Realist dependence and irrealist butterflies

In this paper, I argue that a realist account of the modality of moral supervenience is superior to a non-cognitivist account. According to the recommended realist account, moral supervenience amounts to strong supervenience where the outer ‘necessary’ is conceptual and the inner metaphysical. It is argued that non-cognitivism faces a critical choice between weak and strong supervenience where both options are implausible on this view. However, non-cognitivism seems to have an important advantage: It can explain why the outer ‘necessary’ is conceptual by reference to the function of moral language to influence behaviour. In the main part of the paper, I argue that realism is able to explain why ‘necessary’ in moral supervenience needs to be understood in the recommended manner by reference to the connection between moral properties and moral reasons. Moreover, I argue that the realist account has other attractive features. In contrast to non-cognitivism, it can unify the normative sphere by being generalizable to other normative notions. In addition, it can be part of an explanation of why moral language can have the function to influence behaviour.


Introduction
In a wonderful metaphor, Toni Rønnow-Rasmussen observes that 'Values are not like butterflies that happen to settle on a flower' (Rønnow-Rasmussen, 2006, p. 2)).The moral depends on the non-moral: Necessarily, moral terms apply to objects because, or in virtue of, their having non-moral properties.It is generally agreed that in order for a metaethical view to account for this notion of moral dependence, it needs to maintain some version of moral supervenience, which entails that there is a certain necessary connection between the moral and the non-moral.There agreement ends, however.In particular, it is commonly thought that realism has difficulties to account for the modality of moral supervenience, whereas non-cognitivism is able to do so.In this paper, I argue that the converse is the case: Realism provides a superior account of the modality of moral supervenience.Thus, the paper provides an argument for realism and against non-cognitivism based on supervenience.

Realism and non-cognitivism
As I will understand moral realism, it amounts to three claims: (i) Cognitivism: Moral sentences such as 'x is right' express moral judgments which consist in beliefs that ascribe moral properties to objects like actions and agents.(ii) Moral properties are instantiated which means that some moral judgments are true.(iii) Moral properties are mind independent: Their nature is not counterfactually dependent merely on the mental attitudes of individual agents. 1hus understood, there are different versions of realism.On reductionist realism, moral properties are identical to non-moral properties, i.e. properties that can be fully defined without employing moral terms.2On non-reductionist realism, moral properties are not identical to non-moral properties thus understood.On naturalist realism, moral properties consist in natural properties.There are both reductionist and nonreductionist versions of naturalist realism. 3On non-naturalist realism, moral properties are sui generis and not identical to any other type of properties. 4In this paper, 'realism' refers to the generic sense of realism rather than any particular version of this view.

Realist supervenience
In philosophy, dependence relations are commonly characterized by employing the notion of supervenience.As realism maintains that moral judgments ascribe moral properties to objects, it can characterize moral supervenience directly by reference to connections between properties.There are two main versions of this claim.Consider first: Realist Weak Supervenience (RWS): It is necessary that, for any object x, and for any moral property M, if x is M, then there is some set of non-moral properties G (G 1 , G 2 , G 3 ,…) such that (a) x has G, and (b) for any object y, if y has G, then y is M.
The outer 'necessary' binds the formula as a whole. 6In weak supervenience, there is no inner 'necessary' that prefixes the implication in (b).Thus, it does not extend to all possible worlds.Consider next: Realist Strong Supervenience (RSS): It is necessary that, for any object x, and for any moral property M, if x is M, then there is some set of non-moral properties G (G 1 , G 2 , G 3 ,…) such that (a) x has G, and (b) it is necessary that, for any object y, if y has G, then y is M.
As before, the outer 'necessary' binds the formula as a whole.In strong supervenience, there is in addition an inner 'necessary' that prefixes the implication in (b).Thus, it says that it holds in all possible worlds that any object which has G has M. 7  The dependence relation between the moral and the non-moral is asymmetrical in that the former depends on the latter but not the other way around.One attempt to secure this notion on realism is to add the following claim: Realist Asymmetry: It is not the case that the reverse of the relation between moral properties and non-moral properties as stated in weak or strong supervenience ((RWS) or (RSS)) holds.
As regards strong supervenience, the claim entails that the following is not the case: It is necessary that, for any object x, and for any set of non-moral properties G, if x has G, then there is a moral property M such that (a) x is M, and (b) it is necessary that, for any object y, if y is M, then y has G. Thus understood, it means that there is a general asymmetric relation between the class of moral properties and the class of non-moral properties.However, it is compatible with reductionist versions of realism according to which a particular moral property M is identical with a particular set of non-moral properties G. 8  In this paper, I will assume that moral supervenience and asymmetry are necessary for realists to account for the notion that the moral depends on the non-moral.However, they might not be sufficient and need to be supplemented with further 6 For ease of exposition, I will refer to 'outer' occurrence of 'necessary' also when discussing weak supervenience. 7Moreover, G should be understood not to include any 'superfluous' elements.It contains as many nonmoral properties that are sufficient for a particular object to have M, but not more.The following claim should therefore be added to those above: Non-Redundancy: There is no proper subclass of G, G * , such that if G * is substituted for G, weak or strong supervenience ((RWS) or (RSS)) holds.In what follows, I will take this condition to be implied. 8To explain: According to strong supervenience, it holds, necessarily, for all moral properties that if an object has a moral property, it has some set of non-moral properties such that, necessarily, whatever object which has that set of non-moral properties has the moral property in question.According to realist asymmetry, it is not the case that it holds, necessarily, for all sets of non-moral properties, that if an object has a set of non-moral properties, it has some moral property such that, necessarily, whatever object which has that moral property has the set of non-moral properties in question.This leaves open the possibility that the latter relation holds for some set of non-moral properties.As a result, realist asymmetry is compatible with a moral property M being identical with a set of moral properties G.The fact that we think that M depends on G, but that G does not depend on M, even if M and G are identical might be explained by the pragmatics of our use of terms like 'depend' (Strandberg, 2008, pp. 148-156)).claims.In particular, it might be maintained that the concept of grounding is needed to account for moral dependence, at least on non-naturalism. 9It is important to point out, however, that grounding and supervenience do not provide competing accounts of dependence.Indeed, on the received view a successful view of moral grounding explains and thereby entails moral supervenience. 10 Let us now return to the difference between weak and strong supervenience.It is plausible to think that realists should opt for strong supervenience rather than weak.The primary reason is that weak supervenience is too weak to be part of an account of the notion that the moral depends on the non-moral. 11Assume that we want to claim that an action is morally right because it has a certain set of non-moral properties G. Weak supervenience merely states that within a possible world any action that has G is right.This indicates that, on weak supervenience, it would be mistaken to claim that an action is right because it has G, since an action could have G and yet not be right.In that case, the co-instantiation of rightness and G does not seem to be a matter of dependence, but rather coincidence: actions that have G happen to be right.Strong supervenience provides the required supplement by stating that it holds in all possible worlds that any action that has G is right.
Furthermore, much of our moral thinking is constituted by thought experiments.Assume that one wonders whether the fact that an action causes happiness is relevant as to whether it is morally right.One might then ask if the action would be right in a possible world where it does not cause happiness.We often trust the results of such thought experiments and let our moral decisions be guided by them.However, if only weak supervenience is the case, thought experiments would not be of any help, since we would not be justified to hold beliefs about one possible world based on what we believe about other possible worlds.For example, we would not be justified to believe that causing happiness contributes, or fails to contribute, to actions being right in the same way in our world as it does in the possible worlds employed in our thought experiments.However, on strong supervenience we are justified to trust the result of such thought experiments, since what is the case in one world extents to other worlds.
It might next be asked how the two occurrences of 'necessary' in strong supervenience should be understood.As noticed, it is a requirement on being competent with the meaning of moral terms to acknowledge that they apply in virtue of objects having non-moral properties.As a result, it is generally agreed that the outer 'necessary' needs to be understood as conceptual necessity.By contrast, it does not seem plausible to understand the inner 'necessary' in this manner.One reason is that it does not seem be a matter of linguistic competence to know about a set of nonmoral properties G that if an object has G, it has a certain moral property.Another reason is that some instances of necessary implications from non-moral properties to moral properties constitute moral principles.However, it might be argued that such principles cannot be conceptually necessary, since it would mean that they lack nor-9 See e.g.Bader (2017); Rosen (2017), and Leary (2017).

