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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 terms we have been explaining.

Take for instance as a

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Summum-genus" the mathematical-terin

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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 Summum Genus, "Expression;" (i. e. "expression-inlanguage" of any sucn :nental-operation as those formerly noticed) you may then exhibit, thus, the division and subdivision of —

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

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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.

any

It is a useful practical rule, whenever you find a discussion of 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.

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divisions.

,, caution

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. 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,

branches, bark, &c. of a "Tree;" the Subject, Predicate, and Copula of a "Proposition."

The " ‘logical-definition" consists of the "Genus" and "Difference;" which are called by some writers the "metaphysical" [ideal] parts; as being not two real parts into which an individual-object can (as in the former case) be actually divided, but only different views taken [notions formed] of a class of objects, by one mind.

Genus.

E.G. "A Proposition" would be defined, logically, "a sentence

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affirming-or-denying:" A "Magnet" "an Iron-ore having attrac

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tion for iron;" a "Square," a "Rectangle " [right-angled parallelo

D.

gram] having equal sides.

61 and real

Definitions again have been divided by Logicians into the Nominal Nominal, which explains merely the meaning of the term defined; definitions. and Real, which explains the nature of the thing signified by that

term.

This division is evidently according to the object designed to be effected by each Definition: the former division, on the other hand —into Accidental, Physical, and Logical-being a division according to the means employed by each to effect its object. These therefore are evidently two "cross-divisions;" a circumstance which has been generally overlooked by Logical writers, who have thus introduced confusion and perplexity.

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And here the question may naturally occur to the reader, whether there be properly any distinction between nominal and real-definition; -whether the meaning of a Common-term, and the nature of the thing signified by it, are not one and the same; since the object of our thoughts when we employ a Common-term, is not any such "abstract idea" as some talk of, but-the Term itself, regarded as a Sign &c. as was formerly explained.

And in truth there are many cases in which there does exist this exact coincidence between the meaning of the term and the nature of the thing; so that the same definition which would be rightly styled "nominal," as explaining nothing beyond the exact meaning of the term, might also be considered as entitled to be called a

61 Aldrich, having given as an instance of a Nominal Definition the absurd one of "homo, qui ex humo," has led some to conclude that the Nominal definition must be founded on the etymology; or at least that such was his meaning. But that it was not, is sufficiently plain from the circumstance that Wallis (from whose

work his is almost entirely abridged)
expressly says the contrary. Be this as
it may, however, it is plain that the ety-
mology of a term has nothing to do with
any logical consideration of it. See § 8,
Book III.

See preceding §.

I

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