E3P56D
Demonstration — Part III
Latin
Lætitia et tristitia et consequenter affectus qui ex his componuntur vel ex his derivantur, passiones sunt (per scholium propositionis 11 hujus); nos autem (per propositionem 1 hujus) necessario patimur quatenus ideas habemus inadæquatas et quatenus easdem habemus (per propositionem 3 hujus) eatenus tantum patimur hoc est (vide scholium I propositionis 40 partis II) eatenus tantum necessario patimur quatenus imaginamur sive (vide propositionem 17 partis II cum ejus scholio) quatenus afficimur affectu qui naturam nostri corporis et naturam corporis externi involvit. Natura igitur uniuscujusque passionis ita necessario debet explicari ut objecti a quo afficimur, natura exprimatur. Nempe lætitia quæ ex objecto exempli gratia A oritur, naturam ipsius objecti A et lætitia quæ ex objecto B oritur, ipsius objecti B naturam involvit atque adeo hi duo lætitiæ affectus natura sunt diversi quia ex causis diversæ naturæ oriuntur. Sic etiam tristitiæ affectus qui ex uno objecto oritur, diversus natura est a tristitia quæ ab alia causa oritur, quod etiam de amore, odio, spe, metu, animi fluctuatione etc. intelligendum est ac proinde lætitiæ, tristitiæ, amoris, odii etc. tot species necessario dantur quot sunt species objectorum a quibus afficimur. At cupiditas est ipsa uniuscujusque essentia seu natura quatenus ex data quacunque ejus constitutione determinata concipitur ad aliquid agendum (vide scholium propositionis 9 hujus); ergo prout unusquisque a causis externis hac aut illa lætitiæ, tristitiæ, amoris, odii etc. specie afficitur hoc est prout ejus natura hoc aut alio modo constituitur, ita ejus cupiditas alia atque alia esse et natura unius a natura alterius cupiditatis tantum differre necesse est quantum affectus a quibus unaquæque oritur, inter se differunt. Dantur itaque tot species cupiditatis quot sunt species lætitiæ, tristitiæ, amoris etc. et consequenter (per jam ostensa) quot sunt objectorum species a quibus afficimur. Q.E.D.
English (Elwes 1883)
Pleasure and pain, and consequently the emotions compounded thereof, or derived therefrom, are passions, or passive states (III. xi. note); now we are necessarily passive (III. i.), in so far as we have inadequate ideas; and only in so far as we have such ideas are we passive (III. iii.); that is, we are only necessarily passive (II. xl. note), in so far as we conceive, or (II. xvii. and note) in so far as we are affected by an emotion, which involves the nature of our own body, and the nature of an external body. Wherefore the nature of every passive state must necessarily be so explained, that the nature of the object whereby we are affected be expressed. Namely, the pleasure, which arises from, say, the object A, involves the nature of that object A, and the pleasure, which arises from the object B, involves the nature of the object B; wherefore these two pleasurable emotions are by nature different, inasmuch as the causes whence they arise are by nature different. So again the emotion of pain, which arises from one object, is by nature different from the pain arising from another object, and, similarly, in the case of love, hatred, hope, fear, vacillation, &c.
Thus, there are necessarily as many kinds of pleasure, pain, love, hatred, &c., as there are kinds of objects whereby we are affected. Now desire is each man's essence or nature, in so far as it is conceived as determined to a particular action by any given modification of itself (III. ix. note); therefore, according as a man is affected through external causes by this or that kind of pleasure, pain, love, hatred, &c., in other words, according as his nature is disposed in this or that manner, so will his desire be of one kind or another, and the nature of one desire must necessarily differ from the nature of another desire, as widely as the emotions differ, wherefrom each desire arose. Thus there are as many kinds of desire, as there are kinds of pleasure, pain, love, &c., consequently (by what has been shown) there are as many kinds of desire, as there are kinds of objects whereby we are affected. Q.E.D.
Modern English
Joy and sadness, and consequently the affects composed from or derived from them, are passions (E3P11S). Now we are necessarily passive (E3P1) insofar as we have inadequate ideas, and only insofar as we have them (E3P3), that is, (E2P40S1), we are necessarily passive only insofar as we imagine, or (E2P17S) insofar as we are affected by an affect involving the nature of our body and the nature of an external body. Therefore the nature of every passion must be explained in such a way that the nature of the object by which we are affected is expressed.
The joy that arises from object A, for instance, involves the nature of that object A, and the joy that arises from object B involves the nature of object B. These two affects of joy are therefore different in nature, because they arise from causes of different natures. Likewise, a sadness arising from one object differs in nature from sadness arising from another cause. The same holds for love, hatred, hope, fear, vacillation of mind, and so forth. So there are necessarily as many species of joy, sadness, love, hatred, and so on as there are species of objects by which we are affected.Desire, meanwhile, is the very essence or nature of each person insofar as it is conceived as determined to act in a particular way by any given constitution (E3P9S). Therefore, as each person is affected by external causes with this or that species of joy, sadness, love, hatred, and so forth, that is, as his nature is constituted in one way or another, so his desire must be different, and the nature of one desire must differ from the nature of another as much as the affects from which each arises differ from each other. There are therefore as many species of desire as there are species of joy, sadness, love, and so forth, and consequently, by what has just been shown, as many species as there are species of objects by which we are affected. Q.E.D.