One substance cannot be produced by another
Formal Statement
One substance cannot be produced by another substance. Since no two substances share an attribute (P5), any two substances have nothing in common. But things with nothing in common cannot be cause and effect of one another (by I.Ax.5 and I.Ax.4). Therefore, no substance is causally derived from any other substance — substance is uncaused by anything external to it.
In Plain Language
This is the causal independence of substance. If substance A has nothing in common with substance B (because they cannot share an attribute), then A cannot bring B into being or vice versa. Causation, for Spinoza, requires a shared conceptual link between cause and effect. No commonality, no causation. This means every substance that exists must be self-caused — it cannot owe its being to anything else.
Why This Follows
From P5 (gs-07), no two substances share an attribute, so any two distinct substances would have nothing in common. Spinoza's axioms state that things with nothing in common cannot be understood through each other (Ax.5) and that knowledge of an effect depends on knowledge of its cause (Ax.4). Together this blocks one substance from producing another.
Substance cannot be produced by anything external to itself; it must be self-caused.
Connected Concepts
If substances cannot causally interact, how does Spinoza avoid the problem of isolated, disconnected realities?