One way to object to versions of Protagoreanism is to consider counterfactual situations. We have the attitudes and the judgements that we do. Those give ‘just’ its content and/or those fix what it is for something to be just. We might have had, so goes the objection, different attitudes and we might have made different judgements. Were we to have different attitudes and attending judgements, would not the just be unjust and the unjust just? No, goes the standard reply. ‘Just’ means what it does and/or justice is what it is in light of the attitudes we actually have and the judgements we actually make. It matters not what our attitudes and judgements might have been; what matters is what they are. When we consider counterfactual situations, we do so with our current attitudes and our current judgements. We speak our own language and not some other. So, when we assess other possibilities, we do so ourselves as we are not how we might have been. So, in alternative possibilities, the very same things are just and unjust as they are in our own circumstances. Even if we might have used ‘leg’ to include not only the walking appendages of sheep but their tails as well, sheep would still have only four legs, even under those circumstances. We speak English. Those who use the broader meaning for ‘leg’ speak another language. Sheep have four legs, even if, in their alternative languages, others would answer ‘five’ to the question: “How many legs does a sheep have?” In our vocabulary, sheep have four (genuine) legs. As we report the linguistic behaviour of those other language users, sheep have five so-called legs, or “legs”. Our alternative selves can speak as they like; the facts are what they are and we convey those facts using our language. So, sheep have four legs, regardless of how any speakers of other languages use ‘leg’.
However successful this line of thought is for accounting for hypothetical situations and what is just and unjust in them, its analogue is no help for us in ours. It is a variation of “we call it ‘just’ and they do not”. Instead of comparing actual multiple groups at a given time or comparing an actual single dynamic group over time, we are comparing things as they actually are with how they could be. That such situations are possible needed no defence, since they constitute the threat of relativism that contemporary version of Protagoreanism seeks to avoid. It saves us from having to say that introducing a modal dimension to our considerations introduces a new source of relativism, but the success of this defence of Protagoreanism depends on what we have already seen is not established, i.e., that Protagoreanism can provide sufficient objectivity, sufficient correctness, to provide the beginning point for the strategy for handling counterfactual situations. Worse, if the counterfactual strategy suffices, its advocate should give reasons for thinking that its analogue does not in the simpler situations. It is, after all, a version of “each is right in their own eyes”. If the theoretician denies this gloss on the position, it is perhaps because it is part of the unstated background that each privileges their own attitudes and judgements and when considering the views of others, we call things as we see them. If we judge differently, we declare the others in error. It is a commonplace in epistemology that whatever we believe we believe to be true, if we ascend into a metalanguage to consider the matter. In any act of judgement, we tacitly take ourselves to be accurate. Any basis for thinking ourselves not accurate is itself a basis for withholding relevant judgements. To “rigidify” the content of our moral terms in light of our current attitudes and judgements is to treat ourselves as accurate and our counterfactual selves as wrong or else it is to declare that we and our counterfactual selves talk past each other. If this must be built into the very nature of the strategy for avoiding counterfactual relativism, it is no different from treating ourselves as authorities in the actual cases we considered. Such a privilege is warranted only to the extent that the very same privilege is extended to all and landing us back into the original troubles with Protagoreanism or the account must say why with my/our specific case(s) the moral authority lies. If the substance of that authority is nothing more than a version of the Protagorean measurement thesis, those same troubles are not avoided. If its substance resides elsewhere, Protagoreanism has been forsaken.
An Old Alternative
If the foregoing is roughly correct, then naturalists must forsake either modern Protagorean theories or else forsake any claim on moral objectivity. To the extent that modern Protagoreanism is recommended because moral properties are thought to be queer were they to reside in the non-psychological character of the world, the naturalist moves to an error theory. Strictly speaking, there are no moral facts or moral properties; moral declarations assume that there are such facts or properties, so moral declarations are false. Those not tempted by an error theory must continue the search for a basis for moral objectivity without the measurement thesis.
It is worth revisiting the famous “Euthyphro” dilemma (Plato, 1969). The dilemma is that the moral is a matter of the commands or will of God or not. If it is, then to the extent that God is changeable either temporally or modally, so is the moral. If it is not, then God is not the creator of all and is not supreme over all, since God too is subject to an independent domain of the moral. Consider each horn of the dilemma in turn.
Only if God is “unstable” can the problem arise. If God’s character is both temporally and modally stable, then it is not the case that God might command or might have commanded otherwise. If God’s divine character is essential, then it is both temporally and modally stable and there is no possible prospect of the just being unjust precisely because there is no possible prospect that the relevant divine commands will be or would have been otherwise. The underlying assumption was that God’s character is contingent and there is nothing in the dilemma alone that warrants that assumption. Maintaining the temporal and modal stability of the moral is merely a matter of maintaining the temporal and modal stability of God. Furthermore, unlike the options discussed above, nothing in this horn of the dilemma that raises any problem of undesirable relativism. It is not that there is no possibility of relativism. God might have actually commanded for me differently than God has commanded for you regarding a given class of actions. Whether relativism ensues in light of the divine commands requires accounting for the specifics of God’s commands. It is not the nature of the theory that relativism is inevitable, which was the substance of the repeated charge above. Note, also, that even if there is divinely-instituted relativism, there is at least the degree of objectivity that my thinking moral matters are thus and so does not make them so and neither does yours. This form of relativism clearly permits space for moral error, as well as space for the prophet. If we are convinced by Protagoreans that the important aspects of moral objectivity are moral error and by extension the prophet, then divinely-instituted relativism is not objectionable.
