This paper will outline Spinozas argument in Part 1 of his Ethics of substance. He argues that there is only one substance, which is the same as God, that includes everything in the universe. It will walk through each proposition and explain his proof of it, which relies of his stated definitions. This paper will also explain the difference between Spinozas belief of substance and that of Leibniz from his Discourse on Metaphysics. It will then argue that Leibnizs account of the number of substances superior.
Spinozas first proposition is that substance is by nature prior to its affections (Cahn p. 7). This proposition relies on his definition of a substance which is self created. The affections of the substance, according to his definition, are things that are created by something else. Since the substance is self-created, the substance must have created the affections from itself. Therefore, the substance is prior to its affections since the substance has to be in existence to create its affections. Proposition 2, two substances having different attributes have nothing in common (Cahn p. 417), also relies on the definition that a substance is self-created.
If one attribute of a substance is created from that substance, it belongs only to that substance. Therefore, two different substances having the same attribute are not different, but the same substance. If two substances are truly different, they have none of the same attributes. If all the attributes of the two substances are completely different, they have nothing in common. One thing, which is completely different from the other, cannot have caused the other. This is true because something created must have some knowledge of its creator, as stated in Spinozas axiom 4.
Since the two different things have nothing in common, which includes no knowledge of the other, one cannot have created the other. Spinoza states this in proposition 3. When things have nothing in common, one cannot be the cause of the other (Cahn p. 417). He also reaffirms this in proposition 4 by stating that things are different by the fact of differences in their attributes or affections. This fact is seen easily by looking at the proofs beforehand of propositions 1,2, and 3. Proposition 5 and 6 restate earlier propositions in terms of substances, as opposed to things.
Proposition 5 states: In the universe there cannot be two or more substances of the same nature or attribute (Cahn p. 417). Since two substances are distinguished by a difference in their attributes or affections (proposition 4), the substances would not be different from one another if the had the same attribute. The two substances would be the same. Proposition 6 states that One substance cannot be produced by another substance (Cahn p. 417). If a substance were to create another one, they would have something in common such as an attribute.
However, there cannot be two substances with the same attribute (proposition 5), they must have different attributes and, therefore, be different. If the substances are different, they have nothing in common (proposition 2), and substances with nothing in common on could not have caused the other (proposition3). One substance cannot create another. Spinoza has proved all this about a substance, but has not proved that substance exists. In proposition 7 he does: Existence belongs to the nature of substance (Cahn p. 418).
He states that since substance is self-caused, existence is necessarily involved in it essence, meaning that existence is part of its nature. Now that substance exists, Spinoza proves it is infinite. He says that if substance were finite, it would be limited by another substance with the same attribute of existence. But no two substances can have the same attribute (proposition 5). Therefore, substance is infinite. Since Spinoza has proved that there is a unique, infinite substance that exists, he now goes on to prove that the substance is God, only one of which exists.
He must first include some propositions, which will be used later to help prove this point. He begins by proving that the more real something is, the more attributes it has (proposition 9). He feels that this proposition is evident in the definition of an attribute: that which the intellect perceives of substance as constituting its existence (Cahn p. 416). The more reality that is associated with the essence of a substance the more attributes it has because an attribute is what the intellect perceives the essence of the substance to be.
The substance itself must conceive each of these attributes (proposition 10). According to definition 3, conceiving a substance does not require the conception of something else with which to form the substance. Also, conceiving something is based on its essence. Therefore, attributes used to conceive a substance must be conceived through itself. Now Spinoza proves that God exists in proposition 11: God, or substance consisting of infinite attributes, each of which expresses eternal and infinite essence, necessarily exists (Cahn p. 419).
He easily proves this using axiom 7: if a thing can be conceived as not existing, its essence does not involve existence (Cahn p. 416). He says it is absurd to conceive God as nonexistent since existence belongs to the nature of God, or substance (proposition 7). He also says that there is no substance that can prove that God does not exist since two different substances have nothing in common (proposition 2). Therefore, God exists. Now that Spinoza has proved that the infinite substance of God exists, he proves that substance cannot be divided in proposition 12.
He that if it were divided, each part would be infinite, self-caused, and would have to have different attributes, causing several different substances to be caused from the one substance which is impossible because no substance can be caused from another (proposition 6). Proposition affirms that an absolutely infinite substance is indivisible (Cahn p. 421). It is impossible to divide an absolutely infinite substance because several substances would exist with the same attributes, which is impossible according to proposition 5. Spinoza now proves proposition 14; that no other substance other than God exists.
Since God is an absolutely infinite being, any other existing substance would have to exhibit an attribute of God. This is impossible because no two substances can exist with the same attribute (proposition 5). Existence is an attribute of God; therefore no other substance can exist. Leibnizs position on substance differs form that of Spinoza in the number of substances. Leibniz does not believe in one substance, but in many substances, or as he calls them monads. He believes that everything is made up of monads with their own attributes.
These monads are in harmony throughout the universe, never coming in contact. He believes that anything thing that consists of monads with the same attributes are not different, but the same, similar to the belief of Spinoza. The only difference is the number of substances. Leibnizs account of the number of substances is superior. The many monads, each with its own attributes, allows for the many different things in the universe to exist. Since everything does not have all the same monads, they can be different. A dog and a rock are obviously not the same.
They are not the same because they are composed of monads with different attributes. If they did consist of the same monads, they would be the same, and they obviously are not. According to Spinoza, God is the only substance. Everything we know is part of God. God includes all attributes. If I am part of God, I contain all attributes. However, I do not contain all attributes. There are many that I do not include such and infinity. I am obviously not infinite. Leibnizs account of the number of substances allows me to exist, not containing every attribute.