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, and that the oral monosyllable five is the same number, in an other form; but is still as much at a loss for a proper answer to his question, as if he had never seen either schoolmaster or dictionary.  So is it with a vast number of the simplest things in grammar.

7.  Since what we denominate scientific terms, are seldom, if ever, such as stand for ideas simple and undefinable; and since many of those which represent general ideas, or classes of objects, may be made to stand for more or fewer things, according to the author’s notion of classification; it is sufficiently manifest that the only process by which instruction can effectually reach the understanding of the pupil and remove the difficulties spoken of, is that of delivering accurate definitions.  These are requisite for the information and direction of the learner; and these must be thoroughly impressed upon his mind, as the only means by which