In “Contractualism and Utilitarianism,” and then again in What we Owe to Each Other, T. M. Scanlon compares the alleged objectivity of morality with that of mathematics. In fact, her writes:
In moral judgments, as in mathematical ones, we have a set of putatively objective beliefs in which we are inclined to invest a certain degree of confidence and importance. Yet on reflection it is not at all obvious what, if anything, these judgments can be about, in virtue of which some can be said to be correct and defensible and others not . . . Second, in both morality and mathematics it seems to be possible to discover the truth, just by thinking about it. Experience and observation may be helpful, but observation in the normal sense is not the standard means of discovery in either subject.
Scanlon goes on to plump for a Brouwer sort of mathematical intuitionism (a sort of constructionism, really), which he seems to think stands as a plausible third way between naturalistic nominalism and platonism in mathematics. He wants us to think of morality in the same way. Straightforward non-cognitivism is like nominalism, Moore/Prichard/Ross intuitionism is like Platonism, and contractualism is like Brouwerian intuitionism.
He goes on to write,
Neither mathematics nor morality can be taken to describe a realm of facts existing in isolation from the rest of reality. Each is supopsed to be connected with other things. Mathematical judgments give rise to predictions about those realms to which mathematics is applied. This connection is something that a philosophical account of mathematical truth must explain, but the fact that we can observe and learn from the correctness of such predicitions also gives support to our belief in objective mathematical truth. In the case of morality the main connection is, or is supposed to be, with the will. Given any candidate for the role of subject matter or morality we must explain why anyone should care about it, and the answer to this question of motivation has given strong support to subjectivist views [Emphasis added.]
So, as Scanlon has it, in both cases, we take our intersubjective agreement to provide support for the objectivity of the relevant domain. Secondarily, we take the connection of math and morals to other things as evidence of objectivity. We think math is objective not only because we agree a priori on procedures of correct mathematical reasoning, but because bridges stay up and planes fly. For morals, there is some connection to the will. What might this mean?
I want to play along with the analogy, but it's worthwhile to first point out the significant differences between math and morals. Scanlon is on firmest ground when he notes that math and morals are alike in the sense that they both seem more or less objective, but that it's not clear what mathematical and moral judgments are really about. Some of us get queasy when we start thinking about Numbers and Moral Properties. So, OK.
But in much of math we have formal, mechanical, algorithmic decision procedures. We have PROOF. This is why we think intersubjective consensus is so hot in math. Morality is of course not at all like this. Moral reasoning is messy, often inconclusive, and subject to lots of disagreement about cases, even if there is agreement on principles, and also lots of disagreement on principles, even if there is agreement on cases. You cannot tell someone that it is incorrect to oppose free trade because they forgot to carry the one. Second, the way in which mathematics successfully and precisely describes real physical systems is EXTREMELY IMPRESSIVE. The fact that bridges stay up, planes fly, and that I can be writing all this on a laptop, is to my mind the knock-down case for the objectivity of mathematics. If I was already a Kantian, then of course math would decribe the world, since math is in that case a bunch of very general relationships between the forms of intuition, from which, in the first instance, my mind “constructs” “the world.” But I am not a Kantian. I think math just is an extremely abstract characterization of the world out there, and it's objective because the world is mind-independent. And morals has, what? A connection to the will.
Let's take this seriously. Start with Kant. An action is right just in case the maxim of the action can be willed as a law of nature. What's this about? My somewhat anachronistic hunch is that Kant, in his talk about a Kingdom of Ends, is talking about a system of optimal social coordination. If you can will a maxim as a law of nature, you are conceiving of it as a viable part of a stable, harmonious, mutually advantageous system of individual behavior. A kingdom of ends has the same pleasing complex harmony of a natural, emergently ordered complex system. In the case of a natural system, the macro-level order is a function of the bona-fide natural laws governing the micro elements. In a kingdom of ends, citizens freely WILL maxims, but the system as a whole looks AS IF each individual was deterministically governed by natural law. That a certain macro-level social order is generally beneficial to its members is just a fact about the world. If we grant that that suitably universalizable maxims are consistent with that kind of objectively good order, and other maxims are not so consistent, then our moral judgments will have some kind ojective subject matter.
The connection to the will, however, is obscure. Although an optimal social order will be by definition good for us, its realization often requires considerable forebearance on our part. If we attempt to locally maximize our well-being, and others do as well, we'll all do worse than we might. That's why we generally won't be able to universalize maxims based in present desire. But my ability to constrain maximization now requires an expectation of constraint in others. How do we ensure commitment to mutual constraint and mutual gains? Kant stipulates a thing called the good will, which, although not related to desire (it is part of the noumenal self) is able to motivate action according to qualifying maxims. It's not clear how this helps, though. It doesn't seem like it makes sense to do one's part in bringing about a kingdom of ends if not enough others will. Perhaps our interest in autonomy provides a compensating benefit. (NOTE: This is by no means Kant scholarship! This is a idiosyncratic pet quasi-Kant.)
Scanlon, like Kant, takes the content of our moral judgments to be about a kind of social ordering. Instead of a good will, he posits a general desire to be able to justify our actions to others in terms they cannot reasonably reject ('reasonably reject' meaning something like “reject as part of an 'informed, unforced general agreement' about our terms of association”). Now, if you could catch Scanlon saying something about an optimal social order, you could take him to be saying that our judgments about what we could reasonably reject are really judgments about the kinds of prinicples that are consistent with an objectiviely optimal order. But Scanlon won't have that, since there is no clear, independent standard for optimality. That is, well-being can't be understood independently of our conception of ourselves as beings who act on reasons we could justify to others, and considerations of well-being is just one consideration in the fuzzy calculus of who could reasonably reject what. (E.g., Bob, Bart and Bill have a choice over two distributions of utils. Suppose that no transfer or redistribution is possible. A: Bob: 100; Bart: 200; Bill: 300, or B: Bob: 99; Bart: 200; Bill: 1000. Bob has a superficial reason to reject B because he gets one less util. [Indeed, maximin demands A.] But Bill certainly has a reason to reject A, because he gets 700 less. It's not really reasonable for Bob to deprive Bill of 700 utils just to get an extra one for himself. How do we know? WE KNOW!) But, if there is some objective fact of the matter about a really worthwhile social order, and our judgments about wrongness, and our dispositions to act consistently with out judgments, tended to track truths about the kind of actions consistent with this kind of social order, then Scanlon would have a strong claim to objectivity connected in the right sort of way with the will.