If 'unlimited' cannot analytically ground existence, it equally cannot ground the possession of infinite determinate attributes, which are synthetic claims about substance's nature.
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synthetic claims(as used in epistemology and logic)
Statements about the world that cannot be proven just by understanding the definitions of the words—you have to actually observe or investigate reality to know if they're true.
unlimited(Presocratic cosmology)
A continuum not yet limited in any way; the surrounding expanse from which time, breath, and void are drawn into the cosmos