Moral property eliminativism

This paper argues that there is signiﬁcant motivation for contemporary ethicists to afﬁrm a view I call ‘‘moral property eliminativism.’’ On this eliminativist view, there are no moral properties, but there are moral truths that are made true by only nonmoral entities. Moral property eliminativism parallels eliminativist views defended in other domains of philosophical inquiry, but has gone nearly entirely overlooked by contemporary ethicists. I argue that moral property eliminativism is motivated by the claim that there cannot be differences in moral truths without differences in nonmoral ontology—a claim widely endorsed by contemporary ethicists. Engaging with a variety of ways whereby one might resist the motivation I cite for moral property eliminativism, I argue that alternative contemporary metaethical views tend to purchase moral properties at the price of unnecessary theoretical complexity.


Introduction
One of the most widely endorsed views in contemporary ethics is the view that there cannot be any difference in moral truths without a difference in nonmoral ontology . In this paper, I argue that this claim motivates a view that is endorsed by few if any contemporary ethicists, especially ethicists who think there are moral truths: namely, the view that there are no moral properties.
In Sect. 2, I offer a short statement of the central argument I wish to advance against the existence of moral properties. In Sect. 3, I further defend this argument by replying to five important objections to it. My goal is not so much to convince all readers that there is no possible route to resisting the argument in question, but rather to show through its defense that there is very substantial motivation for this view that is so commonly overlooked in contemporary ethical theorizing.

The no moral properties argument
In this paper, I argue that there is substantial motivation for contemporary ethicists to maintain that there are no moral properties. This motivation derives from a claim that is among the most widely endorsed in contemporary theorizing-the claim that there cannot be differences across possible worlds in moral truths without differences across those worlds in nonmoral ontology. Some writers have labeled this claim ''moral supervenience.'' But the application of this term has become a hotbed of debate, and so I will use the more neutral term ''truthervenience.'' 1 Thus, I will be arguing that moral truthervenience motivates the view that there are no moral properties-a view I will call ''moral property eliminativism.'' The variety of moral property eliminativism I will defend is one according to which, while there are no moral properties, there nonetheless are moral truths. The truthmakers for moral truths do not involve moral properties, but involve nonmoral ontological items instead. In this way, my moral property eliminativism parallels eliminativist views recently defended in other domains of philosophy, such as eliminativist views about composite objects. 2 Before getting into my argument, it is important for me to comment on how I will be using certain terms, beginning with the term ''moral property.'' I wish to use this term in a way that is neutral between defenders of a wide range of ethical theories. And so I follow the recent practice of Cuneo and Shafer-Landau (2014) in not attempting to define what a moral property is, but instead offering a list of prima facie plausible candidates for moral properties. The list includes: the property of being vicious, the property of being morally wrong, the property of being morally right, the property of being morally obligated, and the property of being morally permissible. What I aim to argue is that prima facie plausible candidates for moral properties such as these are not properties at all. There is no property of being vicious or property of being morally wrong or property of being morally right, etc.
By contrast with moral properties are nonmoral properties and nonmoral ontological items more generally. Again, I won't offer a definition of nonmoral properties, but will list some paradigmatic candidates. These include properties which seem to have little if anything to do with morality such as the downward spin of an electron and the rectangularity of a geometric figure. They also include properties that more plausibly do have something to do with morality, but that are not obvious candidates for themselves being moral properties in the way that the properties listed in the previous paragraph are. Examples here include the property of being painful and the property of being willed by God. Such properties are often called ''natural'' properties, though I will not insist on this usage here. Nonmoral ontological items more generally include not only such properties, but the nonmoral substances that bear them.
Notably, this way of characterizing moral properties and nonmoral properties leaves it open whether on final analysis it will turn out that there is overlap between the moral properties and the nonmoral properties. In other words, it is left open at the outset whether it might be that each moral property is identical to a nonmoral property. On the moral property eliminativist view advocated in this paper, this is not the case. There is not overlap between moral and nonmoral properties because there are no moral properties. Nonetheless, certain important and influential contemporary views are best interpreted as proposing that there is such overlap. In Sect. 3, I discuss more thoroughly the relationship between moral property eliminativism and these rival and more popular views.
