If phenomenal properties are grounded in physical properties, the mind depends on the body via a necessary metaphysical relation that exceeds mere causal dependence without requiring analytic reduction.

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Analytic reduction(as used in metaphysics and philosophy of mind): Breaking something complex down into simpler parts and showing that it's nothing more than those parts combined; for example, proving that water is 'nothing but' hydrogen and oxygen atoms.
Metaphysical relation(as used in metaphysics): A deep, fundamental connection between things that goes beyond just one event causing another—it's about how things are connected in their basic nature.
Physical properties(as used in philosophy of physics): Characteristics of objects that exist in the physical world, like mass, color, size, or temperature—things you could theoretically measure or observe.
causal dependence(Lewis's counterfactual theory of causation): A counterfactual relation in which an effect depends on a cause such that, had the cause not occurred, the effect would not have occurred.
grounded in(whether distinctness or identity is explained by intrinsic features): To be explained by or to have its reason or basis in something else—like how a tree being wet is grounded in (explained by) recent rain.
phenomenal properties(Used in the context of higher-order thought theory to refer to properties whose presence is explained by higher-order representations): The qualitative, 'what-it-is-like' features of conscious experience that characterize how perceptual states feel to the subject

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