First, I would say that reducibility is a property of statements. In the sense I use it:
The statement “14+14=28” is reducible to aether.
The statement “I have 28 apples” is reducible to phyisics.
The statement “There are 28 fundamental rules that one must obey to lead a just life” is reducible to ethics.
Moral statements are irreducible to physics in the sense that “P is red” is irreducible to physics—for any particular physical “P”, it is reducible. The logical properties of P-statements, like “P is red or P is not red” are given as a set of purely logical statements—that’s their analogue of the ought-function. If P-statements had some useful role in producing behavior, they would have a corresponding meaning.
Random, probably unnecessary math:
A reducible-class is a subalgebra of the Boolean algebra of statements, closed under logical equivalence. The statements reducible to aether are those in the reducible-class generated by True and False. The statements reducible to physics are those in the reducible-class generated by “The world is in exactly state X”. The statements reducible to morality are those in the reducible-class generated by “Exactly set-of-actions Y are forbidden and set-of-actions Z are obligatory”.
First, I would say that reducibility is a property of statements. In the sense I use it:
The statement “14+14=28” is reducible to aether.
The statement “I have 28 apples” is reducible to phyisics.
The statement “There are 28 fundamental rules that one must obey to lead a just life” is reducible to ethics.
Moral statements are irreducible to physics in the sense that “P is red” is irreducible to physics—for any particular physical “P”, it is reducible. The logical properties of P-statements, like “P is red or P is not red” are given as a set of purely logical statements—that’s their analogue of the ought-function. If P-statements had some useful role in producing behavior, they would have a corresponding meaning.
Random, probably unnecessary math:
A reducible-class is a subalgebra of the Boolean algebra of statements, closed under logical equivalence. The statements reducible to aether are those in the reducible-class generated by True and False. The statements reducible to physics are those in the reducible-class generated by “The world is in exactly state X”. The statements reducible to morality are those in the reducible-class generated by “Exactly set-of-actions Y are forbidden and set-of-actions Z are obligatory”.