The theoretical utility of quantifying over Xs does not establish that Xs exist as mind-independent entities, as Carnap's distinction between internal and external questions demonstrates.

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Rudolf Carnap(as a philosopher of language and logic): A 20th-century German-American philosopher who thought the best way to understand scientific language was to translate it into a basic, logical framework.
internal and external questions(in Carnap's philosophy of language): Carnap's distinction between questions about things *within* a system we've already accepted (internal) versus questions about whether the entire system itself is real or useful (external). For example, 'Does 7 exist?' within mathematics is internal, but 'Do numbers really exist?' is external.
mind-independent entities(as used in metaphysics and epistemology): Things that exist and have properties whether or not anyone is thinking about them, like rocks, trees, or planets—they don't need a mind to observe them in order to be real.
quantifying over Xs(in logic and philosophy of language): A way of talking about or counting things in a category—like saying 'some things are red' or 'all numbers are divisible by one.' Here it means treating Xs as if they're real things we can discuss and measure.
theoretical utility(in philosophy of science and metaphysics): Whether something is useful or practical for explaining, predicting, or understanding things—even if it might not be 'real' in an objective sense.

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