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mativity.Instead, it seems more plausible to think that the inner 'necessary' should be understood as metaphysical necessity.In Sect. 10, I return to the claim that moral principles would lack normativity if they are understood as conceptually rather than metaphysically necessary. 125 Non-cognitivist supervenience According to non-cognitivism, moral judgments do not ascribe moral properties to objects, but consist in non-cognitive attitudes.As a result, this view cannot characterize moral supervenience by reference to any relation between properties.Instead, it is accounted for in terms of the connection between an agent's moral attitudes and her beliefs about what non-moral properties objects have.It is maintained that to be competent with the meaning of moral terms, an agent needs to be consistent in having the same moral attitude towards objects that she believes have the same non-moral properties. 13 It is rarely stated clearly how moral supervenience should be understood according to non-cognitivism. 14In what follows, I suggest ways of formulating moral supervenience on this view.Assume that an agent's moral judgment to the effect that x is morally right consists in her having moral attitude M towards x.Weak supervenience might then be formulated as follows: Non-Cognitivist Weak Supervenience (NWS): It is necessary that, for any object x, and for any agent S, if S has moral attitude M towards x, then there is some set of non-moral properties G (G 1 , G 2 , G 3 ,…) such that (a) S has attitude M towards x because she believes that x has G, and (b) for any object y, if S believes that y has G, then S has attitude M towards y. 15   Similarly, strong supervenience can be formulated as follows: 12 There are philosophers who deny strong supervenience and argue that the inner 'necessary' should be understood as normative necessity (see e.g.Rosen (2020)).Roughly: In any worlds in which the same moral principles hold, for any object y, if y has G, then y is M. The view is compatible with different moral principles holding in different worlds such that objects that have G in one world have M and objects that have G in another world do not have M.It is generally argued that normative necessity is insufficient to explain moral dependence (see e.g.Bader (2017, pp. 107-112); Väyrynen (2018, pp. 181-182), and Dreier (2019, pp. 1404-1407)).Cf. footnote 34 below.For an independent argument against strong supervenience and for the normative necessity reading, see Hattiangadi (2018).Unfortunately, I do not have space to comment on these important contributions. 13See e.g.Hare (1952, pp. 131-134) and Blackburn (1993, pp. 136-137, 146).
14 However, see Gibbard (2003, p. 90). 15It might be worried that the formulation 'S has attitude M towards x because she believes that x has G' is too demanding since an agent who is fully competent with a moral term need not have any comprehensive belief about the content of a set of non-moral properties G.However, as I understand the formulation, it merely entails that the agent has attitude M towards x because she has a belief to the effect that x has some set of non-moral properties G, which is compatible with her not having any detailed view about in which non-moral properties G consists.

