Hempel's theorist dilemma applies here: either the added physical predicates absorb all the nomic work and the mental predicates become explanatorily idle, or the law remains irreducibly psychophysical and still fails Davidson's strictness criterion.
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The job of explaining why something happens according to the laws of nature; basically, doing the explanatory heavy lifting.
Physical predicates(as used in philosophy of mind)
Descriptions or properties that refer only to physical things—like 'is moving' or 'has mass'—as opposed to mental descriptions like 'feels pain'.
Psychophysical law(as used in philosophy of mind)
A rule or pattern that connects mental events (like thoughts or feelings) to physical events (like brain activity), rather than staying entirely in one domain.
mental predicates(the main subject being analyzed in the statement)
Words or phrases we use to describe mental states, like 'believes,' 'desires,' 'feels happy,' or 'is conscious.'