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Ethics, Demonstrated in Geometrical Order
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.
PROP. 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.
PROP. XXIII. He who conceives, that an object of his hatred is painfully affected, will feel pleasure. Contrariwise, if he thinks that the said object is pleasurably affected, he will feel pain. Each of these emotions will be greater or less, according as its contrary is greater or less in the object of hatred.

Proof.—In so far as an object of hatred is painfully affected, it is destroyed, to an extent proportioned to the strength of the pain (III. xi. note). Therefore, he (III. xx.) who conceives, that some object of his hatred is painfully affected, will feel pleasure, to an extent proportioned to the amount of pain he conceives in the object of his hatred. This was our first point. Again, pleasure Postulates the existence of the pleasurably affected thing (III. xi. note), in proportion as the pleasure is greater or less. If anyone imagines that an object of his hatred is pleasurably affected, this conception (III. xiii.) will hinder his own endeavour to persist; in other words (III. xi. note), he who hates will be painfully affected. Q.E.D.

Note.—This pleasure can scarcely be felt unalloyed, and without any mental conflict. For (as I am about to show in Prop. xxvii.), in so far as a man conceives that something similar to himself is affected by pain, he will himself be affected in like manner; and he will have the contrary emotion in contrary circumstances. But here we are regarding hatred only.
PROP. XXIV. If we conceive that anyone pleasurably affects an object of our hate, we shall feel hatred towards him also. If we conceive that he painfully affects that said object, we shall feel love towards him.
Proof.—This proposition is proved in the same way as III. xxii., which see.
Note.—These and similar emotions of hatred are attributable to envy, which, accordingly, is nothing else but hatred, in so far as it is regarded as disposing a man to rejoice in another’s hurt, and to grieve at another’s advantage.
PROP. XXV. We endeavour to affirm, concerning ourselves, and concerning what we love, everything that we can conceive to affect pleasurably ourselves, or the loved object. Contrariwise, we endeavour to negative everything, which we conceive to affect painfully ourselves or the loved object.
Proof.—That, which we conceive to affect an object of our love pleasurably or painfully, affects us also pleasurably or painfully (III. xxi.). But the mind (III. xii.) endeavours, as far as possible, to conceive those things which affect us pleasurably; in other words (II. xvii. and Coroll.), it endeavours to regard them as present. And, contrariwise (III. xiii.), it endeavours to exclude the existence of such things as affect us painfully; therefore, we endeavour to affirm concerning ourselves, and concerning the loved object, whatever we conceive to affect ourselves, or the love object pleasurably. Q.E.D.
PROP. XXVI. We endeavour to affirm, concerning that which we hate, everything which we conceive to affect it painfully; and, contrariwise, we endeavour to deny, concerning it, everything which we conceive to affect it pleasurably.

Proof.—This proposition follows from III. xxiii., as the foregoing proposition followed from III. xxi.
Note.—Thus we see that it may readily happen, that a man may easily think too highly of himself, or a loved object, and, contrariwise, too meanly of a hated object. This feeling is called pride, in reference to the man who thinks too highly of himself, and is a species of madness, wherein a man dreams with his eyes open, thinking that he can accomplish all things that fall within the scope of his conception, and thereupon accounting them real, and exulting in them, so long as he is unable to conceive anything which excludes their existence, and determines his own power of action. Pride, therefore, is pleasure springing from a man thinking too highly of himself. Again, the pleasure which arises from a man thinking too highly of another is called over—esteem. Whereas the pleasure which arises from thinking too little of a man is called disdain.
PROP. XXVII. By the very fact that we conceive a thing, which is like ourselves, and which we have not regarded with any emotion, to be affected with any emotion, we are ourselves affected with a like emotion (affectus).

Proof.—The images of things are modifications of the human body, whereof the ideas represent external bodies as present to us (II. xvii.); in other words (II. x.), whereof the ideas involve the nature of our body, and, at the same time, the nature of the external bodies as present. If, therefore, the nature of the external body be similar to the nature of our body, then the idea which we form of the external body will involve a modification of our own body similar to the modification of the external body. Consequently, if we conceive anyone similar to ourselves as affected by any emotion, this conception will express a modification of our body similar to that emotion. Thus, from the fact of conceiving a thing like ourselves to be affected with any emotion, we are ourselves affected with a like emotion. If, however, we hate the said thing like ourselves, we shall, to that extent, be affected by a contrary, and not similar, emotion. Q.E.D.

Note I.—This imitation of emotions, when it is referred to pain, is called compassion (cf. III. xxii. note); when it is referred to desire, it is called emulation, which is nothing else but the desire of anything, engendered in us by the fact that we conceive that others have the like desire.
Corollary I.—If we conceive that anyone, whom we have hitherto regarded with no emotion, pleasurably affects something similar to ourselves, we shall be affected with love towards him. If, on the other hand, we conceive that he painfully affects the same, we shall be affected with hatred towards him.
Proof.—This is proved from the last proposition in the same manner as III. xxii. is proved from III. xxi.
Corollary II.—We cannot hate a thing which we pity, because its misery affects us painfully.
Proof.—If we could hate it for this reason, we should rejoice in its pain, which is contrary to the hypothesis.
Corollary III.—We seek to free from misery, as far as we can, a thing which we pity.

Proof.—That, which painfully affects the object of our pity, affects us also with similar pain (by the foregoing proposition); therefore, we shall endeavour to recall everything which removes its existence, or which destroys it (cf. III. xiii.); in other words (III. ix. note), we shall desire to destroy it, or we shall be determined for its destruction; thus, we shall endeavour to free from misery a thing which we pity. Q.E.D.
Note II.—This will or appetite for doing good, which arises from pity of the thing whereon we would confer a benefit, is called benevolence, and is nothing else but desire arising from compassion. Concerning love or hate towards him who has done good or harm to something, which we conceive to be like ourselves, see III. xxii. note.
PROP. XXVIII. We endeavour to bring about whatsoever we conceive to conduce to pleasure; but we endeavour to remove or destroy whatsoever we conceive to be truly repugnant thereto, or to conduce to pain.

Proof.—We endeavour, as far as possible, to conceive that which we imagine to conduce to pleasure

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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