ments. First, They maybe produced when there has been no Physical Motion nor alteration in the Subject to which they belong, nay, indeed, when there hath been nothing at all done to the Subject to which they do accrue. As for example, suppose one side of a Room whitened, the other not touch'd or meddled with, this other has thus become unlike, and hath the Notion of Dissimile necessarily belonging to it, although there has nothing at all been done thereunto. So suppose two Pounds of Lead, which therefore are two Equal Pieces of that Metall; cut away half from one of them, the other Pound, nothing at all being done unto it, has lost its Notion of Equal, and hath acquired a new one of Double unto the other. Nor is, it to any purpose to answer, That though there was nothing done to this Pound of Lead, yet there was to the other; for that does not at all enervate the reason, but shews that the Notion of Sub-double, which accrued to that Lead which had half cutaway, is but our Mode of conceiving, as well as the other, and not any Physical affection that strikes the corporeal Organs of the Body, as Hot and Cold, Hard and Soft, White and Black, and the like do. Wherefore the Ideas of Equal and Unequal, Double and Sub-double, Like and Unlike, with the rest, are no external Impresses upon the Senses, but the Souls own active manner of conceiving those things which are discovered by the outward Senses.
5. The Second Argument is, That one and the same part of the Matter is capable at one and the same time wholly and entirely of two contrary Ideas of this kind. As for example, any piece of Matter that is a Middle proportional betwixt two other pieces is Double, suppose, and Sub-double, or Triple and Sub-triple, at once. Which is a manifest sign that these Ideas are no affections of the Matter, and therefore do not affect our Senses; else they would affect the Senses of Beasts, and they might also grow good Geometricians and Arithmeticians. And they not affecting our Senses, it is plain that we have some Ideas that we are not beholding to our Senses for, but are the mere exertions of the Mind occasionally awakened by the Appulses of the outward Objects, which the outward Senses do no more teach us, then he that awakened the Musician to sing taught him his skill.
6. And now in the third and last place it is manifest, besides these single Ideas I have proved to be in the Mind, that there are also severall complex Notions in the same, such as are these. The Whole is bigger then the Part; if you take Equall from equall, the Remainders are Equall; Every Number is either Even or Odde; which are true to the Soul at the very first proposal, as any one that is in his wits does plainly perceive.