Corresponding to the distinction between moral and nonmoral properties is a distinction between moral and nonmoral predicates. Again following Cuneo and Shafer-Landau (2014), I will not offer a definition of what it is for a predicate to be moral, but a list of predicates which, in at least a wide variety of their usages, are good candidates for being moral predicates. The list includes ''vicious man/woman,'' ''virtuous man/woman,'' ''morally wrong action,'' ''morally right action,'' and ''action which should have been performed.'' The list of nonmoral predicates includes ''is in spin down,'' ''is painful,'' and ''is willed by God.'' I will pitch my argument for moral property eliminativism primarily at contemporary ethicists who think there are moral truths. These are ethicists who think that sentences that apply moral predicates are sometimes true. An ethicist who thought the sentence ''Hitler was vicious'' is true would be an example. Such ethicists are sometimes called ''realists,'' 3 though I will not insist on this usage. Employing this label innocuously, my argument can be thought of as aiming primarily to convince moral realists to seriously consider moral property eliminativism. 4 I'll state my argument against the existence of moral properties in a rough and intuitive way first, and then develop a more careful formal version of the argument to defend at length. The rough statement is as follows. Suppose that there cannot be 3 See Sayre-McCord (2009). 4 The argument may also be attractive to some quasi-realists. Typically, quasi-realists wish to affirm that there are moral truths, but only in a sense that is regarded by realists as less than full-blooded. Examples include Blackburn (1993) and Gibbard (2003). Notably, Gibbard very clearly rejects the existence of moral properties, and so his view is in this respect much like that defended in this paper. Yet, there are important differences between his view and mine. One chief difference is that his view appeals to relations of constitution or realization where mine appeals to relations of truthmaking. differences across possible worlds in moral truths without differences across those worlds in nonmoral ontology. If this is so, then it seems that what is doing the work of making moral truths true is only nonmoral entities. But, if only nonmoral entities are doing the work of making moral truths true, then positing the existence of moral properties is an unnecessary theoretical addition. And such theoretical additions should be avoided. 5 Here is a formal version, which I'll call the No Moral Properties Argument: 1. Necessarily, for any worlds W and W*, the set of moral truths in W differs from the set of moral truths in W* only if the nonmoral ontology of W differs from the nonmoral ontology of W*. 2. The best explanation for 1 is that differences in moral truths between any worlds W and W* are explained exclusively by differences in nonmoral ontology between W and W*. 3. So, for any worlds W and W*, differences in moral truths between W and W* are explained exclusively by differences in nonmoral ontology between W and W*. 4. If 3, then there are no moral properties. 5. So, there are no moral properties. I conclude this section by offering a brief explanatory commentary and defense of the No Moral Properties Argument. The full defense includes Sect. 3, however, where I wrestle with the best objections to the argument of which I am aware.
The first premise of the No Moral Properties Argument is simply a more precise formulation of the claim that there cannot be differences across possible worlds in moral truths without differences across those worlds in nonmoral ontology. As I have said, this view enjoys widespread support among contemporary ethicists.
Skip to claim 3. Claim 3 is inferred from claims 1 and 2 by inference to the best explanation. If 1 and 2 are true, it is unlikely that 3 will be disputed.
Claim 4, I propose, is imminently plausible. It is plausible because it is implausible to think that moral properties would exist but not play a role in making true moral sentences true. If moral properties did exist, surely they would play this role. Yet, if they did play a role in making moral sentences true, then they would play a role in making true those true moral sentences that differ in truth value from one world to another. Thus, by contraposition, if moral properties do not play a role in making true those true moral sentences that differ in truth value from one world to another, then they do not exist. The conclusion, 5, of course follows form 3 and 4 by modus ponens.
Return finally to claim 2, the premise in the No Moral Properties Argument most in need of a further defense. I offer a defense of it in two steps.
The first step is to argue that the most plausible explanation for 1 will say that differences across worlds in nonmoral ontology explain differences across worlds in moral truth. To see this, suppose that claim 1 is true: there can be no difference between worlds in moral truth without a difference in nonmoral being. Now, one might wonder why this is so. Why, that is, is there this necessary correlation between differences in moral truth and differences in nonmoral ontology? There are four ways to answer this question. The first answer is that the relationship between differences in moral truth and differences in nonmoral ontology is brute-i.e., there is no explanatory relationship linking these differences. The second is that differences in nonmoral ontology explain differences in moral truth. The third is that differences in moral truth explain differences in nonmoral ontology. And, the fourth is that there is something other than nonmoral ontology and moral truth that explains both differences across worlds in nonmoral ontology and differences across worlds in moral truth.
Let me argue briefly that every answer to the question but the second answer is deeply unattractive. The first answer is unattractive because it leaves unexplained something that cries out for explanation. We want to know why it is that it is only when the nonmoral ontology of worlds differs that moral truth differs between those worlds. The first answer tells us that there is no explanation for this. This is just how things are. The first answer, then, strictly speaking, cannot provide the best explanation for the correlation in question, simply because it is not an explanation but a refusal to offer an explanation. If any of the answers to our question offers a good explanation of the correlation, we should prefer it to this first answer.
The third answer is unattractive because it implies an unattractive view about truth-namely, that what is true explains how the world is rather than how the world is explaining what is true. 6 And not only is it implied that what is true explains how the world is, but it is implied that moral truths explain nonmoral being. Now, arguably there have been some who in recent times have endorsed the unattractive view that what is true explains how the world is. This seems to be so of those who advocate the so-called 'Reversal Argument,' which proposes that true moral principles can explain the presence of moral properties (e.g., Fitzpatrick 2008). For example, advocates of this argument might propose that the true moral principle It is wrong to humiliate others simply for pleasure explains why a senior colleague's publicly humiliating a junior colleague simply for pleasure has the property of being wrong. But, notice that even advocates of this argument are not proposing that moral truths explain nonmoral ontology; they are only proposing (a still unattractive view, in my opinion) that the presence of a moral property is explained by moral truth. Moreover, they are not proposing that differences across worlds in moral truth explain differences across worlds in moral properties. For, they think that the principles in question are necessarily true and so do not differ across worlds. Thus, even those who one might have initially thought would be attracted to the third answer should not be attracted to it.
