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 (Sec. 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, 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.