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the nature of an adverbial, expressing the time or occasion when this is found to be the case.

As a last example we take the sentence given below:

“ The law of gravitation, the most universal truth at which human reason has yet arrived, expresses not merely the general fact of the mutual attraction of all matter; not merely the vague statement that its influence decreases as the distance increases, but the exact numerical rate at which that decrease takes place; so that when its amount is known at any one distance it may be exactly calculated fór any other.” at which human reason has yet arrived

!
the most universal truth

The law of gravitation expresses
not merely the not merely the
general fact

vague statement
1
of the mutual that its influence
attraction of all decreases
matter

1
as the distance

increases

but the exact numerical rate

1 at which that decrease takes

place

so that its amount may be calculated for any other dis

[tance when it is known at any one distance.

W. S. Dalgleish's Grammatical Analysis, or
J. D. Morell's Analysis of Sentences.
Alex. Bain's English Composition and Rhe-

toric, pp. 91–117, treats of construction of
sentences.

LESSON XII.

THE PREDICABLES, DIVISION, AND

DEFINITION.

It is desirable that the reader, before proceeding further, should acquire an exact comprehension of the meaning of certain logical terms which are known as the Predicables, meaning the kinds of terms or attributes which can always be predicated of any subject. These terms are five in number; genus, species, difference, property, and accident; and when properly employed are of exceeding use and importance in logical science. It would neither be possible nor desirable in this work to attempt to give any idea of the various and subtle meanings which have been attributed to the predicables by ancient writers, and the most simple and useful view of the subject is what alone can be given here.

Any class of things may be called a genus (Greek gévos, race or kind), if it be regarded as made up of two or more species. “Element” is a genus when we consider it as divided into the two species “metallic and non-metallic.” Triangle is a genus as regards the species acute-angled, right-angled, and obtuse-angled.

On the other hand, a species is any class which is regarded as forming part of the next larger class, so that the terms genus and species are relative to each other, the genus being the larger class which is divided, and the species the two or more smaller classes into which the genus is divided.

It is indispensable, however, to regard these expressions in the double meaning of extension and intension.

From the explanation of these different meanings in Lesson V. it will be apparent that the extent of a genus or species is simply the number of individuals included in it, and there will always be fewer individuals in the species than in the genus. In extent the genus book includes all books of whatever size, language, or contents; if divided in respect to size the species of book are folio, quarto, octavo, duodecimo, &c.; and, of course, each of these species contains much fewer individual books than the whole genus.

In intension the genus means, not the individual things contained in it, but the sum of the qualities common to all those things, and sufficient to mark them out clearly from other classes. The species similarly means the sum of the qualities common to all the individuals forming part of the genus, and sufficient to mark them out from the rest of the genus, as well as from all other things. It is evident, therefore, that there must be more qualities implied in the meaning of the species than of the genus, for the species must contain all the qualities of the genus, as well as a certain additional quality or qualities by which the several species are distinguished from each other. Now these additional qualities form the difference, which may be defined as the quality or sum of qualities which mark out one part of a genus from the other part or parts. The difference (Latin differentia, Greek diapopá) cannot have any meaning except in intension; and when we use all the terms wholly in intension we may say that the difference added to the genus makes the species. Thus if “building" be the genus, and we add the difference “used for a dwelling," we get the species “house." If we take “triangle” as the genus, it means the sum of the qualities of "three-sided rectilineal figure;” if we add the quality of “having two sides equal,” we obtain the species “isosceles triangle.”

It will easily be seen that the same class of things may be both a genus and a species at the same time, according as we regard it as divided into smaller classes or forming part of a larger class. Thus triangle, which is a genus as regards isosceles triangle, is a species as regards right-lined geometrical figures. House is a species of building, but a genus with respect to mansion, cottage, villa, or other kinds of houses. We may, in fact, have an almost interminable chain of genera and species, each class being a species of the class next above it, and a genus as regards that next below. Thus the genus British subject has the species Born in the United Kingdom, Colonial-born, and Naturalised. Each of these becomes a genus as regards the species male and female; each species again may be divided into adult and minor, educated, uneducated, employed in some occupation or unemployed, self-maintaining, maintained by friends, or pauper; and so on.

The subdivision may thus proceed until we reach a class of so restricted extent, that it cannot be divided except into individuals; in this case the species is called the lowest species or infima species. All the intermediate genera and species of the chain are called subaltern (Latin sub, under, and alter, the other of two), because they stand one under the other. If there be a genus which is not regarded as a species, that is as part of any higher genus, it is called the summum genus, the highest genus, or genus generalissimum, the most general genus. It is questionable whether we can thus set any limit to the chain of classes. The class British subject is certainly not an absolute summum genus, since it is but a species of man, which is a species of animal, living being, inhabitant of the earth, substance, and so on. If there were any real summum genus it would probably be “Being,” or “ Thing,” or “ Object conceivable;" but we may usefully employ the term to signify

the highest class of things comprehended in any science or classification. Thus “material substance" is the summum genus examined in the science of chemistry; "inhabitant of the United Kingdom” is the summum genus enumerated and classified in the British census. Logical terms are only a species of words or phrases, but they are the summum genus as regards logic, which has nothing to do with the various parts of speech and the relations of words, syllables, and letters, examined by grammarians.

Several very useful expressions have been derived from the words genus and species. When a thing is so peculiar and unlike other things that it cannot easily be brought into one class with them, it is said to be sui generis, or of its own genus; thus the rings of Saturn are so different from anything else among the heavenly bodies that they may fairly be called sui generis. In zoology, the Ornithorhynchus, or Australian Duck-bill, the Amphioxus, and some other animals, are so peculiar that they may be called sui generis. When a substance is the same in all its parts, or when a number of things are all alike, we say that they are homogeneous (Greek óuós, like, yévos, kind), that is of the same nature; otherwise they may be called heterogeneous (Greek érepos, other).

It is necessary to distinguish carefully the purely logical use of the terms genus and species from their peculiar use in natural history. A species is there a class of plants and animals supposed to have descended from common parents, and to be the narrowest class possessing a fixed form; the genus is the next higher class. But if we accept Darwin's theory of the origin of species, this definition of species becomes entirely illusory, since different genera and species must have according to this theory descended from common parents. The species then denotes a merely arbitrary amount of resemblance

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