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Non-Cognitivist Strong Supervenience (NSS): It is necessary that, for any object x, and for any agent S, if S has moral attitude M towards x, then there is some set of non-moral properties G (G 1 , G 2 , G 3 ,…) such that (a) S has attitude M towards x because she believes that x has G, and (b) it is necessary that for any object y, if S believes that y has G, then S has attitude M towards y.
It follows on both supervenience claims that in case an agent does not comply with them, she does not make a moral judgment, since she does not have a moral attitude of which such a judgment is constituted.
In order to secure the asymmetric relation between the moral and the non-moral, non-cognitivists might add the following claim: Non-cognitivist Asymmetry: It is not the case that the reverse of the relation between moral attitudes and beliefs as regards non-moral properties as stated in weak or strong supervenience ((NWS) or (NSS)) holds.
With regard to strong supervenience, this claim entails that the following is not the case: It is necessary that, for any object x and any agent S, if S believes that x has a set of non-moral properties G, then she has a moral attitude M such that (a) she believes that x has G because she has moral attitude M towards x and (b) it is necessary that for any object y, if she has attitude M towards y, she believes that y has G.
We might now query whether non-cognitivists should adopt weak or strong supervenience.Importantly, in this regard they seem to face a critical choice.As far as I know, Rønnow-Rasmussen was first to pay attention to it: It is one thing to claim that in endorsing Va [a having value V] we commit ourselves by conceptual necessity to subscribe to a principle like the one in premise p [for all x, if Nx, then Vx].It is quite another thing to say that endorsing Va commits you, by conceptual necessity, to subscribe to a principle that in part expresses that there holds a necessity relation between certain natural properties and a certain value property.The latter claim squares badly with his idea that value terms have no fixed descriptive content.(Rønnow-Rasmussen, 2006, p. 8)) 16   In the frame of the present discussion, we can formulate the choice in the following manner.On the one hand, non-cognitivists have reason to adopt strong supervenience.Contemporary non-cognitivists generally concede that realism in many respects seems to agree with how we talk and think about morality.Consequently, they try to save as much as possible of the appearance of realism while arguing that, ultimately, non-cognitivism is correct. 17As we have seen, realism should adopt strong supervenience to account for the notion that the moral depends on the nonmoral.Thus, insofar as non-cognitivists aim to account for this notion in a way that accords with our conception of it, they should adopt strong supervenience.In case 16 Cf.Dreier (2015, pp. 289-290) and Franzén (Forthcoming,p. 8).

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they do not, they need to provide a particular argument why weak supervenience should be preferred to strong.On the other hand, it is difficult for non-cognitivism to adopt strong supervenience.As we have seen, there are reasons to understand the inner 'necessary' in this claim as metaphysical rather than conceptual necessity.A metaphysically necessary connection is a connection that holds between properties or facts.For example, an account of why it is metaphysically necessary that if an object has certain properties, it has a certain other property, is provided by reference to the nature of the properties mentioned in the antecedent.However, non-cognitivists explain moral supervenience in terms of the connection between attitudes and beliefs as regards non-moral properties.Consequently, it is difficult to see that they can understand the inner 'necessary' as metaphysical necessity. 18However, to interpret it as conceptual necessity appears implausible for reasons mentioned above.In that case, it might be more plausible for non-cognitivists to reject strong supervenience and argue for weak supervenience.
We have already touched on how non-cognitivists understand the outer 'necessary' in moral supervenience.They maintain that to be competent with the meaning of moral terms, an agent needs be consistent in her moral attitudes in a manner complying with this claim.Thus, as Rønnow-Rasmussen observes, they understand the outer 'necessary' as conceptual necessity.
It was argued above that non-cognitivists face a critical choice as to whether they should opt from weak or strong supervenience.However, non-cognitivism seems to have a crucial advantage over a realist account of moral supervenience: It is able to explain why the outer 'necessary' needs to be understood as conceptual necessity.A plausible idea motivating non-cognitivism is that an essential function of moral language is to influence attitudes and actions. 19It is reasonable to argue that in order for moral language to fulfil this function, it needs to be a condition on linguistic 18 An anonymous reviewer suggests that non-cognitivists can appeal to the connection between beliefs as regards non-moral properties and moral judgments in the form of non-cognitive attitudes to argue that the inner 'necessary' amounts to metaphysical necessity.On this view, it would be metaphysically necessary that if an agent believes that an object has a certain set of non-moral properties G, then she has a moral attitude M towards the object.Unfortunately, I do not have space to discuss this interesting suggestion in detail.Two comments: First, as indicated, metaphysical necessity is considered to hold between properties or facts, rather than between beliefs and attitudes.Second, it seems metaphysically possible that two agents that both believe that an object has G differ in their moral attitudes.For example, in one world an agent who believes that an action, say, maximizes happiness has a positive moral attitude towards the action; in another world an agent who believes that an action maximizes happiness has a negative attitude towards the action.According to another suggestion, non-cognitivists can employ a deflationary notion of metaphysical necessity.On this alternative, metaphysical necessity does not involve any 'worldly' metaphysical relation between properties that is incompatible with non-cognitivism.However, I doubt that this view is able to account for the contention that moral principles are substantive, and hence not conceptual, as I will argue below.The reason is that non-cognitivists seem committed to explaining a deflationary notion of metaphysical necessity ultimately by reference to the meaning of relevant terms.According to a further suggestion, non-cognitivists can employ a non-cognitivist interpretation of judgments of the type 'x because y', such as 'The action is M because it is G'.However, on this view it is judgments about the because relation that have the function to express non-cognitive attitudes.It is not judgments to the effect that something is x (such as 'The action is M') that is thought to have this function.To the contrary, the view seems to rest on the assumption that x and y in 'x because y' refer to facts or properties. 19See e.g.Blackburn (1984, p. 186) and(1993, p. 137).
1 3 competence that we are consistent in our attitudes in a way conforming to moral supervenience.
To summarize: There are good reasons for realists to adopt strong supervenience where the outer 'necessary' is conceptual and the inner is metaphysical necessity.As realists opt for strong supervenience, they are in the position to account for the notion that the moral depends on the non-moral.Non-cognitivists face a crucial choice.If they opt for weak supervenience, they have difficulties to account for moral dependence.If they opt for strong supervenience, they have difficulties to account for the inner 'necessary'.However, non-cognitivism has an important advantage over realism in that it can explain why the outer 'necessary' in moral supervenience needs to be conceptual.

