6. When mental propositions contain real truth, and when verbal.
Every one's experience will satisfy him, that the
mind, either by perceiving, or supposing, the agreement or disagreement of any of its ideas, does tacitly within
itself put them into a kind of proposition affirmative or negative; which I have endeavoured to express by the
terms putting together and separating. But this action of the mind, which is so familiar to every thinking and
reasoning man, is easier to be conceived by reflecting on what passes in us when we affirm or deny, than to be
explained by words. When a man has in his head the idea of two lines, viz., the side and diagonal of a square,
whereof the diagonal is an inch long, he may have the idea also of the division of that line into a certain number of
equal parts: v.g. into five, ten, a hundred, a thousand, or any other number, and may have the idea of that inch line
being divisible, or not divisible, into such equal parts, as a certain number of them will be equal to the sideline.
Now, whenever he perceives, believes, or supposes such a kind of divisibility to agree or disagree to his idea of
that line, he, as it were, joins or separates those two ideas, viz., the idea of that line, and the idea of that kind of
divisibility; and so makes a mental proposition, which is true or false, according as such a kind of divisibility; a
divisibility into such aliquot parts, does really agree to that line or no. When ideas are so put together, or separated
in the mind, as they or the things they stand for do agree or not, that is, as I may call it, mental truth. But truth of
words is something more; and that is the affirming or denying of words one of another, as the ideas they stand for
agree or disagree: and this again is two-fold; either purely verbal and trifling, which I shall speak of, (chap. viii.,)
or real and instructive; which is the object of that real knowledge which we have spoken of already.
