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.
PROP. 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.
PROP. 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.