M. Condillac[91] exemplifies this doctrine by translating this proposition, "The measure of every triangle is the product of its height by half its base," into self-evident, or, as he calls them, identical propositions. The whole ultimately referring to the ideas which we have obtained by our senses of a triangle; of its base, of measure, height, and number. If a child had not previously acquired any one of these ideas, it would be in vain to explain one term by another, or to translate one phrase or proposition into another; they might be identical, but they would not be self-evident propositions to the pupil; and no conclusion, except what relates merely to words, could be formed from such reasoning. The moral which we should draw from Condillac's observations for Practical Education must be, that clear ideas should first be acquired by the exercise of the senses, and that afterwards, when we reason about things in words, we should use few and accurate terms, that we may have as little trouble as possible in changing or translating one phrase or proposition into another.
Children, if they are not overawed by authority, if they are encouraged in the habit of observing their own sensations, and if they are taught precision in the use of the words by which they describe them, will probably reason accurately where their own feelings are concerned.
In appreciating the testimony of others, and in judging of chances and probability, we must not expect our pupils to proceed very rapidly. There is more danger that they should overrate, than that they should undervalue, the evidence of others; because, as we formerly stated, we take it for granted, that they have had little experience of falsehood. We should, to preserve them from credulity, excite them in all cases where it can be obtained, never to rest satisfied without the strongest species of evidence, that of their own senses. If a child says, "I am sure of such a thing," we should immediately examine into his reasons for believing it. "Mr. A. or Mr. B. told me so," is not a sufficient cause of belief, unless the child has had long experience of A. and B.'s truth and accuracy; and, at all events, the indolent habit of relying upon the assertions of others, instead of verifying them, should not be indulged.