Spinoza believes that God must exist. In order to defend this claim he goes on to assert that God is a substance and that existence is part of the idea of substance. In proposition 7, Spinoza argues that “existence belongs to the nature of substance.” This could mean that (Premise 1) nothing outside of a substance can cause a substance to exist. (Premise 2) Everything must have a cause. (Premise 3) The substance must cause itself to exist.
If a substance cannot be caused by anything else and has to be caused by something, then it must be caused by itself. Everything which exists does so either in itself or in something else and that substances exist in themselves and modes exist in something else. Therefore, there exists only substances and modes in the world. Also, we know that there is only one substance because there are only two ways to distinguish things, by their modes or by their attributes. If we distinguish according to their attributes, then we are saying that one lacks an attribute that the other has, which is to conceive one substance by means of another, which is contrary to substance’s definition as self-conceivable. If we distinguish them in terms of modes, we are not distinguishing substances as they truly are, because we do not define substances in terms of their modes. Thus there is only one substance because there is no means to distinguish multiple substances.
So if there is only one substance, no substance can be produced by anything external to it. If the substance was created by an external cause then the knowledge of it would depend on the knowledge of its cause. Furthermore, it would itself not be substance. Also, if one substance was produced by another, then one is the cause of the other. We understand effects by knowing their causes, so we would understand the caused substance by means of what causes it. But this contradicts the definition of substances as being self-conceivable.
In the universe, there cannot exist two substances with the same attribute, or in other words, which have anything in common with each other. Consequently, one attribute cannot be the cause of the other attribute, and also cannot be produced by the other.
It seems as if Spinoza believes that the second premise is easily understood. He barely mentions this premise and makes it seem as though it is so evident when in fact it is not. The first premise is basically a result of the definition of substance. Substances must depend on nothing else for their existence, therefore, substances must be independent. If something else caused a substance to exist, then that would mean that substance was brought into existence by something external to it. Spinoza argues that substance causes itself to exist, which is irrational. People usually assume that everything in the world was created by an external force and that every cause follows its effects, but we usually do not assume that a thing follows its own existence.
Spinoza goes on to argue against this belief by identifying two things that we think of as different, specifically causation and logical necessity. It is causally necessary that if one billiard ball hits another, the second billiard ball begins to move (other things being equal). It is logically necessary that, given that ‘P’ and ‘if P, then Q’ are true, ‘Q’ must be true as well. We think of these as two very different kinds of necessity, but for Spinoza, they come to the same thing. So for a thing to cause its own existence is for its existence to be logically necessary because of some fact about it rather than because of any facts about other things. If something about a substance makes it the case that it has to exist, then its essence must include existence.
Nothing outside a substance can explain its existence; everything must have an explanation; so a substance must explain its own existence. If to explain something requires making it logically necessary, then this seems to show that substance necessarily exists.
There is something deeply messed up here, though. What is the reason that there is no substance with only the attribute of thinking? it is that there is a substance with all attributes, and there cannot be two substances with overlapping attributes. But then the reason why there is no substance with only the attribute of thinking comes from outside the nature of such a substance: it is essentially prevented from existing by the fact that there is a substance with all attributes. But then this looks like a case of a substance with one attribute being prevented from existing by something with a different set of attributes: so either things with nothing in common can cause each other (contrary to proposition 3) or else the substance with one attribute and the substance with all attributes do have something in common (namely the one attribute), in which case proposition 2 must be interpreted in such a way that it does not apply to substances with overlapping attributes, in which case it will not support the conclusion that nothing external to God could prevent his existence.