Logical division, metaphori

cally so

called

distinct [i.e. separate] enumeration of several things signified by

one common name.

This operation is directly opposite to generalization, (which is performed by means of "Abstraction ;") for as, in that, you lay aside the differences by which several things are distinguished, so as to call them all by one common name, so, in Division, you add on the Differences, so as to enumerate them by their several distinct names. Thus, "mineral" is said to be divided into " stones, metals," &c.; and metals again into "gold, iron," &c.; and these are called the Parts [or members] of the division.

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Division," in its primary sense, means separating from each other (either actually, or in enumeration) the parts of which some really-existing single object consists: as when you divide "an animal" (that is, any single animal) into its several members; or again, into its "bones, muscles, nerves, blood-vessels," &c. And so, with any single Vegetable, &c.

Now, each of the parts into which you thus "physically" (as it is called) divide "an animal," is strictly and properly a "part," and is really less than the whole for you could not say of a bone, for instance, or of a limb, that it is " an Animal."

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But when you "divide❞—in the secondary sense of the word (or, as it is called, "metaphysically")-" Animal," that is, the Genus Animal," into Beast, Bird, Fish, Reptile, Insect, &c. each of the parts [or "members"] is metaphorically called a "part," and is, in another sense, more than the whole [the Genus] that is thus divided. For you may say of a Beast or Bird that it is an “Animal ;” and the term "Beast" implies not only the term “ Animal," but something more besides; namely, whatever "Difference" characterizes " Beast," and separates it from "Bird," "Fish," &c.

And so also any Singular-term [denoting one individual] implies not only the whole of what is understood by the Species it belongs to, but also more: namely, whatever distinguishes that single object from others of the same Species: as "London" implies all that is denoted by the term " City," and also all that distinguishes that individual-city.

The "parts" ["members"] in that figurative sense with which we are now occupied, are each of them less than the whole, in another sense; that is, of less comprehensive signification. Thus, the Singular-term " Romulus" embracing only an individual-king, is less extensive than the Species "King" and that, again, less extensive than the Genus Magistrate," &c.

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An "Individual" then is so called from its being incapable of being (in this figurative sense) divided.

And though the two senses of the word "Division" are easily distinguishable when explained, it is so commonly employed in each sense, that through inattention, confusion often ensues.

We speak as familiarly of the "division" of Mankind into the

several races of "Europeans, Tartars, Hindoos, Negroes," &c. as of the "division" of the Earth into "Europe, Asia, Africa," &c. though "the Earth" [or "the World"] is a Singular-term, and denotes what we call one individual. And it is plain we could not say of Europe, for instance, or of Asia, that it is "a World." But we can predicate "Man" of every individual European, Hindoo, &c. And here observe that there is a common colloquial incorrectness (increasing the liability to confusion) in the use of the word 'division," in each of these cases, to denote one of the " parts, into which the whole is divided. Thus you will sometimes hear a person speak of Europe as one "division" of the Earth; or of such and such a "division" of an Army: meaning portion." And so again a person will sometimes speak of "animals that belong to the feline division of the Carnivora" [flesh-eating-animals] meaning, that portion of the Class" Carnivora."

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Division

It is usual when a long and complex course of Division is to be Schemes of stated to draw it out, for the sake of clearness and brevity, in a form like that of a genealogical "Tree." And by carefully examining any specimen of such a "Tree" (going over it repeatedly, and comparing each portion of it with the explanations above given) you will be able perfectly to fix in your mind the technical termis we have been explaining.

Take for instance as a

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Summum-genus" the mathematical-terın

Such a "Tree of division" the Student may easily fill up for himself. And the employment of such & form will be found exceedingly useful in obtaining clear views in any study you are engaged in.

For instance, in the one we have been now occupied with, take for a Summus Genus, "Expression;" (i. e. "expression-inlanguage" of any sucn nental-operation as those formerly noticed) you may then exhibit, thus, the divisio and subdivision of

See the Division of Fallacies, Book III. § 4.

