little inclined
or accustomed to reflection, they often hear, read, or even rehearse from
memory, the plainest language that can be uttered, and yet have no very
distinct apprehension of what it means. What marvel then, that in a study
abounding with terms taken in a peculiar or technical sense, many of which,
in the common manuals, are either left undefined, or are explained but
loosely or erroneously, they should often be greatly puzzled, and sometimes
totally discouraged?

6. _Simple ideas_ are derived, not from teaching, but from sensation or
consciousness; but _complex ideas_, or the notions which we have of such
things as consist of various parts, or such as stand in any known
relations, are definable. A person can have no better definition of _heat_,
or of _motion_, than what he will naturally get by _moving_ towards a
_fire_. Not so of our complex or general ideas, which constitute science.
The proper objects of scientific instruction consist in those genuine
perceptions of pure mind, which form the true meaning of generic names, or
common nouns; and he who is properly qualified to teach, can for the most
part readily tell what should be understood by such words. But are not many
teachers too careless here? For instance: a boy commencing the process of
calculation, is first told, that, "Arithmetic is the art of computing by
numbers," which sentence he partly understands; but should he ask his
teacher, "What is a _number_, in arithmetic?" what answer will he get? Were
Goold Brown so asked, he would simply say, "_A number, in arithmetic, is an
expression that tells how many_;" for every expression that tells how many,
is a number in arithmetic, and nothing else is. But as no such definition
is contained in _the books_,[66] there are ten chances to one, that, simple
as the matter is, the readiest master you shall find, will give an
erroneous answer. Suppose the teacher should say, "That is a question which
I have not thought of; turn to your dictionary." The boy reads from Dr.
Webster: "NUMBER--the designation of a unit in reference to other units, or
in reckoning, counting, enumerating."--"Yes," replies the master, "that is
it; Dr. Webster is unrivalled in giving definitions." Now, has the boy been
instructed, or only puzzled? Can he conceive how the number _five_ can be a
_unit_? or how the word _five_, the figure 5, or the numeral letter V, is
"the designation of a _unit_?" He knows that each of these is a number