# An Antidote Against Atheism/Book I/Chapter VI

Chap. VI.
1. Sundry Instances arguing actual Knowledge in the Soul: as that she has a mere accurate Idea of a Circle and Triangle then Matter can exhibite to her: 2. And that upon one single consideration she assures her self of the Universal Affection of a Triangle. 3. The same argued from the nature of Mathematical and Logical Notions, which come not in by the Senses, as being no Physical affections of the Matter; 4. Because they are produced without any Physical motion upon the Matter; 5. And that contrary kindes may be intirely in one and the same part of Matter at once. 6. That there are certain sure Complex Notions of the Mind for which she was not beholden to Sense.
1. And that this is the condition of the Soul is discoverable by sundry observations. As for example, Exhibite to the Soul through the outward Senses the figure of a Circle; she acknowledgeth presently this to be one kind of Figure, and can adde forthwith, that if it be perfect, all the lines from some one point of it drawn to the Perimeter must be exactly Equal. In like manner shew her a Triangle, she will straightway pronounce, that if that be the right figure it makes toward, the Angles must be closed in indivisible points. But this accuracy either in the Circle or the Triangle cannot be set out in any material Subject: therefore it remains that she hath a more full and exquisite knowledge of things in herself then the Matter can lay open before her.
2. Let us cast in a third Instance: Let some body now demonstrate this Triangle described in the Matterto have its three Angles equal to two right ones. Why yes, faith the Soul, this is true, and not only in this particular Triangle, but in all plain Triangles that can possibly be describ'd in the Matter. And thus, you see, the Soul sings out the whole Song upon the first hint, as knowing it very well before.
3. Besides this, there are a multitude of Relative Notions or Ideas in the Mind of Man, as well Mathematical as Logical, which if we prove cannot be the Impresses of any material Object from without, it will necessarily follow that they are from the Soul her self within, and are the natural furniture of humane Understanding. Such as are these, Cause, Effect, Whole and Part, Like and Unlike, and the rest. So Equality and Inequality, λόγος and ἁναλογία, Proportion and Analogy, Symmetry and Asymmetry, and such like: all which Relative Ideas I shall easily prove to be no material Impresses from without upon the Soul, but her own active conception proceeding from her self whilest she takes notice of external Objects. For that these Ideas can make no Impresses upon the outward Senses is plain from hence, because they are no sensible nor Physical affections of the Matter. And how can that that is no Physical affection of the Matter, affect our corporeal Organs of Sense?
But now that these Relative Ideas, whether Logical or Mathematical, be no Physical affections of the Matter, is manifest from these two ​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.