See also:term for the
See also:action of breaking up a whole into parts . Thus, in
See also:economy, the phrase " division of labour " implies the
See also:assignment to particular workmen of the various portions of a whole piece of
See also:work; in
See also:mathematics division•is the
See also:process of finding how many times one number or quantity, the " divisor," is contained in another, the " dividend " (see ARITHMETIC and
See also: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
See also: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
See also: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
See also:species . Thus the genus "animal " may be divided, according to the habitat of the various kinds, into animals which live on
See also:land, those which live in
See also: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 " (
See also:Joseph, Introduction to Logic, 1906); each one has the generic, and also certain
See also:peculiar, qualities (differentiae), which latter distinguish them from other species of the same genus . The process of division is thus the obverse of
See also: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
See also:argument both
See also:practical and theoretical, accurate division is of
See also:great importance . It is governed by the following rules .
(1) Division must be exhaustive; all the members of the genus must find aplace 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
See also:function of a cricket team by omitting to provide himself with
See also: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
See also: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
See also: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
See also:form into
See also:octavo, &c., or according to binding into calf,
See also: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 "
See also: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
See also:colour, &c.), and
See also:physical division or
See also:partition, the breaking up of. an
See also:object into its parts (a
See also:watch is thought of as being composed of case,
See also:works, &c.) .
Logical division is closely allied with logicaldefinition (q.v.) .
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