s the term for the science of probable reasoning as opposed to
demonstrative reasoning ([Greek: apodeiktike]). The Stoics divided
[Greek: logike] (logic) into rhetoric and dialectic, and from their time
till the end of the middle ages dialectic was either synonymous with, or
a part of, logic.

In modern philosophy the word has received certain special meanings. In
Kantian terminology _Dialektik_ is the name of that portion of the
_Kritik d. reinen Vernunft_ in which Kant discusses the impossibility of
applying to "things-in-themselves" the principles which are found to
govern phenomena. In the system of Hegel the word resumes its original
Socratic sense, as the name of that intellectual process whereby the
inadequacy of popular conceptions is exposed. Throughout its history,
therefore, "dialectic" has been connected with that which is remote
from, or alien to, unsystematic thought, with the a priori, or
transcendental, rather than with the facts of common experience and
material things.

DIALLAGE, an important mineral of the pyroxene group, distinguished by
its thin foliated structure and bronzy lustre. The chemical composition
is the same as diopside, Ca Mg (SiO_{3})_{2}, but it sometimes contains
the molecules (Mg, Fe") (Al, Fe"')_{2} SiO_{6} and Na Fe"'
(SiO_{3})_{2}, in addition, when it approaches to augite in composition.
Diallage is in fact an altered form of these varieties of pyroxene; the
particular kind of alteration which they have undergone being known as
"schillerization." This, as described by Prof. J. W. Judd, consists in
the development of a fine lamellar structure or parting due to secondary
twinning and the separation of secondary products along these and other
planes of chemical weakness ("solution planes") in the crystal. The
secondary products consist of mixtures of various hydrated oxides--opal,
goethite, limonite, &c--and appear as microscopic inclusions filling or
partly filling cavities, which have definite outlines with respect to
the enclosing crystal and are known as negative crystals. It is to the
reflection and interference of light from these minute inclusions that
the peculiar bronzy sheen or "schiller" of the mineral is due. The most
pronounced lamination is that parallel to the orthopinacoid; another,
less distinct, is parallel to the basal plane, and a third parallel to
the plane of symmetry; these planes of secondary parting are in addition
to the ordinary prismatic cleavage of al