The inference from 'common natures are real' to 'what ties them to individuals must be equally real' commits a category error, since relational functions need not posit new ontological kinds.

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Category error(as used in logic and philosophy of language): A logical mistake where you apply a rule or concept to something it doesn't actually fit, like using a math formula on a poem.
Ontological: "Ontological" refers to questions about what actually exists or is real. It's concerned with the fundamental nature of being—asking "What kinds of things are there?" rather than "How do we know about them?" For example, an ontological question might be whether numbers, ideas, or God actually exist as real things, or if they're just human inventions.
Ontological kinds(as the categories being discussed as stabilized): Categories of what exists or what is real; basically, the different types of things philosophers and scientists say are fundamental to reality.
Relational functions(used in metaphysics and logic): Ways that things connect or relate to each other, or the rules that describe how one thing depends on or connects with another.

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