Ethics, Part III, Proposition 38
If a man has begun to hate an object of his love, so that love is thoroughly destroyed, he will, causes being equal, regard it with more hatred than if he had never loved it, and his hatred will be in proportion to the strength of his former love.
Proof
If a man begins to hate that which he had loved, more of his appetites are put under restraint than if he had never loved it. For love is a pleasure (III. xiii. note) which a man endeavours as far as he can to render permanent (III. xxviii.); he does so by regarding the object of his love as present, and by affecting it as far as he can pleasurably; this endeavour is greater in proportion as the love is greater, and so also is the endeavour to bring about that the beloved should return his affection (III. xxxiii.). Now these endeavours are constrained by hatred towards the object of love (III. xiii. Coroll. and III. xxiii.); wherefore the lover (III. xi. note) will for this cause also be affected with pain, the more so in proportion as his love has been greater; that is, in addition to the pain caused by hatred, there is a pain caused by the fact that he has loved the object; wherefore the lover will regard the beloved with greater pain, or in other words, will hate it more than if he had never loved it, and with the more intensity in proportion as his former love was greater. Q.E.D.
Benedict de Spinoza, The Ethics (Ethica Ordine Geometrico Demonstrata), translated from the Latin by R. H. M. Elwes.
First published in The Chief Works of Benedict de Spinoza, vol. II (London: George Bell and Sons, 1884).
This translation is out of copyright in the United States, where it was published in 1884, and wherever the copyright term is the author's life plus 100 years or less; its translator died in 1892.
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Digital text: Project Gutenberg eBook #3800