Move then to the fourth answer. Recall: it proposes that differences in nonmoral ontology and differences in moral truth share a common explanation. This answer to our question is unattractive because there simply aren't any good candidates for what this shared explanation would be. What could it be that both explains why nonmoral ontology is different between worlds W and W* and also explains why moral truth is different between W and W*? The best candidates for that which explains differences in moral truth across worlds seem to be poor candidates for explaining differences in nonmoral ontology across worlds. For, the best candidates for explaining differences in truth across worlds are differences in nonmoral ontology and differences in moral ontology or being. 7 But, differences in nonmoral ontology can't explain differences in nonmoral ontology, since this would be circular. Nor is it plausible that differences in moral being explain differences in nonmoral ontology. For, good candidates for moral entities, such as the candidates for moral properties listed earlier, do not seem to explain nonmoral ontology. An action's being wrong or permissible or obligatory doesn't explain the nonmoral ontology of the action. Nor does a person's being vicious or virtuous explain the nonmoral ontology of this person. If anything, this gets the explanatory order reversed. 8 So, again, it is implausible that differences across worlds in nonmoral ontology and differences across worlds in moral truth share a common explanation.
This leaves us with our second answer: differences across worlds in moral truth are explained by differences across worlds in nonmoral ontology. This answer to our question does not face the difficulties facing the other answers. So, if there are not other independent difficulties facing the second answer, it will be better than the other three answers.
Are there other independent difficulties facing the second answer? I know of only two, and I take them up in the next section. For now, let me simply report that, at least at first glance, the second answer has much going for it. After all, examples of major ethical theories are not implausibly interpreted as offering proposals about exactly how it is that nonmoral ontology explains moral truth. For example, utilitarianism explains moral truths in terms of nonmoral pleasure and pain. Divine voluntarist theories explain moral truth in terms of nonmoral divine volitions. It may be that none of these theories is ultimately persuasive. But, we do not and should not object to the theories just because they attempt to explain moral truth in terms of nonmoral ontology. If we object to them, we object to them because we think the particular details of their proposed explanations of moral truth in terms of nonmoral ontology go awry. Accordingly, there is at least prima facie excellent reason to think that the second answer to our question is the best of the four answers. Differences across worlds in moral truth are best explained by differences across worlds in nonmoral ontology.
I said I would offer a two-step defense of claim 2. The first step was to argue that differences in moral truth are explained by differences in nonmoral ontology. The second step is to argue that if this is so, then differences in moral truth are explained exclusively by differences in nonmoral ontology. In defense of this step, I argue as follows. If differences in moral truth are explained by differences in moral ontology, but they are not explained exclusively by differences in nonmoral ontology, then differences in moral truth are explained redundantly. There is a presumption against redundant explanations, though; and this presumption can only be overcome if there is something that is exclusively explained by each member of a set of redundant explanations (see Merricks 2001). In other words, we should posit additional explainers of moral truths beyond nonmoral ontology only if there is something that is exclusively explained by these additional explainers-something that nonmoral ontology does not already explain. I propose, though, that there is no such thing. There is nothing that is exclusively explained by whatever we would propose explains moral truth in addition to nonmoral ontology. So, we should posit that differences in nonmoral ontology alone explain differences in moral truth. And this is what claim 2 says.
This ends my brief explanation and defense of the No Moral Properties Argument. In the next section, I take up the best objections to the No Moral Properties Argument of which I am aware, and argue that these objections are not persuasive. If my arguments are sound, then the No Moral Properties Argument demonstrates that there is very substantial motivation for contemporary ethicists to endorse moral property eliminativism.

The no moral properties argument defended
Here I will discuss the five best objections I know of to the No Moral Properties Argument. Each of the first three objections targets claim 2-the claim that differences across worlds in moral truth are explained exclusively by differences across worlds in nonmoral ontology.

Nonmoral ontology doesn't account for similarity
The first objection targets the first step in my defense of claim 2. In the first step of my defense, I argued that the view that differences in nonmoral ontology across worlds explain differences in moral truth across worlds provides the best available explanation for why there is a correlation between differences in moral truth and differences in nonmoral ontology. As part of my defense of this step, I claimed not only that this proposed explanation doesn't suffer from the same problems facing other proposed explanations, but that it doesn't suffer from other independent difficulties. The first objection to the No Moral Properties Argument disputes this latter claim, arguing that explaining differences in moral truth with differences in nonmoral ontology does face an independent difficulty.
