Prop. XXXI. In so far as a thing is in harmony with our nature, it is necessarily good.

Proof.—In so far as a thing is in harmony with our nature, it cannot be bad for it. It will therefore necessarily be either good or indifferent. If it be assumed that it be neither good nor bad, nothing will follow from its nature (IV. Def. i.), which tends to the preservation of our nature, that is (by the hypothesis), which tends to the preservation of the thing itself ; but this (III. vi.) is absurd ; therefore, in so far as a thing is in harmony with our nature, it is necessarily good. Q.E.D.

Corollary.—Hence it follows, that, in proportion as a thing is in harmony with our nature, so is it more useful or better for us, and vice versâ, in proportion as a thing is more useful for us, so is it more in harmony with our nature. For, in so far as it is not in harmony with our nature, it will necessarily be different therefrom or contrary thereto. If different, it can neither be good nor bad (IV. xxix.); if contrary, it will be contrary to that which is in harmony with our nature, that is, contrary to what is good-in short, bad. Nothing, therefore, can be good, except in so far as it is in harmony with our nature; and hence a thing is useful, in proportion as it is in harmony with our nature, and vice versâ. Q.E.D.

Prop. XXXII. In so far as men are a prey to passion, they cannot, in that respect, be said to be naturally in harmony.

Proof.—Things, which are said to be in harmony naturally, are understood to agree in power (III. vii.), not in want of power or negation, and consequently not in passion (III. iii. note); wherefore men, in so far as they are a prey to their passions, cannot be said to be naturally in harmony. Q.E.D.

Note.—This is also self-evident; for, if we say that white and black only agree in the fact that neither is red, we absolutely affirm that they do not agree in any respect. So, if we say that a man and a stone only agree in the fact that both are finite—wanting in power, not existing by the necessity of their own nature, or, lastly, indefinitely surpassed by the power of external causes—we should certainly affirm that a man and a stone are in no respect alike ; therefore, things which agree only in negation, or in qualities which neither possess, really agree in no respect.

Prop. XXXIII. Men can differ in nature, in so far as they are assailed by those emotions, which are passions, or passive states; and to this extent one and the same man is variable and inconstant.

Proof.—The nature or essence of the emotions cannot be explained solely through our essence or nature (III. Deff. i., ii.), but it must be defined by the power, that is (III. vii.), by the nature of external causes in comparison with our own; hence it follows, that there are as many kinds of each emotion as there are external objects whereby we are affected (III. lvi.), and that men may be differently affected by one and the same object (III. li.), and to this extent differ in nature; lastly, that one and the same man may be differently affected towards the same object, and may therefore be variable and inconstant. Q.E.D.