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_, Sec. 5).

Whilst in Botany and Zoology the species is fixed at the lowest step of
the classification (varieties not being reckoned as classes), and the
genus is also fixed on the step next above it, in Logic these
predicables are treated as movable up and down the ladder: any lower
class being species in relation to any higher; which higher class,
wherever taken, thus becomes a genus. Lion may logically be regarded as
a species of digitigrade, or mammal, or animal; and then each of these
is a genus as to lion: or, again, digitigrade may be regarded as a
species of mammal, or mammal as a species of animal. The highest class,
however, is never a species; wherefore it is called a _Summum Genus_:
and the lowest class is never a genus; wherefore it is called an _Infima
Species_. Between these two any step may be either species or genus,
according to the relation in which it is viewed to other classes, and is
then called Subaltern. The _summum genus_, again, may be viewed in
relation to a _given_ universe or _suppositio_ (that is, any limited
area of existence now the object of attention), or to the _whole_
universe. If we take the animal kingdom as our _suppositio_, Animal is
the _summum genus_; but if we take the whole universe, 'All things' is
the _summum genus_.

"Porphyry's tree" is used to illustrate this doctrine. It begins with a
_summum genus_, 'Substance,' and descends by adding differences, step by
step, to the _infima species_, 'Man.' It also illustrates Division by
Dichotomy.

SUBSTANCE
/ \
CORPOREAL || INCORPOREAL
||
BODY
/ \
ANIMATE || INANIMATE
||
LIVING BODY
/