includes more objects.

But conceptions have another capacity. Whilst plant has more objects under it than geranium, it has fewer marks in it-fewer properties by which we assign it a place under some appropriate conception. I can describe the leaves, petals, stamina, and pistils of geranium, but of plant no such description is possible. I cannot say that every plant has a stem, for there are the lichens to contradict me; nor a flower, for ferns have none, and so on. I can say little more about plant, than that all plants have growth and vegetable life. The logical expression of this defect is, that its intension is very limited.

The greater the extension, the less the intension; the more objects a conception embraces, the more slender the knowledge which it conveys of any of those objects; and vice versa.

With the help of the important distinction between extension and inten

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UTILITY OF ABSTRACT IDEAS.

The power of abstraction is one of the most important belonging to the understanding, and the practice of it in science and in business is of the most extensive use. It will afterwards be explained, that all definitions are regulated by the arrangements of abstraction, and that they consist entirely in referring an individual to its species, with the addition of some quality which distinguishes it from the other individuals of its species; or in referring a species to its genus, with the addition of some quality which characterizes it as a species.

To evince the exceedingly extensive utility of abstrac tion, I must observe, that all science, almost all reasoning, indeed almost all the words of language, are conversant about abstract ideas. You will readily apprehend, that the two sciences of quantity, mathematics and arithmetic, are occupied entirely about abstract ideas.

No property is demonstrated of any triangle in the elements of geometry, that is not true of all triangles, at least all triangles of the same kind. The figure delineated on the board of the mathematician is not particular or local; it represents every figure of the same species, and the demonstration is equally extensive in its application, namely, to all figures of the species. Were not this the case, science would have no existence, and the mind of man could make no progress in knowledge. Were not this the case, the mathematician would be obliged to demonstrate the properties of every particular figure he should employ, and all progress in knowledge would be suspended, because the new figures of the same species which may occur are infinite.

All the operations in arithmetic, the objects of which are dis

sion, or as others express it, the sphere and matter of the conception, we can understand the meaning of the saying, that the subject of a judgment is in the predicate, and the predicate in the subject. "Man is an animal:" this conveys two notions, that man is contained in animal, as a species in a genus; and that whatever makes up our notion of animal-all the marks of animal-are contained in man. So they are mutually contained. Instead of "man is an animal," Aristotle would say "animal inheres in man."-Thomson.]