Supervenience arguments against moral realism
It is common to maintain that realism has difficulties to account for moral supervenience.However, there are different arguments that need to be kept separate.One type of argument is that non-reductionist realism cannot explain that moral properties strongly supervene on non-moral properties, since strong supervenience entails property identity. 20A second type of argument is that non-naturalist realism cannot explain the strong supervenience of sui generis moral properties on non-moral properties, since there cannot be any metaphysically necessary connections between 'distinct existences'. 21A third type of argument is that there is no version of realism that can account of moral supervenience, since there is no version of this view that is able to explain the modality of this notion.If such an argument is successful, it would constitute a general reason to reject all versions of realism.This is the type of argument in which I am interested in the present paper.
Next, I consider a renowned argument against realism and for non-cognitivism.On this argument, non-cognitivists are correct in assuming weak supervenience rather than strong.In response, I argue that realists can avoid this argument in a way that casts further light on how they should understand the modality of moral supervenience.Thereafter, I argue that realism can explain why 'necessary' in moral supervenience needs to be read in the manner outlined above.

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tains that non-cognitivists can adopt weak supervenience in a way that both avoids the 'explanatory problem' and accounts for the correct reading of 'necessary'.This argument is exactly what non-cognitivists need: An argument demonstrating that they are correct in opting for weak supervenience instead of strong, at the same as they get 'necessary' in moral supervenience right. 22

Weak supervenience: the explanatory problem
Assume that there is an object x which has a moral property M. On strong supervenience, it then follows that there is a necessary implication of the follow type: (N) It is necessary that, for any object y, if y is G, then y is M.
As we shall see, Blackburn argues that realists should not adopt strong supervenience.To avoid this claim, they then need to adopt weak supervenience in combination with the denial of (N): (P) It is possible that there is an object y that has G, but which is not M.
According to this view, realists would allow that there are two types of possible worlds: worlds in which every object that has G has M, and worlds in which no object that has G has M. The type of world that would not be accepted are 'mixed worlds': worlds in which some objects that have G have M, and some objects that have G do not have M. Blackburn argues that the denial of 'mixed worlds' confronts realists with the 'explanatory problem'.If an object's moral property M depends on G, then objects that have G should have M in every world or the co-existence of G and M is not a matter of dependence, in which case the combination of G and the presence or absence of M should not be excluded in any world.
The point that realists have the 'explanatory problem' if they adopt weak supervenience and (P) is basically a dramatization of the contention that weak supervenience is too weak to account for the notion that the moral depends on the non-moral.Why, then, should realists not adopt strong supervenience in Blackburn's view?

Strong supervenience: problem with necessity
Blackburn's argument as regards strong supervenience takes point of departure in a familiar point about linguistic competence with moral terms: 'It seems to be a conceptual matter that moral claims supervene on natural ones' (Blackburn, 1993, p.   22 Allan Gibbard provides a more recent treatment of moral supervenience (Gibbard, 2003, Ch. 5)).However, there are reasons to focus on Blackburn's discussion rather than Gibbard's.First, Blackburn's arguments are directly relevant to the present topic, since they concern whether realism or non-cognitivism provides the preferable account of moral supervenience and, in particular, the modality of moral supervenience, whereas Gibbard's discussion is not involved in this debate.Second, Blackburn's arguments are more general and not directly connected to a particular version of non-cognitivism, whereas Gibbard's discussion is concerned with his particular view.For criticism of Blackburn's arguments, see e.g.Dreier (1992); Zangwill (1997), andShafer-Landau (2003, pp. 84-89).

137))
. He further observes that it might seem plausible for realists to read 'necessary' in (N) as metaphysical necessity, (N m ): [S]omeone who holds that a particular natural state, G*, underlies a moral judgement is very likely to hold that this is true as a matter of metaphysical necessity.For example, if I hold that the fact that someone enjoys the misery of others underlies the judgement that he is evil, I should also hold that, in any possible world, the fact that someone is like this is enough to make him evil.(Blackburn, 1993, p. 136)) Blackburn then asks whether adopting strong supervenience would make realists able to avoid the 'explanatory problem'.He answers in the negative.His basic argument is that realists are unable to provide plausible interpretations of the two occurrences of 'necessary'.In particular, there is no version of strong supervenience where the outer 'necessary' amounts to conceptual necessity and the inner 'necessary' is understood in any plausible manner.
Blackburn starts with considering a version of strong supervenience where both the outer and inner 'necessary' consist in conceptual necessity: (RSS a,a ).This alternative would commit realists to reading 'necessary' in (N) as conceptual necessity, (N a ).Blackburn thinks realists should reject it for reasons similar to those mentioned above.Blackburn next considers a version of strong supervenience where both the outer and inner 'necessary' consist in metaphysical necessity: (RSS m,m ).However, he argues that this alternative would not avoid the 'explanatory problem': Then there will be metaphysically necessities of the form of the consequent, that is, of the form (N m ), but they will not help to resolve the original mystery, since that is now proceeding at the level of analytical necessity.It is the possibility, so far as conceptual constraints go, of mixed worlds that is to be avoided.(Blackburn, 1993, p. 138).Italics added) That is, for realists to avoid the 'explanatory problem', it does not help to adopt a version of strong supervenience where the inner 'necessary' is understood as metaphysical necessity, which commits realists to (N m ).The reason indicated by Blackburn is that in order to solve the 'explanatory problem' on realism, it is not sufficient to rule out that there are any 'mixed worlds'.It must rule out that it conceptually possible that there are any 'mixed worlds', which means that realists cannot understand the inner 'necessary' as metaphysical necessity.I return to this argument in Sect.9.