The difficulty derives from the fact that predications of common predicates to distinct subjects ought to be explained by similarities between those subjects. For example, when we predicate ''is a dog'' of both Tilly and Bisquick, we do so appropriately only because there is some similarity between Tilly and Bisquick. This is true regardless of the ontology that accounts for these similarities. For example, the Platonist may think that the similarity between Tilly and Bisquick is explained by there being a property that Tilly has and that Bisquick also has, while the nominalist may believe that the similarity is explained by Tilly and Bisquick having distinct but exactly resembling properties. In both cases, predicating a common predicate of distinct subjects is appropriate only if there is a similarity between the subjects. This observation might be turned against my defense of Claim 2 when we notice that moral predicates appear to be appropriately predicated of distinct subjects when the nonmoral ontology of the relevant subjects is not similar (see Audi 2012: 106-107). For example, the nonmoral ontology of an action of murder differs dramatically from the nonmoral ontology of an action of gossip, but the predicate ''is a wrong action'' is arguably appropriately predicated of each. Such cases reveal, then, that nonmoral ontological items are not good candidates for explaining moral predications. Instead, there must be something else-something that is not an item of nonmoral ontology-that both accounts for the similarity between the subjects in these cases and explains the appropriateness of the predications. One candidate for such a thing might be moral properties, the very things I wish to argue do not exist. It is appropriate to predicate ''is a wrong action'' of the gossip and the murder because each has the property of being a wrong action, for instance. I offer two responses to this objection. First, as noted in the previous section, I point out that advocates of certain major ethical theories are not implausibly interpreted as attempting to identify exactly what nonmoral similarities there are between subjects to which the same moral predicates are applicable. The theological voluntarist, for example, proposes that God wills that gossip not take place and that murder not take place, and that these willings explain why ''is a wrong action'' is appropriately predicated of both acts of gossip and acts of murder. If she is right, then plausibly there are items of nonmoral ontology that both explain the similarity between acts of gossip and acts of murder and that make assigning the same moral predicate to these acts appropriate. Namely, each act has been willed by God not to occur. Similar things can be said about other ethical theories. To the extent that these theories are plausible, it is plausible that there are similarities in nonmoral ontology between distinct subjects to which the same moral predicates are applicable. And, if there are, then the first objection never gets up and running.
Suppose, though, that the objection does get up and running. Suppose, that is, that there are persistent cases where even the best available ethical theories cannot point us toward specific similarities in nonmoral ontology between subjects to which the same moral predicate is appropriately applied. I still think there is a problem with the present objection. My second response to this objection is that the objection ends up only replacing one mystery with another parallel and equally perplexing mystery, and it does so at a price of theoretical complexity.
To see this, note that the present objection tells us that if there is a difference between moral truth in worlds W and W*, there will be a difference in the exemplification of moral properties in W and W*. For it is moral properties, the objector says, that explain moral predications. But, given claim 1 from the No Moral Properties Argument, it is also true that there must be a difference in nonmoral ontology between any worlds W and W* that differ in moral truth. It will follow that necessarily, for any worlds W and W*, if there is to be a difference between the exemplification of moral properties between W and W* there must also be a difference in nonmoral ontology between W and W*. Now, just as we asked in section one why it is that differences in nonmoral ontology are correlated with differences in moral truth, we might ask why it is that differences in nonmoral ontology are, according to the present objection, correlated with differences in moral properties. The question is: why is it that we only get differences in moral properties if we get differences in nonmoral ontology? I propose that the best answer is that differences in nonmoral ontology explain differences in moral properties. All other available answers here are worse. We shouldn't say that there is no explanation for this correlation, as this leaves unexplained something that cries out for explanation. Not even those who posit socalled ''brute'' necessary connections between nonmoral ontology and moral properties think that the necessary correlation between differences in nonmoral ontology and moral properties across worlds is unexplained; they think it is explained by the very brute necessary connections they posit. Nor should we say that it is differences in moral properties that explain differences in nonmoral ontology, since there can be differences in nonmoral ontology without differences in moral properties (for example, if one instance of gossiping were replaced by an exactly similar one). Nor, finally, should we say that differences in nonmoral ontology and differences in moral properties have a common explanation, since there just aren't any good candidates for what this common explanation would be.
Suppose, then, that differences in nonmoral ontology explain differences in moral properties. If they do, however, we get a new puzzle. For, if differences in nonmoral ontology explain differences in moral properties, then nonmoral ontology will need to explain moral properties. For example, the nonmoral ontology of an act of murder or an act of gossip will need to explain the moral properties of these acts. But, if it is a puzzle how the nonmoral ontology of these acts could explain the appropriateness of predicating ''is a wrong act'' of these acts, it is equally puzzling how the nonmoral ontology of these acts could explain the moral properties of these acts (presumably their both having the property of being wrong). The old puzzle was to explain how the quite diverse nonmoral ontology of gossiping and murdering could explain the appropriateness of predicating ''is a wrong act'' of these acts. The new puzzle is to explain how the quite diverse nonmoral ontology of gossiping and murdering could explain the exemplification of the property of being wrong by these two acts.
As far as I can see, neither puzzle is any less mysterious than the other. Thus, both the view I am advocating and the view advocated by a person who endorses the first objection to my view face a difficult puzzle. However, there is something that sets my view apart from the view endorsed by the objector. My view is less theoretically complex. The specific kind of complexity at issue will differ depending on what kind of existence the objector thinks moral properties have. If she claims they have ontological existence (a natural interpretation, since many will think this is the only kind of existence), then my view will be less ontologically complex. If she follows the lead of certain recent authors in metaethics and claims instead that moral properties exist, but do not exist in an ontological sense, 9 her view will still be more complex-just not more ontologically complex. We might say that her view is more existentially complex, requiring additional kinds of things to exist, even if not in an ontological sense. Thus, both my view and the view faced by this objector will face equally difficult puzzles about explanatory relations between nonmoral ontology and something else (moral truths in my case-moral properties in the objectors' case); but the objectors' view also faces the difficulty of being more complex than my view.
