thing."

9. Let it here be observed that scientific definitions are of _things_, and
not merely of _words_; or if equally of words _and_ things, they are rather
of nouns than of the other parts of speech. For a definition, in the proper
sense of the term, consists not in a mere change or explanation of the
verbal sign, but in a direct and true answer to the question, What is such
or such a thing? In respect to its extent, it must with equal exactness
include every thing which comes under the name, and exclude every thing
which does not come under the name: then will it perfectly serve the
purpose for which it is intended. To furnish such definitions, (as I have
suggested,) is work for those who are capable of great accuracy both of
thought and expression. Those who would qualify themselves for teaching any
particular branch of knowledge, should make it their first concern to
acquire clear and accurate ideas of all things that ought to be embraced in
their instructions. These ideas are to be gained, either by contemplation
upon the things themselves as they are presented naturally, or by the study
of those books in which they are rationally and clearly explained. Nor will
such study ever be irksome to him whose generous desire after knowledge, is
thus deservedly gratified.

10. But it must be understood, that although scientific definitions are
said to be _of things_, they are not copied immediately from the real
essence of the things, but are formed from the conceptions of the author's
mind concerning that essence. Hence, as Duncan justly remarks, "A mistaken
idea never fails to occasion a mistake also in the definition." Hence, too,
the common distinction of the logicians, between definitions of the _name_
and definitions of the _thing_, seems to have little or no foundation. The
former term they applied to those definitions which describe the objects of
pure intellection, such as triangles, and other geometrical figures; the
latter, to those which define objects actually existing in external nature.
The mathematical definitions, so noted for their certainty and
completeness, have been supposed to have some peculiar preeminence, as
belonging to the former class. But, in fact the idea of a triangle exists
as substantively in the mind, as that of a tree, if not indeed more so; and
if I define these two objects, my description will, in either case, be
equally a definition both of the name and of the thing; but in neither,