The second horn of the dilemma is that an independent moral law makes God subservient in a way inappropriate for one worthy of worship. Again, this assumption is dubious. God being subject to laws to which others are not might be problematic, assuming such differences are differences in greatness in some respect. One not seeking some version of the measurement thesis regarding morals should maintain that the domain of the moral is part of the domain of the necessary. Murder (of one human by another) is wrong, even if there are no humans. Likewise, for other fundamental moral laws. If such laws are necessary truths, then they are what they are independently of God’s commands. As necessary truths, they are laws to which all are “subject”. No difference in greatness is to be found in God’s being subject to what any being at all must be subject. Not to be so subject is not to be, not to be a being at all. Even if one is loath to declare existence a great-making attribute, it is hard to see how it is some metaphysical or moral greatness not to be. So, on this score, metaphysical life is tough all over. Even more, to be and not to be subject to the moral law is to be amoral or a moral monster and neither being amoral nor a monster is a sign of greatness that befits one worthy of worship. So, even if the moral is not to be commanded, permitted, or prohibited by God and even if God is subject to the same moral necessities as are all others, this alone does not impugn God’s standing as one to be worshipped.
There is, of course, the necessary qualifier that even if the moral laws is a set of necessary truths to which all are subject and not even God can alter them, it does not follow that the actions of all are subject to identical restrictions. Some may be permitted to do what others are not, as a matter of necessity. This, in itself, is not problematic. We are troubled by moral differentials only when there is no good reason for them. That is the typical case when one person thinks they are exempt from the moral demands shouldered by the rest of us. As Roman emperors were allegedly wont to do, some forget that they, like the rest of us, are just human. So long as there are morally sufficient grounds for different demands, there can be no legitimate source of objection when God, for instance, is permitted to do what we are not. Since the kind of theory we are considering is that moral laws are necessary truths, there is no real prospect for the differences being morally insufficient.
In this essay I have examined Protagoras’s thesis that man is the measure of all things and found it wanting. Not only was his original version insufficient as an account of the moral domain that permits moral error as well as moral loneliness, more contemporary versions of it suffer similar deficiencies. Though the divine command theory may not be mandatory for Christians, the standard Euthyphro dilemma is insufficient to undermine that theory. If there is moral relativism, it is neither inevitable nor morally objectionable on that theory.
For those who think that philosophical theories are warranted on the basis of inferences to the best explanations, we have a small component of such an inference that prefers theism over naturalism. With the rejection of theism, naturalists must search for other foundations of morality. If it is agreed that moral properties, if such there be, are too queer to be properties that are wholly independent of moral agents and their attitudes and judgements, the problems for naturalism noted above are significant. Naturalists are left with the options of error theories or the search for natural properties that are the moral properties. From neither option does the basis of morality fall out naturally. In contrast, the foundations of morality can fall out quite naturally from the very nature of theism. One worthy of worship is morally perfect and essentially so. Whether the substance of the moral is the commands, permissions, and prohibitions of God, any such are reliable guides to the moral. This plank of the inference is only a small portion of the best explanation, but it is one that falls out of theism quite naturally and that is significant.
 To make the main point, I omit fairly obvious complications concerning expertise and how the judgement of experts on matters about which they are experts legitimately undermine the confidence in contrary judgements on those same matters by amateurs.
 The easy, but ultimately incorrect, way to think about the projectivist programme is to say that we mistake something subjective for something objective. This way of making the distinction is not quite right because there are objective facts about subjectivity. When I rank flavours of ice cream and rank vanilla higher than maple walnut, I do so on the basis of my own—subjective—preferences. It is, though, a perfectly objective fact about me that I prefer vanilla to maple walnut. The objective is not the same as the mind-independent and the subjective is not the same as the mind-dependent.
 I note here and then set aside a question that pertains to the entire discussion of the general Protagorean program. The unqualified, universal statement of the measurement thesis seems to be against the assumption that all facts end in measurement facts. So stated, measurement facts end in measurement facts. Even though that appears trivial, it is not. The unqualified version of the measurement thesis is that things are the ways they are only to the extent that they are measured to be those ways. This covers the measuring agents as well as the items measured by those agents. This appears to result in a regress. A room is hot only to the extent that some agent judges it to be hot. The agent measure the room to be hot only to the extent that the agent is measured to measure the room to be hot. And, so on. The regress can be halted at the first stage of measurement, only if facts of measurement are “self-standing” facts that depend on no further measurements. The Protagorean faces a dilemma: either an infinite hierarchy of distinct judgements must be legitimized for any of the usual judgements to make the world the way it is or what appears to be an hierarchy is not but is a single self-standing judgement by an agent. The first horn preserves the initial form of the measurement thesis, with every fact dependent upon some (further) measurement. The second horn requires both a revision to the initial measurement thesis as well as some justification for the key difference between the original and the revision: that facts of measurement demand no further measurement.
 Platonists maintain that languages are abstract entities not of our creation. Nominalists deny this. Each, however, can affirm this claim. Within the context of a given linguistic community, speakers try to speak the same language. Being out of step, on a Platonist view, means that one fails to be correct about the user-independent fact about syntax or meaning, assuming that the rest are correct. On the nominalist view, the use of the language determine the meaning, if anything does. So, being out of step is, again, to be incorrect, to misalign one’s linguistic judgements and behaviour with what constitutes the linguistic facts.
 It is an interesting sociological question whether projectivists hold their own moral judgements hostage to those of others.