A universal 'said of many' is an epistemological product of the mind's comparison across instances, whereas demonstrative universality is an ontological feature of the connection between essential cause and effect.
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demonstrative universality(contrasted with universals that just come from our minds comparing things)
A universal principle that is proven or shown through the actual causal relationship between things in the world—what *must* be true because of how reality works.
essential cause(Aristotle's criterion for inclusion in scientific definitions, Metaphysics VIII,4)
A cause such that a thing would not be what it is if it were not caused in this way; distinguished from accidental causes and required to appear in scientific definitions