E2P13D
Demonstration — Part II
Latin
Si enim corpus non esset humanæ mentis objectum, ideæ affectionum corporis non essent in Deo (per corollarium propositionis 9 hujus) quatenus mentem nostram sed quatenus alterius rei mentem constitueret hoc est (per corollarium propositionis 11 hujus) ideæ affectionum corporis non essent in nostra mente; atqui (per axioma 4 hujus) ideas affectionum corporis habemus. Ergo objectum ideæ humanam mentem constituentis est corpus idque (per propositionem 11 hujus) actu existens. Deinde si præter corpus etiam aliud esset mentis objectum, cum nihil (per propositionem 36 partis I) existat ex quo aliquis effectus non sequatur, deberet (per propositionem 12 hujus) necessario alicujus ejus effectus idea in mente nostra dari; atqui (per axioma 5 hujus) nulla ejus idea datur. Ergo objectum nostræ mentis est corpus existens et nihil aliud. Q.E.D.
English (Elwes 1883)
If indeed the body were not the object of the human mind, the ideas of the modifications of the body would not be in God (II. ix. Coroll.) in virtue of his constituting our mind, but in virtue of his constituting the mind of something else; that is (II. xi. Coroll.) the ideas of the modifications of the body would not be in our mind: now (by II. Ax. iv.) we do possess the idea of the modifications of the body. Therefore the object of the idea constituting the human mind is the body, and the body as it actually exists (II. xi.). Further, if there were any other object of the idea constituting the mind besides body, then, as nothing can exist from which some effect does not follow (I. xxxvi.) there would necessarily have to be in our mind an idea, which would be the effect of that other object (II. xi.); but (I. Ax. v.) there is no such idea. Wherefore the object of our mind is the body as it exists, and nothing else. Q.E.D.
Modern English
If the body were not the object of the human mind, then the ideas of the body's affections would not be in God (E2P9C) insofar as he constitutes our mind, but insofar as he constitutes the mind of something else, that is, (E2P11C), the ideas of the body's affections would not be in our mind. But (E2A4) we do have ideas of the body's affections. Therefore the object of the idea constituting the human mind is the body, and the body (E2P11) as it actually exists. Further, if there were some other object of the mind besides the body, then since nothing exists from which no effect follows (E1P36), there would necessarily have to be in our mind an idea that is the effect of that other object (E2P12); but (E2A5) no such idea is given. Therefore the object of our mind is the body as it actually exists, and nothing else. Q.E.D.