Propositions 1 to 8
5 minutes • 930 words
Substance is by nature prior to its modifications.
Two substances, whose attributes are different, have nothing in common.
- For each must exist in itself, and be conceived through itself.
- In other words, the conception of one does not imply the conception of the other.
- Things which have nothing in common cannot be one the cause of the other.
Proof: If they have nothing in common, it follows that one cannot be apprehended by means of the other (Axiom 5).
- Therefore, one cannot be the cause of the other (Axiom 4). Q.E.D.
- Two or more distinct things are distinguished one from the other, either:
- by the difference of the attributes of the substances, or
- the difference of their modifications.
Proof: Everything which exists, exists either in itself or in something else (Axiom 1).
- Nothing is granted (by Def.3 and 5.) in addition to the understanding, except substance and its modifications.
- Therefore, nothing is given besides the understanding.
- The understanding allows several things to be distinguished from the other, except the substances.
- Two or more substances cannot have the same nature or attribute.
Proof: Distinct substances must be distinguished from the other, either:
- by the difference of their attributes, or
- In this case, an identical attribute can only exist in one.
- by the difference of their modifications (Prop. 4).
- In this case, since substance is naturally prior to its modifications (Prop. 1) then, setting the modifications aside, and considering substance in itself, (Def. 3. and 6), we cannot conceive one substance different from another
- This means there is only 1 subtance
- One substance cannot be produced by another substance.
Proof: It is impossible for 2 substances to have an identical attribute (Prop. 2).
- Therefore (Prop. 3), one cannot be the cause of the other, neither can one be produced by the other. Q.E.D.
Corollary: It follows that a substance cannot be produced by anything external to itself.
- This is because, in the universe, nothing is granted other than substances and their modifications. This is from Axiom 1 and Def. 3 and 5.
By the last Proposition, substance cannot be produced by another substance.
- Therefore, it cannot be produced by anything external to itself. Q.E.D.
- If substance were produced by an external cause, the knowledge of it would depend on the knowledge of its cause (Axiom 4), and (by Def. 3) it would itself not be substance.
- Existence belongs to the nature of substances.
Proof: Substance cannot be produced by anything external (Corollary, Prop 6).
- Therefore, it must be its own cause.
- Its essence necessarily involves existence, or existence belongs to its nature.
- Every substance is necessarily infinite.
Proof: There can only be 1 substance with an identical attribute.
- Existence follows from its nature (Prop. 7).
Therefore, its nature involves existence, either as finite or infinite.
- If it were finite then (by Def. 2) it would then be limited by something else of the same kind.
- This would mean there would be 2 substances with an identical attribute, which is absurd (Prop. 5).
Therefore it exists as infinite. Q.E.D.
- Finite existence involves a partial negation.
- Infinite existence is the absolute affirmation of the given nature.
It follows (solely from Prop. 7) that every substance is necessarily infinite.
People who think about things loosely, and have not been used to know them by their primary causes will find it difficult to comprehend the demonstration of Prop. 7.
- make no distinction between the modifications of substances and the substances themselves, and
- are ignorant of how 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. They think that:
- trees might talk just as well as men
- men might be formed from stones as well as from seed
- any form might be changed into any other.
So, also, those who confuse the 2 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 considered the nature of substance, they would have no doubt about the truth of Prop. 7.
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. It 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 thing 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.