Non-cognitivism and weak supervenience
We might next consider how non-cognitivism is able to account for moral supervenience in a way that avoids the arguments against realism.
The basic idea is that non-cognitivists should adopt weak supervenience in which the outer 'necessary' amounts to conceptual necessity (NWS a ) and combine it with (P) which is understood as a conceptual claim, (P a ).It might be argued that this alter-native constitutes an attractive view of moral supervenience.First, it can explain why the outer 'necessary' in weak supervenience needs to be understood as conceptual necessity.As mentioned, non-cognitivists provide a reason for this reading in terms of the function of moral language.Second, it does not entail strong supervenience.Thus, there is no conceptually necessary implication such as (N a ).As a result, it does not have any of the difficulties associated with this claim.Third, in spite of not involving strong supervenience, it might avoid the 'explanatory problem'.Consider an agent who makes a moral judgment that consists in having a moral attitude M towards an object.Weak supervenience in the form of (NWS a ) is the case.This means that within a given possible world, if an agent believes that objects have G, she is committed to have attitude M towards them.This claim is combined with (P a ), which means that it is conceptually possible that in another world in which the agent believes that objects have G, she does not have attitude M towards them.It might still be argued that there are no 'mixed worlds': There are no worlds in which the agent has attitude M towards some objects that she believes have G, but does not have attitude M towards other objects that she believes have G.The reason is that it would be incompatible with the function of moral language to influence attitudes and actions.For moral language to have this function, we need to be consistent in our moral attitudes within a given world. 23 However, a version of non-cognitivism that adopts weak supervenience has difficulties to account for the notion that the moral depends on the non-moral.The contention that there are no 'mixed worlds' does not solve this problem.Assume that there are no worlds in which an agent has attitude M towards some objects she believes have G, but does not have attitude M towards other objects she believes have G.However, weak supervenience in (NWS a ) does not contain any inner 'necessary', which means that there are worlds in which the agent believes that objects have G but does not have attitude M towards them.In that case, it seems incorrect to claim that actions are right because they have G, since, intuitively, there could be actions that have G but are not right. 24By contrast, realists can account for this notion insofar as 23 Cf.Blackburn (1984, p. 186);(1993, pp. 122, 137, 146). 24Cf.Dreier (2019Dreier ( , pp. 1394Dreier ( -1395) ) and Franzén (Forthcoming, p. 7).It might be objected that an agent may have different normative views in different possible worlds and therefore have attitude M towards objects that she believes have G in some worlds but not have attitude M towards objects that she believes have G in other worlds.It might then seem that it is correct to say that what is right depends on G in some worlds but not in other worlds.However, the argument rests on a misunderstanding.Assume that an agent has a normative view in some worlds and has attitude M towards objects that she believes have G in these worlds.Assume that she has another normative view in other worlds and does not have attitude M towards objects that she believes have G in these worlds.This does not mean that actions are right because they have G in some worlds and that it is not the case that actions are right because they have G in other worlds.Rather, a given normative view determines that actions are right because they have a certain set of nonmoral properties, and it does so across all worlds.Thus: On one normative view, actions are right because they have G and this is the case in all worlds on this view; on another normative view, actions are right because they have G* and this is the case in all worlds on that view.Etc.By contrast, assume that an agent who has a certain normative view has attitude M towards objects that she believes have G in some worlds but does not have attitude M towards objects that she believes have G in other worlds.This means that she is not consistent in her moral attitudes given her own normative view.In that case, it is mistaken to claim that what is right depends on G in any world.they adopt strong supervenience.We should therefore take another look at the argument in the last section and see whether realists are able to respond to it.

Realism and strong supervenience
Let us return to Blackburn's argument why realists should not adopt strong supervenience.Blackburn only discusses versions of strong supervenience where the outer and inner 'necessary' are understood in the same manner, as conceptual necessity (RSS a,a ) or as metaphysical necessity (RSS m,m ).The possibility of reading the outer 'necessary' as conceptual and the inner as metaphysical (RSS a,m ) is never considered.Why? Blackburn's argument is not explicit, and we are left to reconstruct it.
As noticed, in commenting on (RSS m,m ) Blackburn maintains that if realists adopt this alternative, they have the 'explanatory problem': 'It is the possibility, so far as conceptual constraints go, of mixed worlds that has to be avoided'.Thus, to avoid the problem realists need to maintain that it is not conceptually possible that there are any 'mixed worlds'. 25More precisely, on realism there should be a requirement on linguistic competence to deny that the following is possible: a moral property M depends on G, but there are worlds in which some objects that have G have M, and some objects that have G do not have M.As a consequence, strong supervenience where the inner 'necessary' is understood as metaphysical necessity is insufficient for realism to avoid the 'explanatory problem'.It rules out that it is metaphysically possible that there are worlds in which some objects that have G have M and some objects that have G do not have M, but it does not rule out that it is conceptually possible that there are worlds in which this is the case.That is, it does not rule out 'the possibility, so far as conceptual constraints go, of mixed worlds'.It follows that understanding the outer 'necessary' as conceptual and the inner as metaphysical would not enable realists to avoid this problem.
However, I think that realists can argue that it is a matter of linguistic competence to disallow the possibility of 'mixed worlds'.As argued, realists should adopt strong supervenience where the outer 'necessary' amounts to conceptual necessity and the inner to metaphysically necessity: (RSS a,m ).What is important to notice is that 'conceptually necessary' binds the entire claim in which the metaphysically necessary implication from G to M is embedded: It is conceptually necessary that if an object has a moral property M, then it has some set of non-moral properties G such that it is metaphysically necessary that whatever object has G has M. Thus, it is not conceptually possible that it is metaphysically possible that there are worlds in which some objects that have G have M and some objects that have G do not have M.This claim does not rule out that it is conceptually possible that there are worlds in which some objects that have G have M and some objects that have G do not have M.However, it does rule out that it is conceptually possible that there are worlds in which it is metaphysically possible that this is the case.The contention that it would be a matter of linguistic competence to deny that there are any 'mixed worlds' can then be explained in terms of 'conceptually necessary' in which 'metaphysically necessary' is embedded.Assume that an agent claims that an action is right because it maximizes happiness, but also maintains that it is possible that some actions that maximize happiness are right and that some actions that maximize happiness are not right.The agent can then be said to lack linguistic competence with respect to 'right', since she does not realize that as a matter of the meaning of 'right' her first claim entails that it is necessary that if an action maximizes happiness, it is right.Thus, realism does rule out 'the possibility, so far as conceptual constraints go, of mixed worlds'.

