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§ 16. A child knows not that three and four are equal to seven, till he comes to be able to count seven, and has got the name and idea of equality: and then, upon explaining those words, he presently assents to, or rather perceives the truth of that proposition. But neither does he then readily assent, because it is an innate truth, nor was his assent wanting till then, because he wanted the use of reason; but the truth of it appears to him, as soon as he has settled in his mind the clear and distinct ideas, that these names stand for: and then he knows the truth of that proposition, upon the same grounds, and by the same means, that he knew before, that a rod and a cherry are not the same thing; and upon the same grounds also, that he may come to know afterwards, “that it is impossible for the same thing to be, and not to be,” as shall be more fully shown hereafter. So that the later it is before any one comes to have those general ideas, about which those maxims are; or to know the signification of those general terms that stand for them; or to put together in his mind the ideas they stand for; the later also will it be before he comes to assent to those maxims, whose terms, with the ideas they stand for, being no more innate than those of a cat or a weasel, he must stay till time and observation have acquainted him with them; and then he will be in a capacity to know the truth of these maxims, upon the first occasion that shall make him put together those ideas in his mind, and observe whether they agree or disagree, according as is expressed in those propositions. And therefore it is, that a man knows that eighteen and nineteen are equal to thirty-seven, by the same self-evidence, that he knows one and two to be equal to three: yet a child knows this not so soon as the other; not for want of the use of reason, but because the ideas the words eighteen, nineteen, and thirty-seven stand for, are not so soon got, as those which are signified by one, two, and three.
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§ 23. There is, I fear, this farther weakness in the foregoing argument, which would persuade us, that therefore those maxims are to be thought innate, which men admit at first hearing, because they assent to propositions, which they are not taught, nor do receive from the force of any argument or demonstration, but a bare explication or understanding of the terms. Under which, there seems to me to lie this fallacy, that men are supposed not to be taught, nor to learn any thing when, in truth, they are taught, and do learn something they were ignorant of before. For first it is evident, that they have learned the terms, and their signification; neither of which was born with them. But this is not all the acquired knowledge in the case: the ideas themselves, about which the proposition is, are not born with them, no more than their names, but got afterwards. So that in all propositions that are assented to at first hearing, the terms of the proposition, their standing for such ideas, and the ideas themselves that they stand for, being neither of them innate; I would fain know what there is remaining in such propositions, that is innate. For I would gladly have any one name that proposition, whose terms or ideas were either of them innate. We by degrees get ideas and names, and learn their appropriated connexion one with another; and then to propositions, made in such terms, whose signification we have learnt, and wherein the agreement or disagreement we can perceive in our ideas, when put together, is expressed, we at first hearing assent; though to other propositions, in themselves as certain and evident, but which are concerning ideas, not so soon or so easily got, we are at the same time no way capable of assenting. For though a child quickly assents to this proposition, “that an apple is not fire,” when, by familiar acquaintance, he has got the ideas of those two different things distinctly imprinted on his mind, and has learnt that the names apple and fire stand for them; yet it will be some years after, perhaps, before the same child will assent to this proposition, “that it is impossible for the same thing to be, and not to be:” because that, though, perhaps the words are as easy to be learnt, yet the signification of them being more large, comprehensive, and abstract, than of the names annexed to those sensible things the child hath to do with, it is longer before he learns their precise meaning, and it requires more time plainly to form in his mind those general ideas they stand for. Till that be done, you will in vain endeavour to make any child assent to a proposition made up of such general terms: but as soon as ever he has got those ideas, and learned their names, he forwardly closes with the one, as well as the other of the forementioned propositions, and with both for the same reason; viz. because he finds the ideas he has in his mind to agree or disagree, according as the words standing for them, are affirmed or denied one of another in the proposition. But if propositions be brought to him in words, which stand for ideas he has not yet in his mind; to such propositions, however evidently true or false in themselves, he affords neither assent nor dissent, but is ignorant. For words being but empty sounds, any farther than they are signs of our ideas, we cannot but assent to them, as they correspond to those ideas we have, but no farther than that. But the showing by what steps and ways knowledge comes into our minds, and the grounds of several degrees of assent, being the business of the following discourse, it may suffice to have only touched on it here, as one reason that made me doubt of those innate principles.