>>>>>Proof—This is evident from III. xvi.
XLVII. Joy arising from the fact, that anything we hate is destroyed, or suffers other injury, is never unaccompanied by a certain pain in us.
>>>>>Proof—This is evident from III. xxvii. For in so far as we conceive a thing similar to ourselves to be affected with pain, we ourselves feel pain.
*****Note—This proposition can also be proved from the Corollary to II. xvii. Whenever we remember anything, even if it does not actually exist, we regard it only as present, and the body is affected in the same manner; wherefore, in so far as the remembrance of the thing is strong, a man is determined to regard it with pain; this determination, while the image of the thing in question lasts, is indeed checked by the remembrance of other things excluding the existence of the aforesaid thing, but is not destroyed: hence, a man only feels pleasure in so far as the said determination is checked: for this reason the joy arising from the injury done to what we hate is repeated, every time we remember that object of hatred. For, as we have said, when the image of the thing in question, is aroused, inasmuch as it involves the thing's existence, it determines the man to regard the thing with the same pain as he was wont to do, when it actually did exist. However, since he has joined to the image of the thing other images, which exclude its existence, this determination to pain is forthwith checked, and the man rejoices afresh as often as the repetition takes place. This is the cause of men's pleasure in recalling past evils, and delight in narrating dangers from which they have escaped. For when men conceive a danger, they conceive it as still future, and are determined to fear it; this determination is checked afresh by the idea of freedom, which became associated with the idea of the danger when they escaped therefrom: this renders them secure afresh: therefore they rejoice afresh.
XLVIII. Love or hatred towards, for instance, Peter is destroyed, if the pleasure involved in the former, or the pain involved in the latter emotion, be associated with the idea of another cause: and will be diminished in proportion as we conceive Peter not to have been the sole cause of either emotion.
>>>>>Proof—This Prop. is evident from the mere definition of love and hatred (III. xiii. note). For pleasure is called love towards Peter, and pain is called hatred towards Peter, simply in so far as Peter is regarded as the cause of one emotion or the other. When this condition of causality is either wholly or partly removed, the emotion towards Peter also wholly or in part vanishes. Q.E.D.
XLIX. Love or hatred towards a thing, which we conceive to be free, must, other conditions being similar, be greater than if it were felt towards a thing acting by necessity.
>>>>>Proof—A thing which we conceive as free must (I. Def. vii.) be perceived through itself without anything else. If, therefore, we conceive it as the cause of pleasure or pain, we shall therefore (III. xiii. note) love it or hate it, and shall do so with the utmost love or hatred that can arise from the given emotion. But if the thing which causes the emotion be conceived as acting by necessity, we shall then (by the same Def. vii. Part I.) conceive it not as the sole cause, but as one of the causes of the emotion, and therefore our love or hatred towards it will be less. Q.E.D.
*****Note—Hence it follows, that men, thinking themselves to be free, feel more love or hatred towards one another than towards anything else: to this consideration we must add the imitation of emotions treated of in III. xxvii., xxxiv., xl. and xliii.
L. Anything whatever can be, accidentally, a cause of hope or fear.