XIII. When the mind conceives things which diminish or hinder the body's power of activity, it endeavours, as far as possible, to remember things which exclude the existence of the first-named things.

>>>>>Proof—So long as the mind conceives anything of the kind alluded to, the power of the mind and body is diminished or constrained (cf. III. xii. Proof); nevertheless it will continue to conceive it, until the mind conceives something else, which excludes the present existence thereof (II. xvii.); that is (as I have just shown), the power of the mind and of the body is diminished, or constrained, until the mind conceives something else, which excludes the existence of the former thing conceived: therefore the mind (III. ix.), as far as it can, will endeavour to conceive or remember the latter. Q.E.D.

<<<<<Corollary—Hence it follows that the mind shrinks from conceiving those things, which diminish or constrain the power of itself and of the body.

*****Note—From what has been said we may clearly understand the nature of Love and Hate. "Love" is nothing else but "pleasure accompanied by the idea of an external cause." We further see, that he who loves necessarily endeavours to have, and to keep present to him, the object of his love; while he who hates endeavours to remove and destroy the object of his hatred. But I will treat of these matters at more length hereafter.

XIV. If the mind has once been affected by two emotions at the same time, it will, whenever it is afterwards affected by one of these two, be also affected by the other.

>>>>>Proof—If the human body has once been affected by two bodies at once, whenever afterwards the mind conceives one of them, it will straightway remember the other also (II. xviii.). But the mind's conceptions indicate rather the emotions of our body than the nature of external bodies (II. xvi. Cor. ii.); therefore, if the body, and consequently the mind (III. Def. iii.) has been once affected by two emotions at the same time, it will, whenever it is afterwards affected by one of the two, be also affected by the other.

XV. Anything can, accidentally, be the cause of pleasure, pain, or desire.

>>>>>Proof—Let it be granted that the mind is simultaneously affected by two emotions, of which one neither increases nor diminishes its power of activity, and the other does either increase or diminish the said power (III. Post. i.). From the foregoing proposition it is evident that, whenever the mind is afterwards affected by the former, through its true cause, which (by hypothesis) neither increases nor diminishes its power of action, it will be at the same time affected by the latter, which does increase or diminish its power of activity, that is (III. xi. note) it will be affected with pleasure or pain. Thus the former of the two emotions will, not through itself, but accidentally, be the cause of pleasure or pain. In the same way also it can be easily shown, that a thing may be accidentally the cause of desire. Q.E.D.

<<<<<Corollary—Simply from the fact that we have regarded a thing with the emotion of pleasure or pain, though that thing be not the efficient cause of the emotion, we can either love or hate it.

>>>>>Proof—For from this fact alone it arises (III. xiv.), that the mind afterwards conceiving the said thing is affected with the emotion of pleasure or pain, that is (III. xi. note), according as the power of the mind and body may be increased or diminished, &c.; and consequently (III. xii.), according as the mind may desire or shrink from the conception of it (III. xiii. Cor.), in other words (III. xiii. note), according as it may love or hate the same. Q.E.D.