DIVISION (from

See also:

• LAT

Lat. dividere, to break up into parts,

See also:

• SEPARATE

separate)  , a general term for the action of breaking up a whole into parts . Thus, in political economy, the phrase " division of labour " implies the assignment to particular workmen of the various portions of a whole piece of work; in mathematics division•is the process of finding how many times one number or quantity, the " divisor," is contained in another, the " dividend " (see ARITHMETIC and ALGEBRA); in the musical terminology of the 17th and 8th centuries, the term was used for rapid passages consisting of a few slow notes amplified into a florid passage, i.e. into a larger number of quick ones . The word is used also in concrete senses for the parts into which a thing is divided, e.g. a division of an army, an administrative or electoral division; similarly, a "division" is taken in a legislative body when votes are recorded for and against a proposed measure . In logic, division is a technical term for the process by which a genus is broken up into its species . Thus the genus "animal " may be divided, according to the habitat of the various kinds, into animals which live on land, those which live in water, those which live in the air . Each of these may be subdivided according to whether their constituent members do or do not possess certain other qualities . The basis of each of these divisions is called the fundamentum divisions . It is clear that there can be no division in respect of those qualities which make the genus what it is . The various species are all alike in the possession of the generic attributes, but differ in other respects; they are " variations on the same theme " (Joseph, Introduction to Logic, 1906); each one has the generic, and also certain peculiar, qualities (differentiae), which latter distinguish them from other species of the same genus . The process of division is thus the obverse of classification (q.v.); it proceeds from genus to species, whereas classification begins with the particulars and rises through species to genus . In the exact sciences, and indeed in all argument both practical and theoretical, accurate division is of great importance . It is governed by the following rules .

(1) Division must be exhaustive; all the members of the genus must find a

place in one or other of the species; a captain who selects for his team skilful batsmen and bowlers only is guilty of an incomplete division of the whole function of a cricket team by omitting to provide himself with good fielders . Rectilinear figures cannot be divided into triangles and quadrilaterals because there are rectilinear figures which have more than four sides . On the other hand, triangles can bedivided into equilateral, isosceles and scalene, since no other kind of triangle can exist . (2) Division must be exclusive, that is, each species must be complete in itself and not contain members of another species . No member of a genus must be included in more than one of the species . (3) In every division there must be but one principle (fundamentum divisions) . The members of a genus may differ from one another in many respects, e.g. books may be divided according to external form into quarto, octavo, &c., or according to binding into calf, cloth, paper-backed and so on . They cannot, however, be divided logically into quarto, paper-backed, novels and remainders . When more than one principle is used in a division it is called " cross division." (4) Division must proceed gradually (" Divisio non facit saltum "), i.e. the genus must be resolved into the next highest (" proximate ") species . To go straight from a summum genus to very small species is of no scientific value . It is to be observed that logical division is concerned exclusively with universals or concepts; division is of genus and species, not of particulars . Two other kinds of division are recognized:—metaphysical division, the separation in thought of the various qualities possessed by an individual thing (a piece of lead has weight, colour, &c.), and physical division or partition, the breaking up of. an object into its parts (a watch is thought of as being composed of case, dial, works, &c.) .

Logical division is closely allied with logical

definition (q.v.) .