Of course, ontological or existential complexity is not itself a problem for a view. But, unnecessary ontological or existential complexity is. Whether moral properties are thought to exist in an ontological sense or only in a non-ontological sense, positing them should be justified by their ability to enhance the explanatory power of our ethical theories-a point granted by those who claim that moral properties exist only in a non-ontological sense. 10 I've argued in this subsection that moral properties do not offer the explanatory advantage of enabling metaethical theories to better explain similar moral predications in the face of diverse nonmoral ontology. To the extent that there is a puzzle about such predications, it is equally puzzling with and without moral properties. Thus, if moral properties are to offer an explanatory advantage, we must find it elsewhere. In the next two subsections, I discuss two further possibilities for locating this advantage.

Moral properties explain nonmoral events
Move, then, to a second objection to the No Moral Properties Argument, one that addresses the very issue just raised concerning the first objection. The second objection proposes that moral properties do perform distinctive explanatory duties. Specifically, they provide the best available explanations for a wide range of nonmoral events. Since they do, positing them is not unnecessarily complex.
What, then, can be said to defend this unique explanatory power of moral properties? The typical defense here has appealed to counterfactual tests for explanatory relevance in order to show that there are certain phenomena which are better accounted for through moral explanations than through non-moral explanations. 11 Here is a summary of the defense from Majors: 9 See especially Parfit (2011, ch. 31) and cf. also Scanlon (2014, ch. 2). 10 Scanlon writes, ''We have reason to introduce additional normative concepts and relations just in case these allow us to give a more coherent and satisfactory account of normative matters (2014: 26).'' Parfit writes, ''There are some claims that are irreducibly normative in the reason-involving sense, and are in the strongest sense true… For such claims to be true, these reason-involving properties need not exist either as natural properties in the spatio-temporal world, or in some non-spatio-temporal part of reality (2011: 486).'' Coupled with Parfit's commitment to the existence of moral properties, this passage makes clear that he thinks that positing these properties is justified because their existence (though only their nonontological existence) is needed in order to make normative truths true-a contention I am resisting in the paper. 11 Sturgeon (1991) is an early example.
Setting aside aberrant cases involving overdetermination and pre-emption, it is a general truth that if c causes e, then it must be the case that had c not occurred, e would not have occurred either…. Take now the claim that the injustice of the society caused a revolt. The moral property of injustice satisfies the constraint. Had the society not been unjust there would have been no revolt. But no non-moral or naturalistic property satisfies the constraint. Suppose that the injustice of the society supervened upon naturalistic properties N 1 , N 2 ,…,N n . It is not true that had these naturalistic properties not been instantiated, the revolt would not have occurred. This is because the property of being unjust is multiply realizable. The closest possible world in which this set of naturalistic properties is not instantiated is a world in which a different set was present, one which is alike sufficient for the instantiation of injustice (pp. 9-10). 12 To respond, I will offer a charitable, formal reconstruction of the defense here offered of the unique explanatory power of moral properties and I will show where the defense fails.
Begin with a charitable, formal reconstruction of the argument outlined in the foregoing passage. Let us take the example of the revolt, and call the revolt R. Let us call the society in which the revolt takes place S and let us call the moral property of being unjust, if there is such a property, U. Finally, let us call the non-moral properties which are the best candidates for explaining the exemplification of U, given that U is exemplified, the Ns. With these abbreviations, and setting aside aberrant cases of overdetermination and preemption, here is a charitable reconstruction of the above argument: 1. There is some x such that ''x explains R'' is true. 2. For any c and e, if ''c explains e'' is true, and c consists in some entities, the Xs, exemplifying some properties, the Ps, then were the Xs not to have exemplified the Ps, e would not have obtained. 3. It is not the case that were S not to have exemplified the Ns, R would not have obtained. 4. It is the case that were S not to have exemplified U, R would not have obtained. 5. So, ''S's exemplifying U explains R'' is true but it is not true that ''S's exemplifying the Ns explains R.'' 6. If ''S's exemplifying U explains R'' is true but it is not true that ''S's exemplifying the Ns explains R,'' then the moral property U performs explanatory work not performed by any nonmoral properties. 7. So, the moral property U performs explanatory work not performed by any nonmoral properties.
If the argument offered here works in the case of the injustice of society explaining the revolt, then presumably adaptations of it will work in other parallel cases. The upshot is that there is indeed explanatory work accomplished by moral properties that is not accomplished by any non-moral properties.
I think this argument suffers from quite a number of problems, though here I will highlight only two. The first problem I wish to highlight does not target any particular premise in the argument, but instead offers a parody of it. By doing so, the response attempts to show, without identifying exactly where the argument goes awry, that it has gone awry somewhere, since it proves too much.