rules for

The rules ordinarily given for Division are three: 1st. each of the Ordinary Parts, or any of them short of all, must contain less (2.e. have a division narrower signification) than the thing divided. 2d. All the Parts together must be exactly equal to the thing divided; therefore we must be careful to ascertain that the summum genus may be predicated of every term placed under it, and of nothing else. 3d. The Parts or Members must be opposed [contradistinguished] i.e. must not be contained in one another: e.g. if you were to divide "book" into "poetical, historical, folio, quarto, french, latin," &c. the members would be contained in each other; for a french book may be a quarto, or octavo, and a quarto, french, english, &c. &c. You must be careful, therefore, to keep in mind the principle of division with which you set out: e.g. whether you begin dividing books according to their matter, their language, or their size, &c. all these being so many cross-divisions. And when any thing is capable (as Crossin the above instance) of being divided in several different ways, we are not to reckon one of these as the true, or real, or right one, without specifying what the object is which we have in view: for one mode of dividing may be the most suitable for one purpose, and another for another: as e.g. one of the above modes of dividing books would be the most suitable to a bookbinder; another in a philosophical, and the other in a philological view.

It is a useful practical rule, whenever you find a discussion of any subject very perplexing, and seemingly confused, to examine whether some "Cross-division" has not crept in unobserved. For this is very apt to take place; (though of course such a glaring instance as that in the above example could not occur in practice) and there is no more fruitful source of indistinctness and confusion of thought.

When you have occasion to divide any thing in several different ways, that is, "on several principles-of-division"-you should take care to state distinctly how many divisions you are making, and on what principle each proceeds.

For instance, in the 'Tree" above given, it is stated, that "Propositions" are divided in different ways, "according to" this and that, &c. And thus the perplexity of Cross-division is avoided.

divisions.

,, caution

Two other rules in addition to those above given, are needful to Additional be kept in mind: viz. 4thly, A Division should not be “arbitrary; that is, its Members should be distinguished from each other by "Differences" either expressed or readily understood; instead of being set apart from each other at random, or without any sufficient ground. For instance, if any one should divide "coins" into "goldcoins,' ""silver," and "copper," the ground of this distinction would be intelligible but if he should, in proceeding to subdivide silvercoin, distinguish as two branches, on the one side, "shillings," and on the other "all silver-coins except shillings," this would be an arbitrary Division.

5thly, A Division should be clearly arranged as to its Members:

Definition.

Essential and accidental

that is, there should be as much subdivision as the occasion may require; and not a mere catalogue of the "lowest-species," omitting intermediate classes ["subaltern"] between these and the "highestgenus:" nor again an intermixture of the "subaltern," and "lowestspecies," so as to have, in any two branches of the division, Species contradistinguished and placed opposite, of which the one ought naturally to be placed higher up [nearer the "Summum"] and the other, lower down in the Tree.

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For instance, to divide "plane-figure" at once, into "equilateraltriangles, squares, circles, ellipses," &c., or again "vegetable,” into Elms, pear-trees, turnips, mushrooms," &c., or again to divide "Animal" into "Birds, Fishes, Reptiles, Horses, Lions," &c. would be a transgression of this rule.

And observe that, (as has been formerly remarked) although such glaring cases as are given by way of examples could not occur in practice, errors precisely corresponding to them, may, and often do occur; and produce much confusion of thought and error.

§ 6.

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Definition is another metaphorical word, which literally signifies, "laying down a boundary;" and is used in Logic to signify an expression which explains any term, so as to separate it from every thing else," as a boundary separates fields.

In reference to the several modes adopted for furnishing such explanation, Logicians distinguish [divide] Definitions into essential definitions. and accidental. They call that an "essential-definition" which states what are regarded as the "constituent parts of the essence" of that which is to be defined; and an accidental-definition" [or Description] one which lays down what are regarded as "circumstances belonging to it;" viz. Properties or Accidents; such as causes, effects, &c.

individuals.

Accidents in the narrowest sense, (as defined above, § 3) cannot, it is plain, be employed in a Description [accidental-definition] of any Species; since no Accident (in that sense) can belong to the whole of a Species, nor consequently furnish an adequate Definition thereof.

Definition of In the "description" of an individual, on the contrary, we employ, not Properties, (which as they do belong to the whole of a Species, cannot serve to distinguish one individual of that Species from another) but Accidents-generally, inseparable-accidents-in con

Physical and logical

Sp.

junction with the Species: as "Philip was a king of Macedon, who

Sp.

subdued Greece;" "Britain is an Island, situated so and so,” &c. The Essential-definition again is divided into physical [natural; definitions and logical [metaphysical] definition: the physical-definition being made by an enumeration of such parts as are actually separable,— such as are the hull, masts, &c. of a "Ship;"-the root, trunk,