Nagel's classic account treats reduction as a logical relation between theory-statements, yet this formal relation simultaneously constrains what ontological identities are permissible.

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Nagel(as a key philosopher cited in this theory): Thomas Nagel is a famous American philosopher known for thinking deeply about consciousness, death, and what makes life meaningful.
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 identities(what reduction constrains): Claims about what things really are in the world—for example, whether water is 'really' just H2O molecules, or whether consciousness is 'really' just brain activity.
Theory-statements(what reduction operates on): Sentences or claims that make up a scientific or philosophical theory—the actual statements scientists use to describe how the world works.

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