A realist explanation of the modality of moral supervenience
In the last section, I maintained that realists are able to respond to an influential argument to the effect that they cannot account for the modality of moral supervenience.However, we noticed earlier that there is a strong argument for a non-cognitivist account of this notion: It can explain why the outer 'necessary' in moral supervenience amounts to conceptual necessity. 26 According to non-cognitivism, moral judgments consist in non-cognitive attitudes.As we express our moral judgments and thereby our attitudes in using moral language, it can have the function to influence attitudes and actions.In Blackburn's view, it has the function of influencing other people to have the same attitudes as we do so as to coordinate our attitudes and thereby our actions. 27In order for moral language to have that function, we need to be consistent in our moral attitudes. 28As a result, to be linguistically competent with the meaning of moral terms, an agent needs to adhere to moral supervenience by being consistent in having the same moral attitude towards objects that she believes have the same non-moral properties.Hence, the outer 'necessary' in this claim amounts to conceptual necessity.
According to realism, by contrast, moral judgments do not consist in non-cognitive attitudes.It therefore seems that realists cannot explain why the outer 'necessary' in moral supervenience is conceptually necessary by referring to the mentioned function of moral language.Moreover, this explanation seems to square badly with understanding the inner 'necessary' as metaphysical necessity.Thus, it might be argued that while non-cognitivists have a straightforward explanation of their understanding of 'necessary' in moral supervenience, realists lack such an account.
However, I think realists are in the position to provide an explanation of why 'necessary' in moral supervenience is to be understood in the manner suggested above.In my view, realists can provide such an explanation by reference to the connection between moral properties and reasons.Moreover, this account is available to all versions of realism.The basic idea is this: The outer 'necessary' is conceptual because the meaning of a sentence to the effect that an object has a moral property entails that there is some moral reason, where such a reason is constituted by non-moral properties on which the moral property strongly supervenes.The inner 'necessary' is 26 See e.g.Blackburn (1993, p. 137).
1 3 metaphysical because moral principles, in the form of implications from moral reasons, constituted by non-moral properties, to moral properties, are substantive.The account rests on three claims that I will consider in turn.
First, a normative standard exhibits a conceptually necessary connection between normative properties and normative reasons.One instance of this connection is the following: Moral Property→Moral Reason: It is conceptually necessary that if an object x has a moral property M, then there is a moral reason pertaining to x.
There are several instances of this connection.For example: If it is morally right to perform an action, then there is a moral reason to perform that action.
It is plausible to maintain that morality is a normative standard that exemplifies this connection between normative properties and reasons.Indeed, terms denoting moral properties, such as 'right', 'wrong', 'good', and 'bad', are frequently used to entail that there is moral reason (not) to perform certain actions or (not) to have certain attitudes.
It might be worried that Moral Property→Moral Reason is not generally true since there appear to be counterexamples to the claim.The most relevant type of case would be attributive uses of 'good' to the effect that an object is good of a certain kind where the kind sets a certain standard.29Thus, 'This is a really good toaster' does not as such entail that there is any reason with regard to the toaster.Two responses: First, it should be pointed out that Moral Property→Moral Reason is a claim about the connection between moral properties and reasons.It seems plausible to maintain that it holds quite generally for uses of 'morally good'.Thus, 'She is a morally good human being' plausibly entails that there is a moral reason to, say, support her actions or treat her well.Second, it might be maintained that Moral Property→Moral Reason applies to all central cases-in particular, judgments stating that actions have moral properties and predicative uses of 'morally good' such as 'She is morally good'-but admitted that it does not apply to attributive uses of 'morally good' if such there are. 30econd, on realism it is conceptually necessary that moral reasons are constituted by the supervenience base of moral properties: Moral Reason/Supervenience: It is conceptually necessary that a moral reason is constituted by a set of non-moral properties G on which a moral property M strongly supervenes.
There are several instances of this claim.For example: A moral reason to do what is morally right is constituted by a set of non-moral properties on which moral rightness strongly supervenes. 31he present claim should not be understood to entail that a moral reason is constituted by all the non-properties included in a set of non-moral properties on which a moral property strongly supervenes.For instance, such a set might include properties on which moral rightness supervenes but that do not make up parts of a moral reason to do what is right.One example is 'enablers': properties that do not constitute reasons but which are relevant for whether an agent has a reason. 32Hence, the claim is compatible with a moral reason to do what is right being constituted by a subset of the non-moral properties on which rightness strongly supervenes.
It should be uncontroversial that realism is committed to this connection between moral reasons and the supervenience base of moral properties.There are both intuitive and more formal grounds for this contention.The intuitive ground: A reason to do what is, say, morally right consists in some feature of the action that 'makes' it right or 'in virtue' of which it is right.Similarly, an action is right 'because' there is reason to perform it.Now, terms like 'make', 'in virtue of', and 'because' denote a dependence relation between moral properties and underlying properties that realists try to account for by employing strong supervenience.The more formal ground: It is conceptually necessary that if an action is morally right, then there is a moral reason to perform it.Moreover, on realism the property of being right depends, and hence strongly supervenes, on a set of non-moral properties.It then seems very plausible to think that a moral reason consists in some set of non-moral properties.Thus, on realism a moral reason to do what is right is constituted by a set of non-moral properties on which rightness strongly supervenes.
Third, moral principles are substantive: Moral Principles are Substantive: A moral principle of the form 'If x has a set of non-moral properties G, which constitutes a moral reason pertaining to x, then x has a moral property M' is not conceptually necessary but metaphysically necessary. 33 simple example of a moral principle of this form is the following: If an action maximizes happiness, which constitutes a conclusive moral reason to perform it, then the action is morally right.
As suggested, it is plausible to think that a moral principle refers to a set of nonmoral properties which constitutes a moral reason to do what is, say, morally right.However, it is implausible to think that such a principle is conceptually necessary.First, it does not seem to be part of competence with the meaning of 'right' to know that there is an implication from a given set of non-moral properties to rightness.Second, and more controversially, it might be argued that such principles cannot be conceptually necessary, since it would imply that they lack normativity.Assume that moral principles were conceptually necessary.In that case, it would be a matter of the meaning of 'right' that such a principle is true: We use 'right' in such a way that if an action has a particular set of non-moral properties, it is correct to say that there is a moral reason to perform it and apply 'right' to it.However, whether we have moral reasons to perform actions that have certain non-moral properties does not seem to be an arbitrary matter of how we choose to use particular words.Instead, it is, at least partly, a matter of the nature of the non-moral properties in question.In the example above, it is the nature of maximizing happiness which would explain why it is the case that if an action has this non-moral property, there is moral reason to perform it and it is right.If this is correct, there are grounds to think that moral principles need to be metaphysically rather than conceptually necessary. 34 It might be worried that it is question begging to employ Moral Principles are Substantive on the ground that it assumes strong supervenience where the inner 'necessary' amounts to metaphysically necessity.Two responses: First, it is plausible to maintain that the claim is independent from strong supervenience.It is a claim about the connection between moral reasons, constituted by non-moral properties, and moral properties, not a claim about the supervenience of moral properties on nonmoral properties.Thus, it is possible to accept this claim without accepting strong supervenience, and vice versa.Second, it is relevant to recall the dialectic of the discussion.It is argued that realism can provide an explanation of why the two occurrences of 'necessary' in strong supervenience are to be understood in the suggested manner.In this argument, it should be allowed to employ an independently plausible claim about the connection between moral reasons and moral properties.
We can now see that realists are in the position to provide an explanation of why 'necessary' in moral supervenience should be understood in the manner recommend above.That the outer 'necessary' amounts to conceptual necessity follows from the connection between moral properties and reasons, and from moral reasons being constituted by non-moral properties on which moral properties strongly supervene.That the inner 'necessary' amounts to metaphysical necessity follows from moral principles being metaphysical necessary.In more detail: According to Moral 34 An alternative is to understand 'necessary' in Moral Principles are Substantive as normative necessity.However, it faces the same type of difficulties as when 'normatively necessary' is inserted in moral supervenience (cf.footnote 12 above).For example, it does not account for what it is about actions that have certain non-moral properties which explains why we have moral reasons to perform them and they are morally right, since there would be worlds where actions have the same non-moral properties but we do not have any moral reasons to perform them and they are morally wrong (cf.Väyrynen (2018, p. 182)).Moreover, it implies that we are subject to universal moral luck.It means that we might perform actions that we have moral reasons to perform and are morally right, but had we performed these actions in other worlds, we would not have any moral reasons to perform them and we would have acted morally wrong (cf.Väyrynen (2018, p. 182) and Dreier (2019Dreier ( , pp. 1405Dreier ( -1406))).

