If X be a connotative name, it is itself a species (_Species
subjicibilis_); and the place of the subject of a proposition is the
usual one for species. The predicate, Y, may then be related to the
species in three different ways. First, it may be a definition, exactly
equivalent to the species;--in fact, nothing else than the species in an
explicit form, the analysis of its connotation. Secondly, the predicate
may be, or connote, some _part only_ of the definition or connotation of
the species; and then it is either genus (2), or difference (3).
Thirdly, the predicate may connote _no part_ of the definition, and then
it is either derivable from it, being a proprium (4), or not derivable
from it, being an accident (5). These points of doctrine will be
expanded and illustrated in subsequent pages.
If X be a singular name, deriving connotation from its constituent terms
(chap. iv. § 2), as 'The present Emperor of China,' it may be treated as
a _Species subjicibilis_. Then that he is 'an absolute monarch,'
predicates a genus; because that is a genus of 'Emperor,' a part of the
singular name that gives it connotation. That he wears a yellow robe is
a proprium, derivable from the ceremonial of his court. That he is
thirty years of age is an accident.
But if X be a proper name, having no connotation, Y must always be an
accident; since there can then be no definition of X, and therefore
neither species, genus, difference, nor proprium. Hence, that 'John Doe
is a man' is an accidental proposition: 'man' is not here a _Species
predicabilis_; for the name might have been given to a dog or a
mountain. That is what enables the proposition to convey information: it
would be useless if the proper name implied 'humanity.'
'Species' is most frequently used (as in Zoology) for the _class
denoted_ by a general name; but in Logic it is better to treat it as a
general name used connotatively for the attributes possessed in common
by the things denoted, and on account of which they are regarded as a
class: it is sometimes called the Essence (§ 9). In this connotative
sense, a species is implicitly what the definition is explicitly; and
therefore the two are always simply convertible. Thus, 'A plane
triangle' (species) is 'a figure enclosed by three straight lines'
(definition): clearly we may equally say, 'A figure enclosed by three
straight lines is a plane triangle.' It is a simple identity.
A genus is also commonly viewed denotatively, as a class containing
smaller classes, its species; but in Logic it is, again, better to treat
it connotatively, as a name whose definition is part of the definition
of a given species.
A difference is the remainder of the definition of any species after
subtracting a given genus. Hence, the genus and difference together make
up the species; whence the method of definition _per genus et
differentiam_ (_ante_, § 5).
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