Genus and Species are a peculiar case of whole and part (_cf._ chaps.
xxi.-ii.-iii.). Sometimes a term connotes all the attributes that
another does, and more besides, which, as distinguishing it, are called
differential. Thus 'man' connotes all that 'animal' does, and also (as
_differentiæ_) the erect gait, articulate speech, and other attributes.
In such a case as this, where there are well-marked classes, the term
whose connotation is included in the others' is called a Genus of that
Species. We have a Genus, triangle; and a Species, isosceles, marked off
from all other triangles by the differential quality of having two equal
sides: again--Genus, book; Species, quarto; Difference, having each
sheet folded into four leaves.

There are other cases where these expressions 'genus' and 'species'
cannot be so applied without a departure from usage, as, e.g., if we
call snow a species of the genus 'white,' for 'white' is not a
recognised class. The connotation of white (i.e., whiteness) is,
however, part of the connotation of snow, just as the qualities of
'animal' are amongst those of 'man'; and for logical purposes it is
desirable to use 'genus and species' to express that relativity of
terms which consists in the connotation of one being part of the
connotation of the other.

Two or more terms whose connotations severally include that of another
term, whilst at the same time exceeding it, are (in relation to that
other term) called Co-ordinate. Thus in relation to 'white,' snow and
silver are co-ordinate; in relation to colour, yellow and red and blue
are co-ordinate. And when all the terms thus related stand for
recognised natural classes, the co-ordinate terms are called co-ordinate
species; thus man and chamois are (in Logic) co-ordinate species of the
genus animal.