Proof--If the human body has once been affected by two bodies at once, whenever afterwards the mind conceives one of them, it will straightway remember the other also (II. xviii.). But the mind's conceptions indicate rather the emotions of our body than the nature of external bodies (II. xvi. Cor. ii.); therefore, if the body, and consequently the mind (III. Def. iii.) has been once affected by two emotions at the same time, it will, whenever it is afterwards affected by one of the two, be also affected by the other.
XV. Anything can, accidentally, be the cause of pleasure, pain, or desire.
Proof--Let it be granted that the mind is simultaneously affected by two emotions, of which one neither increases nor diminishes its power of activity, and the other does either increase or diminish the said power (III. Post. i.). From the foregoing proposition it is evident that, whenever the mind is afterwards affected by the former, through its true cause, which (by hypothesis) neither increases nor diminishes its power of action, it will be at the same time affected by the latter, which does increase or diminish its power of activity, that is (III. xi. note) it will be affected with pleasure or pain. Thus the former of the two emotions will, not through itself, but accidentally, be the cause of pleasure or pain. In the same way also it can be easily shown, that a thing may be accidentally the cause of desire. Q.E.D.
Corollary--Simply from the fact that we have regarded a thing with the emotion of pleasure or pain, though that thing be not the efficient cause of the emotion, we can either love or hate it.
Proof--For from this fact alone it arises (III. xiv.), that the mind afterwards conceiving the said thing is affected with the emotion of pleasure or pain, that is (III. xi. note), according as the power of the mind and body may be increased or diminished, &c.; and consequently (III. xii.), according as the mind may desire or shrink from the conception of it (III. xiii. Cor.), in other words (III. xiii. note), according as it may love or hate the same.
Q.E.D.
*****Note--Hence we understand how it may happen, that we love or hate a thing without any cause for our emotion being known to us; merely, as a phrase is, from "sympathy" or "antipathy." We should refer to the same category those objects, which affect us pleasurably or painfully, simply because they resemble other objects which affect us in the same way. This I will show in the next Prop. I am aware that certain authors, who were the first to introduce these terms "sympathy" and "antipathy," wished to signify thereby some occult qualities in things; nevertheless I think we may be permitted to use the same terms to indicate known or manifest qualities.
XVI. Simply from the fact that we conceive, that a given object has some point of resemblance with another object which is wont to affect the mind pleasurably or painfully, although the point of resemblance be not the efficient cause of the said emotions, we shall still regard the first-named object with love or hate.
Proof--The point of resemblance was in the object (by hypothesis), when we regarded it with pleasure or pain, thus (III. xiv.), when the mind is affected by the image thereof, it will straightway be affected by one or the other emotion, and consequently the thing, which we perceive to have the same point of resemblance, will be accidentally (III. xv.) a cause of pleasure or pain. Thus (by the foregoing Corollary), although the point in which the two objects resemble one another be not the efficient cause of the emotion, we shall still regard the first-named object with love or hate. Q.E.D.
XVII. If we conceive that a thing, which is wont to affect us painfully, has any point of resemblance with another thing which is wont to affect us with an equally strong emotion of pleasure, we shall hate the first-named thing, and at the same time we shall love it.
Proof--The given thing is (by hypothesis) in itself a cause of pain, and (III. xiii. note), in so far as we imagine it with this emotion, we shall hate it: further, inasmuch as we conceive that it has some point of resemblance to something else, which is wont to affect us with an equally strong emotion of pleasure, we shall with an equally strong impulse of pleasure love it (III. xvi.); thus we shall both hate and love the same thing. Q.E.D.
*****Note--This disposition of the mind, which arises from two contrary emotions, is called "vacillation"; it stands to the emotions in the same relation as doubt does to the imagination (II. xliv. note); vacillation and doubt do not differ one from the other, except as greater differs from less. But we must bear in mind that I have deduced this vacillation from causes, which give rise through themselves to one of the emotions, and to the other accidentally.
I have done this, in order that they might be more easily deduced from what went before; but I do not deny that vacillation of the disposition generally arises from an object, which is the efficient cause of both emotions. The human body is composed (II. Post. i.) of a variety of individual parts of different nature, and may therefore (Ax. i. after Lemma iii. after II. xiii.) be affected in a variety of different ways by one and the same body; and contrariwise, as one and the same thing can be affected in many ways, it can also in many different ways affect one and the same part of the body. Hence we can easily conceive, that one and the same object may be the cause of many and conflicting emotions.
XVIII. A man is as much affected pleasurably or painfully by the image of a thing past or future as by the image of a thing present.
