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 in...