ndent says No, you
ask whether four stones form a heap, then five, and so on and he is
puzzled to say when the addition of a single stone makes that a heap
which was not a heap before. Or you may begin by asking whether twenty
stones form a heap, then nineteen, then eighteen, and so on, the
difficulty being to say when what was a heap ceases to be so.

Where the objects classified are mixed states or affections, the
products of interacting factors, or differently interlaced or
interfused growths from common roots, as in the case of virtues, or
emotions, or literary qualities, sharp demarcations are impossible.
To distinguish between wit and humour, or humour and pathos, or pathos
and sublimity is difficult because the same composition may partake
of more than one character. The specific characters cannot be made
rigidly exclusive one of another.

Even in the natural sciences, where the individuals are concrete
objects of perception, it may be difficult to decide in which of
two opposed groups an object should be included. Sydney Smith has
commemorated the perplexities of Naturalists over the newly
discovered animals and plants of Botany Bay, in especial with the
_Ornithorynchus_,--"a quadruped as big as a large cat, with the
eyes, colour, and skin of a mole, and the bill and web-feet of a
duck--puzzling Dr. Shaw, and rendering the latter half of his life
miserable, from his utter inability to determine whether it was a bird
or a beast".

III. The classes in any scheme of division should be of
co-ordinate rank.

The classes may be mutually exclusive, and yet the division imperfect,
owing to their not being of equal rank. Thus in the ordinary division
of the Parts of Speech, parts, that is, of a sentence, Prepositions
and Conjunctions are not co-ordinate in respect of function, which is
the basis of the division, with Nouns, Adjectives, Verbs, and Adverbs.
The preposition is a part of a phrase which serves the same function
as an adjective, _e.g._, _royal_ army, army _of the king_; it is thus
functionally part of a part, or a particle. So with the conjunction:
it also is a part of a part, _i.e._, part of a clause serving the
function of adjective or adverb.

IV. The basis of division (_fundamentum divisionis_) should be
an attribute admitting of important differences.

The importance of the attribute chosen as basis may vary with the
purpose of the division. An attribute that is of no importance in