The parody I will offer argues that the property of containing a hole does unique explanatory work. To set up the parody, suppose that Joe puts a coin in his pocket and later finds out the coin is gone. He then notices a hole in his pocket. Use P to abbreviate ''the pocket,'' G to abbreviate ''the coin's being gone,'' H to abbreviate ''the property of containing a hole'' and the Ns to abbreviate ''the properties that explain the pocket's having a hole, supposing it has a hole.'' The argument then runs as follows: 1. There is some x such that ''x explains G'' is true. 2. For any c and e, if ''c explains e'' is true, and c consists in some entities, the Xs, exemplifying some properties, the Ps, then were the Xs not to have exemplified the Ps, e would not have obtained. 3. It is not the case that were P not to have exemplified the Ns, G would not have obtained. 4. It is the case that were P not to have exemplified H, G would not have obtained. 5. So, ''P's exemplifying H explains G'' is true but it is not true that ''P's exemplifying the Ns explains G.'' 6. If ''P's exemplifying H explains G'' is true but it is not true that ''P's exemplifying the Ns explains G,'' then the property of containing a hole performs unique explanatory work. 7. So, the property of containing a hole performs unique explanatory work.
This argument parallels the argument offered above as an objection to the No Moral Properties Argument precisely. And, the defenses employed in defense of the argument presented as an objection to the No Moral Properties Argument can be modified to support this argument as well. However, any parsimonious metaphysician would reject the conclusion of this argument as absurd. She would do so because positing the existence of the property of containing a hole is unnecessarily complex-whether the existence in question is ontological existence or not. Thus, whatever the argument presented above as an objection to the No Moral Properties Argument shows, it doesn't show that positing moral properties is not unnecessarily complex. But, this is precisely what the argument was supposed to show. So, without identifying precisely where the argument fails, we can be confident that it fails.
This first objection naturally leads us to ask if we can identify exactly where the argument goes wrong. Though I think it goes wrong in multiple places, I will focus on only one here, targeting claim 3 in the formalized reconstruction of the objection. Claim 3 says that it is not the case that were S not to have exemplified the Ns, R would not have obtained. This kind of claim is typically defended by appealing to the fact that if S had not exemplified the Ns, S would have exemplified some other non-moral properties, the N*s, which would have explained S's exemplification of U, and S's exemplification of U would in turn have explained R's obtaining. Indeed, Majors offers just such a defense of claim 3 in the passage cited above. Unfortunately, the claim appealed to here is implausible. For, if the N*s rather than the Ns had been instantiated by S, then if there had been a revolt, we do not have good reason for thinking that this revolt would have been revolt R. There may well have been a revolt, but there is no reason to claim that the revolt that would have obtained would have been revolt R.
Another way of putting the problem is this. Majors and others who would offer the above defense of 3 are confusing causation or explanation between event types with causation or explanation between event tokens. Sure, it is true that a token of the revolt event type would have obtained even in the absence of S's exemplification of the Ns. But, we do not have reason to think that token revolt R would have. Accordingly, we could at best replace claim 3 with claim 3*: It is not the case that were the Ns not to have obtained, a token of the revolt event type would not have obtained. Once we replace 3 with 3*, however, it will not follow from claim 2 that ''S's exemplification of the Ns explains R'' is not true. At best, given a suitably modified claim 2 that focuses on event types rather than particular token events, it will follow that ''S's exemplification of the Ns explains why a token of the revolt event type occurred'' is not true. Yet, even this claim is not plausible. For, we now have no reason to think that ''S's exemplification of the Ns explains R'' is not true, and R is certainly a token of the revolt event type. It seems that what this reveals is that when we replace 2 with a version of the explanatory relevance principle focused on event types rather than particular tokens of event types, the principle is false.
To summarize, the problem is this. The typical reasons advanced in favor of claim 3 do not motivate claim 3, but rather claim 3*. But, claim 3* does not allow for claim 5 to be inferred from claim 2. If we attempt to derive a modified version of claim 5 concerned with event types rather than event tokens, then the necessary modification to claim 2 will render this claim false, as illustrated by the particular example in view here. Once we recognize the difference between event types and tokens of event types, it becomes difficult to construct a version of the argument that supports the unique explanatory power of moral properties.

Moral properties explain moral principles
I consider one final objection to premise 2 of the No Moral Properties Argument. This objection proposes that nonmoral ontology alone cannot account for differences in moral truth between worlds. For, in addition to differences between nonmoral ontology, true moral principles are also needed to explain such differences (cf. Fitzpatrick 2008).
For example, supposing worlds W and W* are alike in all respects except that in W Fred lies to Steve and in W* Fred pats Steve on the back, there will plausibly be a difference in moral truth between W and W*. In W, it will be true, for example, that Fred did something wrong whereas in W* this will not be true. Yet, this difference in moral truth cannot be accounted for solely by the difference in nonmoral ontology between W and W*-i.e., that in W Fred lies to Steve and in W* he pats him on the back. In addition to this difference in nonmoral ontology, we need the necessarily true moral principles that entail that instances of lying are wrong. These principles are not different between W and W*, since they are necessarily true. Nonetheless, they are needed to explain the differences between moral truth in W and W*. It isn't just the fact that Fred lies to Steve in W, but this fact together with the moral principle that, e.g., lying is wrong, that explains why the claim that Fred did something wrong is true in W but not in W*. Yet, moral properties are needed to account for these principles. It is because the moral property of wrongness is the way that it is that it is necessarily true that lying is wrong. The claim that, necessarily lying is wrong is a claim that asserts a necessary connection between two distinct properties: the property of being a lie and the property of being wrong.