Synthese
Property→Moral Reason, it is conceptually necessary that if an object x has a moral property M, then there is a moral reason pertaining to x.According to Moral Reason/ Supervenience, it is conceptually necessary that a moral reason is constituted by a set of non-moral properties G on which M strongly supervenes.It follows that the outer 'necessary' amounts to conceptual necessity.According to Moral Principles are Substantive, moral principles are not conceptually but metaphysically necessary.A moral principle maintains that if an object has a set of non-moral properties G, which constitutes a moral reason pertaining to x, then x has a moral property M. It follows that the inner 'necessary' amounts to metaphysical necessity.
The main contention of this section is that realists are able to explain why 'necessary' in moral supervenience is to be understood as strong supervenience where the outer 'necessary' is conceptual and the inner metaphysical.However, there are also further reasons to accept this view of moral supervenience.
One reason is that it is able to account for an important requirement on normative explanations.A normative explanation is an explanation of why an object has a certain normative property.Pekka Väyrynen argues, convincingly, that such explanations are subject to a 'justification condition': A normative explanation of why an object has a normative property needs to go at least some way towards identifying some feature of the object which justifies a certain response to it. 35For example, a normative explanation of why an action is morally right should identify a feature of the action that provides a moral reason to perform it.It is plausible to assume that a normative explanation of why x has a moral property M refers to some set of nonmoral properties G on which M depends and hence strongly supervenes.According to the suggested view, a moral reason is constituted by a set of non-moral properties G on which M strongly supervenes.Thus, it is able to account for the justification condition on normative explanations.For example, on this view a normative explanation of why an action is right refers to some non-moral properties which constitute a moral reason to perform the action and on which rightness strongly supervenes.
Another reason is that it can account for the function moral principles have in normative explanations.It is reasonable to think that moral principles are part of this type of explanations.For example, one might refer to a moral principle in an explanation of why an action is morally right.As understood here, moral principles have the following form: If an object x has a set of non-moral properties G, which constitutes a moral reason pertaining to x, then x has a moral property M. It can then be part of a normative explanation of why an object is M. In the simple example of a moral principle above, if an action maximizes happiness, which constitutes a conclusive moral reason to perform it, the action is morally right.The principle can then be employed in a normative explanation of why an action is right.Thus, the proposed view recognizes that moral principles have an important function in such explanations.However, it is neutral as regards how this function should be understood in detail.On one view, a moral principle is 'explanatory in content' in that it merely specifies a set of non-moral properties which explains why an action is right.On another view, a moral principle is 'explanatory in role' in that the principle itself has an independent role 35 See Väyrynen (2021).

3
Synthese in normative explanations which goes beyond the non-moral properties it specifies. 36 The suggested view is compatible with either alternative.

