There are some claims that are irreducibly normative in the reason-involving sense, and are in the strongest sense true. But these truths have no ontological implications. For such claims to be true, the reason-involving properties need not exist either as natural properties in the spatio-temporal world, or in some nonspatio-temporal part of reality.
It's an appealing view, and one that I defended in an old post on 'non-spooky moral realism'. But it also raises some puzzling questions.
Parfit motivates his view in part by analogy to metaphysical disputes over the existence of numbers, and the appealing idea that there is no clear question over which Platonists and Nominalists might intelligibly disagree. "It is not yet clear enough in what sense it might be true, or might be false, that numbers really exist, though not in space and time." He later adds:
Nothing could be truer than the truths that 2 is greater than 1, that 2+2=4, and that there are prime numbers greater than 100. Not even God could make these claims false. For such claims to be true, there must be a sense in which there are numbers, or in which numbers exist. But in deciding which mathematical claims are true, we don't need to answer the question whether numbers really exist in an ontological sense, though not in space and time.
Of course, just because mathematicians can go about their practice without asking these metaphysical questions doesn't by itself establish that there's no intelligible metaphysical question here to ask. But regardless, Parfit's anti-metaphysical position may strike us independently plausible. (I sure have trouble grasping what some of these metaphysical disputes are really about!)
Note, though, that Parfit cannot endorse a full-blown Carnapian framework-relativism. He doesn't just want to say that within the framework of morality, we attribute "reasons" under such-and-such conditions. After all, there are competing practical frameworks such as etiquette, or even an inverted 'anti-morality', and Parfit surely doesn't want to say that these are all, objectively speaking, on a par. It is not (normatively) up to us which framework or practice to adopt. The moral framework is really right in a way that the others are not.
In light of this observation, we may begin to worry that it is also "not yet clear enough" in what sense moral claims might be objectively true without any truth-makers to make them so. As Parfit himself notes: "Most truths are true only because things of some other kind exist, in an ontological sense." We may think it is precisely the substance of the desk in front of me which assures me that existence claims about desks are substantial claims to make. They commit us to the world being one way rather than another. It's much less clear what makes normative truths substantial. (Okay, they commit us to the correctness or incorrectness of various attitudes or responses. But it's harder to get a grip on what this amounts to.)
I suspect that Parfit would respond that I am not expressing a sufficiently clear worry. After all, it's clear enough that we have reason to avoid future agony, and that this reason is not contingent on our desires, etc. Perhaps we cannot intelligibly move beyond this first-order moralizing to ask what the truth of the normative claim consists in. But then it's no longer clear what sets Parfit's realism apart from, say, Blackburn's expressivism. Perhaps he would instead say that we can ask the external, metaethical question, but the answer is that it's just a brute fact that certain moral claims are (necessarily) true and others false, without any thing making them so. And maybe that's the right thing to say. But it remains rather mysterious to me.
Oh well. If anyone else can make better sense of this, I'm all ears...