efinite properties to be arrived at by
abstraction, there are classes, viz. _kinds_, distinguished severally by
an unknown multitude of independent properties (and about which classes
therefore many assertions will be made), there must be a name for every
_kind_. That is, besides a terminology, there must be a nomenclature,
i.e. a collection of the names of all the lowest _kinds_, or _infimae
species_. The Linnaean arrangements of plants and animals, and the French
of chemistry, are nomenclatures. The peculiarity of a name which belongs
to a nomenclature is, not that its meaning resides in its denotation
instead of its connotation (for it resides in its connotation, like that
of other concrete general names); but that, besides connoting certain
attributes which its definition explains, it also connotes that these
attributes are distinctive of a _kind_; and this fact its definition
cannot explain.

A philosophical language, then, must possess, first, precision, and next
(the subject of the present chapter), completeness. Some have argued
that, in addition, names are fitted for the purposes of thought in
proportion as they approximate to mere symbols in compactness, through
meaninglessness, and capability of use as counters without reference to
the various objects which, though utterly different, they may thus at
different times equally well represent. Such are, indeed, the qualities
enabling us to employ the figures of arithmetic and the symbols of
algebra perfectly mechanically according to general technical rules.
But, in the first place, in our direct inductions, at all events,
depending as they do on our perception of the particulars of the
agreement and difference of the phenomena, we could never dispense with
a distinct mental image of the latter. Further, even in deduction,
though a syllogism is conclusive from its mere form, if the terms are
unambiguous, yet the _practical_ validity of the reasoning depends on
the hypothesis that no counteracting cause has interfered with the truth
of the premisses. We can assure ourselves of this only by studying the
phenomena at every step. For it is only in geometry and algebra that
there is no danger from the Composition of Causes, or the superseding of
one set of laws by another; and that, therefore, the propositions are
categorically true. In sciences in general, then, the object should be,
so far from keeping individualising peculiarities out of sight, to
contrive the grea