It will likely come as no surprise to the reader that my response to this objection is similar to my response to the first objection concerning the inability of nonmoral ontology to account for similarity. Here again the objector purchases moral properties at the price of unnecessary theoretical complexity. For, in place of the moral principles put forward by the objector, an alternative set of principles that does not necessitate positing moral properties will perform equally well. This alternative set of principles is a set of principles concerning truthmakers for moral truths. Like the moral principles envisioned by the objector, these truthmaking principles are also necessary truths. And, like the principles envisioned by the objector, these truthmaking principles will, together with the relevant nonmoral differences between worlds, completely explain differences in moral truths between worlds. Yet, they will do all of this work without necessitating positing moral properties.
Take the case of Fred's lying, for illustration. Rather than the moral principle lying is wrong, understood in the way forwarded by the objector, contributing to the explanation for the difference in moral truths between W and W*, the relevant necessary truth will be instances of lying make it true that the liar has done a moral wrong. This principle, together with the nonmoral differences between W and W*, will fully explain the differences in moral truths between W and W*. Yet it doesn't necessitate positing moral properties. It needn't be understood as proposing that a necessary connection obtains between the property of being a lie and the property of being morally wrong. Rather, it posits a necessary connection between the property of being a lie and the truth of a certain moral claim. 13 Moreover, it is not implausible that the present objector will (or in any case, should) grant that such truthmaking principles are true. For she will agree that necessarily, if the relevant nonmoral ontological items in these principles are present, then the relevant moral property is present, and that necessarily, if the relevant moral property is present, then the relevant claim is true. Moreover, she will grant that the relevant moral property asymmetrically depends on the relevant nonmoral ontology, and that the truth of the relevant moral claim asymmetrically depends on the relevant moral property. Yet, it plausibly follows from these claims that the relevant nonmoral ontology makes true the relevant moral claim.
So, the objector may very well grant that the relevant truthmaking principles are true. And it is clear that these principles can do exactly the work of the principles she appeals to. Yet, they do this work without necessitating an appeal to moral properties, like her principles do. Thus, the principles she appeals to are purchased at the price of unnecessary theoretical complexity.

The no moral properties argument proves too much
The final two objections resist the No Moral Properties Argument in some way other than by denying claim 2. The fourth objection is that the No Moral Properties Argument proves too much. The objection is that if the argument successfully shows that there are no moral properties, then parallel arguments could be marshaled to show that a whole host of other putative properties with much less questionable status are also not properties. Here again is Majors: [E]xactly the same relationship obtains between other sets of higher-level properties, such as those found in the special sciences, and their realizers or subvenient bases. Why could one not argue that it is not in fact the beliefs and desires of a higher animal which explain its behavior, but rather its neurophysiological states? Come to that, neurophysiological states are themselves supervenient. So they too are surely epiphenomenal, and we must continue to search below for a genuine cause. One ends up with either a great absurdity, or a truly colossal one. It would surely be quite absurd to regard only basic physics as causally efficacious, on the grounds that only basic physical properties do not supervene upon other properties. And this would appear to be the ultimate result of the line of thinking employed here (2007: 9).
The worry is that if my argument shows that moral properties do not exist and do not perform unique explanatory work, then we will have to say similar things about the properties posited in the special sciences. Psychological properties, for example, will also neither exist nor perform unique explanatory work.
My response to this worry is simply that the consequence noted is not absurd, if understood correctly. The consequence that follows from my argument is not that explanations proposed in the special sciences aren't true. Rather, the consequence is that these explanatory postulations, if true, are made true by entities postulated only by the physical sciences. But, this consequence is not obviously troubling. In fact, precisely this proposal has been recommended recently by leading philosophers of science and mind. Heil and Robb (2013) propose that the goal of realism about the mental should be ''not the preservation of mental properties, but the preservation of mental truths. In that case we would seek an account of the mind that provides plausible truthmakers for psychological and psycho-physical claims, including claims concerning mental causation.'' They continue: One possibility is that truthmakers for psychological truths include irreducibly mental properties. This is not the only possibility, however. Another is that psychological assertions are made true by physical states and properties, states and properties answering to predicates belonging to physics and chemistry…. All parties agree that mental predicates and descriptions differ from physical predicates and descriptions. Application conditions for mental terms and physical terms diverge in ways that preclude definitional reduction of the one to the other. Perhaps it is a mistake, however, to move from this linguistic fact to a substantive ontological thesis: mental and physical predicates designate properties belonging to distinct families of properties.
In a way, I am only applying lessons proposed by Heil and Robb in the metaphysics of mind to the field of the metaphysics of morality. Just as they propose that one might maintain realism about the mental by retaining mental truths (including explanatory mental truths) without positing mental properties, I propose that a certain kind of moral realism can be maintained if we retain moral truths (including explanatory moral truths) but not moral properties. The key to upholding the view posited by Heil and Robb is that there be physical or chemical truthmakers for mental truths, whereas the key for my view is that there be nonmoral truthmakers for moral truths. The view that there are such truthmakers is, in each case, a very tempting one for those who are attracted to realism of the relevant sort. This, as I argued in Sects. 2 and 3.3, is true in the moral case because the fact that there cannot be differences in moral truths without differences in nonmoral ontology is best explained by the thesis that moral truths are explained by nonmoral ontologyi.e., they are made true by nonmoral ontology. A similar argument could profitably be advanced in the mental case.
