God is the only Substance that Exists
Spinoza defines God as follows:
"By God I mean an absolutely infinite being, that is, substance consisting of infinite attributes, each of which expresses eternal and infinite essence"
This is simply a definition of God, but Spinoza will demonstrate that God exists and is the only substance.
Here is the argument. First, the propositions out of which it is constructed.
Proposition 4: "Two [substances]... are distinguished from one another either by... attributes... or by... [modes]" (p. 159)
Proposition 5: "there cannot be two or more substances of the same nature or attribute" (p. 159)
Proposition 7: "Existence belongs to the nature of substance" (p. 160)
Proposition 8: "Every substance is necessarily infinite." (p. 160)
Proposition 9: "The more reality or being a thing has, the more attributes it has." (p. 161)
Propsotion 11: "God, or substance consisting of infinite attributes, each of which expresses eternal and infinite essence, necessarily exists." (p. 162)
Proposition 14: "There can be, or be conceived, no other substance but God." (p. 163)
I will put this argument in a slightly different form.
(1) Every substance has a nature or essence.
(2) Attributes are what are perceived to constitute natures or essences.
(3) There cannot exist two substances that have the same nature or essence.
(4) So, there cannot exist two substances that have the same attribute.
(5) A substance having more than one attribute is possible, depending on its nature or essence.
(6) The more reality a substance has, the more attributes it has.
(7) An infinite substance is a substance that has an infinite nature or essence.
(8) So, an infinite substance is a substance that has an infinite number of attributes.
(9) An infinite substance is a substance that has all possible attributes.
(10) An infinite substance is a substance that is the most real substance.
(11) An infinite substance is possible.
(12) A substance other than an infinite substance would have to have a nature or essence.
(13) A substance other than an infinite substance would have to have an attribute.
(14) Since an infinite substance is a substance that has all possible attributes, if there exists an infinite substance, then there is no attribute left for a substance other than an infinite substance to have.
(15) So, if there exists an infinite substance, it is the only substance that exists.
(16) It belongs to the nature of substance to exist.
(17) Every substance is infinite substance.
(18) So, an infinite substance does exist.
(19) God is the name of the one infinite substance.
–––> God, or the one infinite substance, exists, and is the only substance that exists.
-----> "There can be, or be conceived, no other substance but God." (p. 527)
This is the position of Substance Monism (i.e. there is only one substance). Since, according to Spinoza, the single substance that exists is infinite substance, or God, his position is simply the position that only God exists. There is only one substance, but it is an infinite one.
This is Spinoza's claim that there is only one, "Deus, sive Natura" (God, or Nature). In fact, there can only be one (Highlander fans, take note.)
Infinite substance, or God, is one. It is indivisible, or has no parts.
(12) "No attribute of substance can be truly conceived from which it would follow that substance can be divided." (p. 163)
(13) "Absolutely infinite substance is indivisible." (p. 163)
It is eternal, or has no beginning and no end (it has no duration).
Proposition 19: "God [is eternal], that is, all the attributes of God are eternal." (p. 167)
(20) "God's existence and his essence are one and the same." (p. 168)
(21) "All things that follow from the absolute nature of any attribute of God must have existed always, and as infinite; that is, through the said attribute they are eternal and infinite." (p. 168)
Infinite substance or God may be thought of all in one, in which case it is called "Natura naturans" (Nature naturing). Or, infinite substance or God may be thought of in terms of all that follows from God, in which case it is called "Natura naturata" (Nature natured).
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The Argument for God's being the only thing that exists.
Premises (1)-(4) entail that if there are two substances, then to distinguish between them they must have different natures or essences, and thus different different attributes. Otherwise there is only the one substance, with the one nature or essence, and hence, the one attribute. This eliminates the possibility of, say, there being two minds, since these would be two 'substances' that share the attribute of thought.
(To use a non-Spinozistic example, there cannot be 'two golds'. If two 'substances' have the same nature or essence (e.g. atomic no. 79), then they are the same substance, namely, gold).
Premises (5)-(15) establish that an infinite substance is possible and that, since an infinite substance 'uses up' all possible attrributes, if there exists an infinite substance, then there can exist no other substance. For the other substance would either be (a) a finite substance, and thus merely a 'subset' of infinite substance, or (b) another infinite substance, and thus identical to infinite substance.
Premise (16) is the Ontological Argument for the Existence of Substance.
Premise (18) is the inference that infinite substance, since it is a substance, must exist (from the Ontological Argument for the Existence of Substance).
Premise (19) identifies God with the one infinite substance.
However, since we know from premises (5)-(13) that if there exists an infinite substance, then this is the only substance, and since premise (17) tells us that infinite substance does indeed exist, then we may conclude that God, or infinite substance, does indeed exist, and is the only substance that exists.
This argument may be put more briefly as follows:
(1*) An infinite substance is a substance with an infinite number of attributes.
(2*) It is possible for an infinite substance to exist.
(3*) It belongs to the nature of substance to exist.
(4*) So, an infinite substance exists. (from 1*-3*)
(5*) If an infinite substance exists, then it is the only substance that exists.
–––> An infinite substance is the only substance that exists.
This argument is valid. The question is whether it is sound, that is, whether all five premises are true.
Since premise (5*) follows from the previous premises, the real question is whether premises (1*)-(4*) are true.
Now, premise (1*) is merely a definition. However, some philosophers would hold that this definition is self-contradictory. Hence they would reject (2*) as false. Descartes, for example, would say that a substance cannot have more than one attribute. Even God, who is an infinite thinking substance (only) according to Descartes, could not also be extended.
Perhaps Descartes's argument can be put as follows: how can a substance have an "infinite" nature or essence? Isn't that a bit like saying that it has an infinite number of 'natures' or 'essences'? But isn't that peculiar? Isn't that like saying that one thing is an infinite number of different kinds? That one thing is both gold and silver and mercury and hydrogen and (etc.)?
Possibly the weakest premise is (4*), since that is simply the Ontological Argument for the Existence of Substance, and is commonly thought to be invalid. The most that one could conclude would be that substance is that whose nature is such that it exists; but one could still ask: are there any substances? Is there anything whose nature is such that it exists?