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Short Treatise on God, Man, and His Well-Being:
Appendix 1.
- ON GOD.

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AXIOMS
1. Substance is, by its nature, prior to all its modifications.
2. Things which are different are distinguished either realiter or modaliter.
3. Things which are distinguished realiter either have different attributes, such as Thought and Extension, or are referred to different attributes, as in the case of Understanding and Motion; one of which belongs to Thought, and the other to Extension.
4. Things which have different attributes, as also the things which belong to different attributes, do not have anything the one of the other.
5. That which has not in itself something of another thing, can also not be a cause of the existence of such another thing.
6. It is impossible that that which is a cause of itself should have limited itself.
7. That by which the things are sustained is by its nature prior to [N1] such things.
[Note N1]: A: the first (prior) in; B: prior to.

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PROPOSITION 1
    To no substance that exists can one and the same attribute be ascribed that is ascribed to another substance; or (which is the same) in Nature there cannot be two substances, unless they are distinguished realiter.[N1]
[Note N1]: B: ...in Nature there cannot be posited two substances of one and the same nature.

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PROOF
    If there are two substances, then they are distinct; and consequently (Axiom 2) [N1] they are distinguished either realiter or modaliter; not modaliter, for in that case the modes would by their nature be prior to the substance, which is contrary to the first axiom; therefore, realiter; and consequently, what is predicated of the one cannot be predicated of the other, which is what we intended to prove.
[Note N1]: A gives the references to Axioms and Propositions in the margin; B, in the text.

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PROPOSITION 2
    One substance cannot be the cause of the existence of another substance.

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PROOF
    Such a cause cannot contain in itself anything of such an effect (Prop. 1); because the difference between them is real, and therefore it cannot (Axiom 5) produce it.[N1]
[Note N1]: A adds: (existence); B: ...and therefore the one cannot produce the other.

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PROPOSITION 3
    Every attribute or substance [N1] is by nature infinite, and supremely perfect in its kind.
[Note N1]: A: all attributes or substance; B: all substance or its attributes.

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PROOF
    No substance is produced by another (Prop. 2) and consequently, if it exists, it is either an attribute of God, or it has been its own cause outside God. If the first, then it is necessarily infinite, and supremely perfect in its kind, such as are all other attributes of God. If the second, then it is also necessarily such because (Axiom 6) it could not have limited itself.

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PROPOSITION 4
    To such an extent does existence pertain by nature to the essence of every substance,[N1] that it is impossible to posit in an infinite understanding the Idea of the essence of a substance that does not exist in Nature.
[Note N1]: A: to every essence of substance; B: to the essence of a substance.

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PROOF
    The true essence of an object[N1] is something which is realiter different from the Idea of the same object; and this something exists (Axiom 3) either realiter, or is contained in some other thing which exists realiter; from which other thing this essence cannot be distinguished realiter, but only modaliter; such are all the essences of the things [N2] which we see, which before they yet existed were already contained in extension, motion, and rest, and when they do exist are not distinguished from extension realiter, but only modaliter. Moreover, it would involve self-contradiction to suppose that the essence of a substance[N3] is contained thus in some other thing; because in that case it could not be distinguished from this realiter, contrary to the first proposition; also, it could in that case be produced by the subject which contains it, contrary to the second proposition; and lastly, it could not by its nature be infinite and supremely perfect in its kind, contrary to the third proposition. Therefore, as its essence is not contained in any other thing, it must be a thing that exists through itself.
[Note N1]: B: . . of the object of an idea.

[Note N2]: B: essences or things.

[Note N3]: A: that an essence of the substance; B: that an essence of substance.

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COROLLARY
    Nature is known through itself, and not through any other thing. It consists of infinite attributes every one of them infinite and perfect in its kind; to its essence pertains existence, so that outside it there is no other essence or existence, and it thus coincides exactly with the essence of God who alone is glorious and blessed.
 
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