[1] _La Baguette divinatoire_ (Paris, 1845).
DIVISION (from Lat. _dividere_, to break up into parts, 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 18th 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 divisionis_.
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 be divided 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 divisionis)_. 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.).
DIVORCE (Lat. _divortium_, derived from dis-, apart, and vertere, to
turn), the dissolution, in whole or in part, of the tie of marriage. It
includes both the complete abrogation of the marriage relation known as
a divorce _a vinculo matrimonii_, which carries with it a power on the
part of both parties to the marriage to remarry other persons or each
other, and also that incomplete severance not involving powers to
remarry, which was formerly known as divorce a _mensa et thoro_, and has
in England been termed "judicial separation." Less strictly, divorce is
commonly understood to include judicial declarations of nullity of
marriage, which, while practically terminating the marriage relation,
proceed in law on the basis of the marriage never having been legally
established.
The conditions under which, in different communities, divorce has at
different times been permitted, vary with the aspects in which the
relation of marriage (q.v.) has been regarded. When marriage has been
deemed to be the acquisition by the husband of property in the wife, or
when it has been regarded as a mere agreement between persons capable
both to form and to dissolve that contract, we find that marriage has
been dissoluble at the will of the husband, or by agreement of the
husband and wife. Yet even in these cases the interest of the whole
community in the purity of marriage relations, in the pecuniary bearings
of this particular contract, and the condition of children, has led to
the imposition of restrictions on, and the attachment of conditions to,
the termination of the obligations consequent on a marriage legally
contracted. But the main restrictions on liberty of divorce have arisen
from the conception of marriage entertained by religions, and especially
by one religion. Christianity has had no greater practical effect on the
life of mankind than in its belief that marriage is no mere civil
contract, but a vow in the sight of God binding the parties by
obligations of conscience above and beyond those of civil law.
Translating this conception into practice, Christianity not only
profoundly modified the legal conditions of divorce as formulated in the
Roman civil law, but in its own canon law defined its own rule of
divorce, going so far as in the Western (at least in its unreformed
condition), though not the Eastern, branch of Christendom to forbid all
complete divorces, that is to say, all dissolutions of marriage carrying
with them the right to remarry.