Ethics, part 1 | Page 4

the difference of their modifications--as substance is naturally prior to its modifications (Prop. i.)--it follows that setting the modifications aside, and considering substance in itself, that is truly, (Deff. iii and vi.), there cannot be conceived one substance different from another--that is (by Prop. iv.), there cannot be granted several substances, but one substance only. Q.E.D.
VI. One substance cannot be produced by another substance.
>>>>>Proof--It is impossible that there should be in the universe two substances with an identical attribute, i.e. which have anything common to them both (Prop ii.), and, therefore (Prop. iii.), one cannot be the cause of the other, neither can one be produced by the other. Q.E.D.
<<<< VII. Existence belongs to the nature of substances.
>>>>>Proof--Substance cannot be produced by anything external (Cor., Prop vi.), it must, therefore, be its own cause--that is, its essence necessarily involves existence, or existence belongs to its nature.
VIII. Every substance is necessarily infinite.
>>>>>Proof--There can only be one substance with an identical attribute, and existence follows from its nature (Prop. vii.); its nature, therefore, involves existence, either as finite or infinite. It does not exist as finite, for (by Deff. ii.) it would then be limited by something else of the same kind, which would also necessarily exist (Prop. vii.); and there would be two substances with an identical attribute, which is absurd (Prop. v.). It therefore exists as infinite. Q.E.D.
*****Note I.--As finite existence involves a partial negation, and infinite existence is the absolute affirmation of the given nature, it follows (solely from Prop. vii.) that every substance is necessarily infinite.
*****Note II.--No doubt it will be difficult for those who think about things loosely, and have not been accustomed to know them by their primary causes, to comprehend the demonstration of Prop. vii.: for such persons make no distinction between the modifications of substances and the substances themselves, and are ignorant of the manner in which things are produced; hence they may attribute to substances the beginning which they observe in natural objects. Those who are ignorant of true causes make complete confusion--think that trees might talk just as well as men--that men might be formed from stones as well as from seed; and imagine that any form might be changed into any other. So, also, those who confuse the two natures, divine and human, readily attribute human passions to the deity, especially so long as they do not know how passions originate in the mind. But, if people would consider the nature of substance, they would have no doubt about the truth of Prop. vii. In fact, this proposition would be a universal axiom, and accounted a truism. For, by substance, would be understood that which is in itself, and is conceived through itself--that is, something of which the conception requires not the conception of anything else; whereas modifications exist in something external to themselves, and a conception of them is formed by means of a conception of the things in which they exist. Therefore, we may have true ideas of non-existent modifications; for, although they may have no actual existence apart from the conceiving intellect, yet their essence is so involved in something external to themselves that they may through it be conceived. Whereas the only truth substances can have, external to the intellect, must consist in their existence, because they are conceived through themselves. Therefore, for a person to say that he has a clear and distinct--that is, a true--idea of a substance, but that he is not sure whether such substance exists, would be the same as if he said that he had a true idea, but was not sure whether or no it was false (a little consideration will make this plain); or if anyone affirmed that substance is created, it would be the same as saying that a false idea was true--in short, the height of absurdity. It must, then, necessarily be admitted that the existence of substance as its essence is an eternal truth. And we can hence conclude by another process of reasoning--that there is but one such substance. I think that this may profitably be done at once; and, in order to proceed regularly with the demonstration, we must premise:--
+++++1. The