Unifying the normative sphere
The view of the modality of moral supervenience outlined in the last section is available to all forms of realism introduced at the beginning of the paper. 37Thus, it unifies the moral sphere in a significant respect.In this context, it is worth mentioning that it might have implications for an argument against non-naturalism briefly indicated in Sect.6.As pointed out, one objection against this view is that it is unable to account for the supervenience of sui generis moral properties on non-moral properties.It is important to distinguish between different versions of this argument.On one version, there cannot be any metaphysically necessary connections between properties that belong to entirely distinct types.On another version, non-naturalism is unable to account for the modality of the supervenience of moral properties on non-moral properties because moral properties are sui generis on this view.The above account does not offer any response to the first argument.However, it might provide a response to the second one.It does not seem to be any particular reason to think that the modality of the supervenience of moral properties on non-moral properties is different because the former are conceived of as sui generis.The reasoning above, motivating why the outer 'necessary' is conceptual and the inner metaphysical, seems applicable irrespective of whether moral properties are understood as sui generis or not.
More importantly, it is plausible to argue that the suggested account is able to unify the normative sphere at large by being generalizable to other normative properties than moral properties.In this regard, it has a significant advantage over noncognitivism.The same type of problems that non-cognitivists have of accounting for moral supervenience are bound to arise regarding supervenience in relation to other normative notions than morality.For example, for basically the same reasons as those indicated above, non-cognitivists about aesthetic value will face difficulties to explain how aesthetic value depends, and hence strongly supervenes, on non-aesthetic properties.Furthermore, it is not evident that all uses of normative language have the function to influence attitudes and actions, which means that noncognitivism about other normative notions does not receive the same support it does with respect to morality. 38By contrast, it is plausible to argue that all sentences that 36 For clarification and overview of different accounts, see Väyrynen (Forthcoming,.Fogal and Risberg have presented an important argument against the 'explanatory in content' interpretation and for the 'explanatory in role' interpretation (Fogal & Risberg, 2020).Moreover, they argue for the latter alternative on the assumption that moral principles hold with metaphysical necessity (Fogal & Risberg, 2020, pp. 176, 191-192)).Thus, they provide an argument for reading the inner 'necessary' in strong supervenience as metaphysical necessity.By contrast, Selim Berker argues against the 'explanatory in role' interpretation and for the 'explanatory in content' interpretation by maintaining that moral principles cannot fulfil any independent role in normative explanations (Berker 2019).However, this alternative is compatible with moral principles being metaphysically necessary.37 That is, reductionist and non-reductionist versions of realism, and naturalist and non-naturalist versions of this view.38 Cf.Strandberg (2016, pp. 26-55).
Synthese ascribe a normative property to an object entail the existence of some reason that is constituted by a set of non-normative properties on which the normative property strongly supervenes.Hence, there are grounds to think that the realist account of moral supervenience is generalizable to other normative properties.

Explaining the function of moral language
The non-cognitivist explanation of why the outer 'necessary' in moral supervenience amounts to conceptual necessity is that it is needed to account for the function of moral language to influence attitudes and actions.It should be evident that realists are not committed to the claim that moral language has such a function.However, it is possible for realists to concede that moral language does have this function and argue that their preferred reading of 'necessary' is needed for moral language to fulfil it.While non-cognitivists explain this function by referring to the meaning of moral judgments, realists can account for it by referring to the pragmatics of moral utterances.I have defended this view in other contexts and will only indicate the contours of it here. 39 The realist account rests on three assumptions.First, conversations about moral matters generally have the mutually accepted purpose to communicate moral beliefs about which actions are morally right and wrong.Second, such conversations generally have the further mutually accepted purpose to influence attitudes and actions.Third, a moral sentence of the type 'x is right' entails that there is moral reason to perform the action in question.In view of the two purposes of moral conversations, it is plausible to assume that utterances such as 'x is right' standardly conversationally implicates that the utterer has a favourable attitude towards the action being performed.The basic explanation is that it does not seem to be any point in uttering a sentence which entails that there is moral reason to perform an action in a moral conversation which has as a mutually accepted purpose to influence behaviour unless one has a favourable attitude towards the action being carried out.As moral utterances standardly conversationally implicate positive or negative attitudes towards actions, they can fulfil the function to influence attitudes and actions.
It is plausible to argue that for moral language to fulfil this function, 'necessary' in moral supervenience needs to be understood as proposed above.First, it needs to be conceptually necessary that a sentence of the type 'x is right' entails that there is moral reason to perform the action.If this were not the case, an utterance such as 'x is right' made in a moral conversation which has as a mutually accepted purpose to influence behaviour would not entail that there is moral reason to perform the action.Second, this moral reason needs to be constituted by a set of non-moral properties on which rightness strongly supervenes.If this were not the case, the fact that an agent performs the action that she, according to the utterance, has moral reason to perform would not guarantee that she performs an action which is right.In case this condition is not fulfilled, the utterance would not be effective in influencing people to perform this type of action in various possible circumstances.Thus, it should be clear that both these conditions need to be fulfilled for 39 For a full defence, see Strandberg (2012).
1 3 moral utterances to have the function to influence attitudes and actions.Lastly, as indicated earlier, there are grounds to think that moral principles need to be metaphysically rather than conceptually necessary in order to be substantive and provide genuine moral reasons.The crucial point is this: A part of the realist account of why moral language can have the function to influence attitudes and actions is that moral utterances entail the existence of moral reasons in accordance with the suggested view of moral supervenience, where the outer 'necessary' amounts to conceptual necessity and the inner to metaphysical necessity.

Concluding remarks
In this paper, I have argued that realism provides an account of the modality of moral supervenience which is superior to the one offered by non-cognitivism.According to the recommend realist account, moral supervenience amounts to strong supervenience where the outer 'necessary' is conceptual and the inner metaphysical.As it is matter of strong supervenience, it can be part of an explanation of the notion that the moral depends on the non-moral.Moreover, it provides realists with resources to respond to a prominent argument maintaining that this view cannot explain the modality of moral supervenience.Most importantly, it means that realism offers an explanation of why 'necessary' in moral supervenience should be understood in this manner which is available to all versions of this view.Furthermore, this account is generalizable to other normative properties.In addition, it is part of an explanation of why moral language can have the function of influencing attitudes and actions.Non-cognitivists have a difficult choice.If they opt for weak supervenience, they cannot account for the notion that the moral depends on the non-moral.If they opt for strong supervenience, they cannot account for the inner 'necessary'.Non-cognitivism might seem to have an advantage in being able to explain why the outer 'necessary' is conceptual.However, the realist account is superior for reasons indicated above.