When it is understood that the success of my argument would not imply that there are no (explanatory) truths in the special sciences, but that it would at best imply that the truthmakers for these truths are physical or chemical entities, this fourth objection to the No Moral Properties Argument loses its force. It may indeed be that the success of my argument lends credence to the view that we do not need to posit more than physical or chemical properties to account for truths in the special sciences. But, this view is one that is already gaining currency. Indeed, on one way of looking at things, I am simply applying the lessons learned from advocates of this view to the field of the metaphysics of morality.

Moral properties are nonmoral properties
The final objection I will consider targets claim 4 of the No Moral Properties Argument, which claims that if differences across worlds in moral truth are explained exclusively by nonmoral ontology, then there are no moral properties.
The objector claims that each moral property is identical to a nonmoral property. 14 As such, claim 4 is a non-sequitur. For, if the nonmoral properties that explain differences in moral truth across worlds are also moral properties, then despite the fact that it is exclusively nonmoral properties explaining these differences, it will still be true that moral properties explain them as well. The relevant nonmoral properties just are moral properties.
As odd-sounding as this objection may at first seem, it seems to me that it is an objection that coheres quite well with the well-represented contemporary view often called ''moral naturalism''. It is common for advocates of this view to propose that moral properties such as being morally wrong are identical to natural properties, such as decreasing overall welfare. But these natural properties are nonmoral properties, on the account of nonmoral properties sketched at the outset of this paper. So, on this view moral properties are nonmoral properties-an option I emphasized was strictly speaking not ruled out at the outset of the paper.
The present view shares much in common with the eliminativist view defended in this paper, and in fact has been defended on similar grounds. Indeed, the present view appears to be just as ontologically and existentially simple as moral property eliminativism. Advocates of the present view do not believe in any more properties than do their eliminativist counterparts. They just claim, where their eliminativist counterparts do not, that certain identity claims are true about the properties that they believe in.
This begins to make one worry that there couldn't be any reason for adjudicating between these views. And, as such, the motivation I have cited in this paper for moral property eliminativism is limited in an important way. This isn't to say that the argument of the paper doesn't provide significant motivation for moral property eliminativism-motivation that is nearly wholesale overlooked in contemporary theorizing-yet, still, it would be desirable if something could be said in favor of moral property eliminativism versus this very similar rival view.
Apart from the incredulous stare one might be inclined to offer at the apparently theoretically inelegant claim that moral properties are nonmoral properties, I do think that at least one principled reason can be offered for favoring eliminativism to this rival, similar view. The reason appeals to the simplicity of the eliminativist view, albeit not the ontological or existential simplicity of the view. As highlighted above, there is just one simple difference between the eliminativist view and this rival. They hold all things in common, except that the rival adds certain identity claims to her theory that are not included in the eliminativist theory. The rival theory maintains, just like the eliminativist, that differences in moral truths across possible worlds are explained exclusively by nonmoral ontology. She maintains, indeed, that all moral truths are made true exclusively by nonmoral ontology. She agrees with the eliminativist's truthmaking principles for moral truths. She just adds, in addition, that certain nonmoral properties are identical to moral properties, while the eliminativist does not.
This addition doesn't add ontological or existential complexity to her theory. But, nonetheless, it is an addition, and it seems to be a wholly unmotivated addition. What possible reason could there be for the addition, except perhaps to escape from the No Moral Properties Argument? It seems clear that there is none. Thus, while the present view poses a certain threat to the No Moral Properties Argument, and while it is a view that has attracted significant adherents in contemporary ethics, it appears that there is nothing to motivate the view over the eliminativist view. Advocates of the view should instead embrace the eliminativist view as retaining the core of their own theory, without its unnecessary complications.

Conclusion
I've now responded to the five best objections to the No Moral Properties Argument of which I am aware. In light of these responses, I conclude that moral property eliminativism is well-motivated. This is not to say that other important objections to the No Moral Properties Argument are not available. For example, some ethicists may wish to argue that moral properties play an indispensible role in explaining the motivating power of moral facts (cf. Darwall 1983) or our practices of moral deliberation (cf. Enoch 2011). I have not addressed these arguments because they are generally thought to require more controversial assumptions than the arguments with which I have engaged, and it was necessary to be selective because of limitations of space. Nonetheless, the availability of such objections does illuminate a limitation of the force of the argument presented in this paper.
Likewise, I have not engaged with objections that would challenge not only my moral property eliminativism, but eliminativist views more broadly. 15 Such objections have received sustained attention in the literature on eliminativist views in other domains, and so it seemed most appropriate here to focus on objections of special relevance to moral property eliminativism. Again, however, the availability of such objections does illuminate a limitation of the present argument.
Even given these limitations, it should be clear that the present paper has uncovered very significant motivation for moral property eliminativism-motivation that far outstrips the attention the view has thus far received from contemporary ethicists, particularly ethicists who affirm that there are moral truths.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.