Reduction and coordination
The following principles have something in common.
Conditional Coordination Principle.
A rational person's credence in a conditional A->B should equal the ratio of her credence in the corresponding propositions B and A&B; that is, Cr(A->B) = Cr(B/A) = Cr(B)/Cr(A&B).
Normative Coordination Principle.
On the supposition that A is what should be done, a rational agent should be motivated to do A; that is, very roughly, Des(A/Ought(A)) > 0.5.
Probability Coordination Principle.
On the supposition that the chance of A is x, a rational agent should assign credence x to A; that is, roughly, Cr(A/Ch(A)=x) = x.
Nomic Coordination Principle.
On the supposition that it is a law of nature that A, a rational agent should assign credence 1 to A; that is, Cr(A/L(A)) = 1.
All these principles claim that an agent's attitudes towards a certain kind of proposition rationally constrain their attitudes towards other propositions.
That alone is not remarkable. My credence in "there is water on Mars" rationally constrains my credence in "there is water on some planet besides the Earth". What's special about the four examples is that in each case philosophers have argued that the relevant propositions are metaphysically primitive. And arguably this makes it puzzling how our attitudes towards these propositions could constrain our attitudes towards entirely different propositions.
Take the Conditional Coordination Principle. This is rarely endorsed as such, but it is not far from the views of Stalnaker, Bradley, Bacon and others who have defended "Stalnaker's Thesis", that Cr(A->B) = Cr(B/A). For technical reasons, defending this requires assuming that if A is false, then the truth-value of non-trivial conditionals A->B is not determined by any non-conditional facts: two worlds could agree in all non-conditional respects and yet disagree about the truth-value of "if it rains today in Edinburgh, then it also rains in Glasgow". In that sense, we need to postulate primitive conditional facts -- conditional facts that are not grounded in any non-conditional facts.
I find those primitive conditionals unappealing and mysterious. One of their especially mysterious feature is how our credence in the presence or absence of those facts is supposed to be guided by our credence in ordinary non-conditional propositions. OK, let's grant that there is a primitive proposition A->B whose truth-value at least in not-A worlds is left entirely open by all non-conditional facts. Then how could it possibly be a requirement of rationality that my credence in A->B is completely fixed by my credence in the non-conditional hypotheses A and B and their conjunction? For example, why does rationality forbid thinking that in case of not-A, A->B is just as probable as its negation (which is generally incompatible with Conditional Coordination)?
For the Normative Coordination Principle, the problem is much better known, and widely used as an argument against primitive normative truths. Rightly so, I believe. Let's grant that there is a primitive proposition Ought(A) whose truth-value is not settled by ordinary, non-normative facts in the world. How could it possibly be a requirement of rationality that if you believe that this proposition is true, then you must be motivated to do A? That sounds completely mysterious, and not just because it conflicts with general Humean doctrines about motivation.
The problem with Probability Coordination and Nomic Coordination is also fairly well-known in the relevant quarters, but here there is no agreement on whether there even is a problem. Lewis forcefully claims that there is:
Be my guest – posit all the primitive unHumean whatnots you like. ... But play fair in naming your whatnots. Donât call any alleged feature of reality "chance" unless youâve already shown that you have something, knowledge of which could constrain rational credence. I think I see, dimly but well enough, how knowledge of frequencies and symmetries and best systems could constrain rational credence. I don't begin to see, for instance, how knowledge that two universals stand in a certain special relation N* could constrain rational credence about the future coinstantiation of those universals. ("Humean Supervenience Debugged", p. 484)
Others, equally forcefully, refuse to acknowledge the challenge. For example Ned Hall:
... what, exactly, is the problem here? Why is it supposed to be so dificult to 'show' that one has something, knowledge of which could constrain rational credences? In particular, why can't a thoroughgoing non-reductive primitivist about chance reply as follows: What I 'have' are objective chances, which, I assert, are simply an extra ingredient of metaphysical reality, not to be 'reduced' to anything else. What's more, it is just a basic conceptual truth about chance that it is the sort of thing, knowledge of which constrains rational credence. ("Two Mistakes About Credence and Chance", p.106)
Notice that one could make the exact same move in the case of norms and conditionals. Why can't the normative primitivist simply say that normative propositions are extra ingredients of metaphysical reality and that it's a basic conceptual truth about normativity that normative judgements motivate?