XIX. He who conceives that the object of his love is destroyed will feel pain; if he conceives that it is preserved he will feel pleasure.
>>>>>Proof—The mind, as far as possible, endeavours to conceive those things which increase or help the body's power of activity (III. xii.); in other words (III. xii. note), those things which it loves. But conception is helped by those things which postulate the existence of a thing, and contrariwise is hindered by those which exclude the existence of a thing (II. xvii.); therefore the images of things, which postulate the existence of an object of love, help the mind's endeavour to conceive the object of love, in other words (III. xi. note), affect the mind pleasurably; contrariwise those things, which exclude the existence of an object of love, hinder the aforesaid mental endeavour; in other words, affect the mind painfully. He, therefore, who conceives that the object of his love is destroyed will feel pain, &c. Q.E.D.
XX. He who conceives that the object of his hate is destroyed will also feel pleasure.
>>>>>Proof—The mind (III. xiii.) endeavours to conceive those things, which exclude the existence of things whereby the body's power of activity is diminished or constrained; that is (III. xiii. note), it endeavours to conceive such things as exclude the existence of what it hates; therefore the image of a thing, which excludes the existence of what the mind hates, helps the aforesaid mental effort, in other words (III. xi. note), affects the mind pleasurably. Thus he who conceives that the object of his hate is destroyed will feel pleasure. Q.E.D.
XXI. He who conceives, that the object of his love is affected pleasurably or painfully, will himself be affected pleasurably or painfully; and the one or the other emotion will be greater or less in the lover according as it is greater or less in the thing loved.
>>>>>Proof—The images of things (as we showed in III. xix.) which postulate the existence of the object of love, help the mind's endeavour to conceive the said object. But pleasure postulates the existence of something feeling pleasure, so much the more in proportion as the emotion of pleasure is greater; for it is (III. xi. note) a transition to a greater perfection; therefore the image of pleasure in the object of love helps the mental endeavour of the lover; that is, it affects the lover pleasurably, and so much the more, in proportion as this emotion may have been greater in the object of love. This was our first point. Further, in so far as a thing is affected with pain, it is to that extent destroyed, the extent being in proportion to the amount of pain (III. xi. note); therefore (III. xix.) he who conceives, that the object of his love is affected painfully, will himself be affected painfully, in proportion as the said emotion is greater or less in the object of love. Q.E.D.
XXII. If we conceive that anything pleasurably affects some object of our love, we shall be affected with love towards that thing. Contrariwise, if we conceive that it affects an object of our love painfully, we shall be affected with hatred towards it.
>>>>>Proof—He, who affects pleasurably or painfully the object of our love, affects us also pleasurably or painfully—that is, if we conceive the loved object as affected with the said pleasure or pain (III. xxi.). But this pleasure or pain is postulated to come to us accompanied by the idea of an external cause; therefore (III. xiii. note), if we conceive that anyone affects an object of our love pleasurably or painfully, we shall be affected with love or hatred towards him. Q.E.D.
*****Note—Prop. xxi. explains to us the nature of 'Pity,' which we may define as 'pain arising from another's hurt.' What term we can use for pleasure arising from another's gain, I know not.
We will call the 'love towards him who confers a benefit on another,' 'Approval;' and the 'hatred towards him who injures another,' we will call 'Indignation.' We must further remark, that we not only feel pity for a thing which we have loved (as shown in III. xxi.), but also for a thing which we have hitherto regarded without emotion, provided that we deem that it resembles ourselves (as I will show presently). Thus, we bestow approval on one who has benefited anything resembling ourselves, and, contrariwise, are indignant with him who has done it an injury.