In-itself / in-another split
Formal Statement
Axiom 1: Everything that exists, exists either in itself or in something else. Axiom 2: That which cannot be conceived through anything else must be conceived through itself. Together, these axioms enforce an exhaustive ontological partition — nothing escapes the substance/mode divide.
In Plain Language
These two axioms close every exit. There is no third option: everything is either self-standing (substance) or dependent (mode). And if you cannot understand something via something else, then it must be understood through itself. Spinoza is setting up a world with no ontological gaps and no conceptual loose ends. Every being falls on one side of this line, and the way you conceive it tracks the way it exists.
Why This Follows
The definitions of substance (gs-01) and mode (gs-03) introduced "in itself" versus "in another." These axioms elevate that contrast to the status of an exhaustive and self-evident partition of all reality, giving us the logical ground from which the propositions will be derived.
Everything that exists is either substance (in itself) or mode (in another) — there is no third category.
Is this partition genuinely exhaustive? Can you imagine something that is neither fully self-standing nor fully dependent on another?