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.