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It is not the case that Spinoza's Ethics demonstrates that a completed geometric system can adequately express the One Substance without remainder.
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Reasons For
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Reason for
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1.
Geometric language describes spatial extension but struggles to represent qualitative experiential content of consciousness adequately.
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2.
Substance's infinite attributes exceed the two Spinoza addresses; remaining attributes cannot be deductively systematized in geometric form.
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3.
The gap between formal logical necessity and metaphysical being remains unresolved—geometry maps relations but may not capture existence itself.
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Reasons Against
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Reason against
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1.
Geometric proofs establish necessary truths independent of contingent experience, matching Spinoza's rationalist requirement for adequate ideas.
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2.
Spinoza's system derives all properties of Nature from a single set of axioms, demonstrating the geometric method's capacity for complete systematization.
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3.
The Ethics successfully expresses both Thought and Extension—Substance's primary attributes—through unified logical structure without reduction or loss.
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