The first two axioms of the Ethics establish a binary reality: something is either in itself or in another. Alternatively, something is either known through itself or through another. Spinoza's definition of substance puts it firmly in the "in itself" and "known through itself" (I.D3) category. By establishing in the preceding proposition that substance cannot produce substance, Spinoza clears the way to substance with self-caused. If substance cannot be known except through itself, then any knowledge of it implies its existence, an existence that occurs through itself only. In other words, it is "self-caused."
His demonstration is much more succinct than my attempt to work out the
reasoning behind his proposition. Here we get a glimpse into the
fundamental difference between substance and modifications. A substance
necessarily exists, while modifications do not necessarily exist.
Ad naturam substantiae pertinet existere.
Translated as,
To exist belongs to the nature of a substance.
Demonstratio: Substantia non potest produci ab alio (per corollarium propositionis praecedentis); erit itaque causa sui id est (per definitionem 1) ipsius essentia involvit necessario existentiam sive ad ejus naturam pertinet existere. Q.E.D.
Translated as,
A substance is not able to be produced by anything else (through the corollary of the preceding proposition); so it will be the cause of itself, that is (through D1), whose essence necessarily involves existence, or stated differently, to exist belongs to its nature.
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