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Necessarily Coextensive Predicates and Reduction

In: International Journal for the Study of Skepticism
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  • 1 University of Reading
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Bart Streumer argues that all normative properties are descriptive properties. His first argument is based on the principle that necessarily coextensive predicates ascribe the same property (N), and the claim that there is a descriptive predicate that is necessarily coextensive with normative predicates. From this Streumer concludes that normative properties are identical with descriptive properties. I argue that, even if we accept (N), this conclusion does not follow. Normative properties could only be descriptive properties if there is some descriptive way in which all instances of normative properties are similar. But Streumer does not show that, and the prospects for doing so are, I believe, not good. His second argument rests on the premise that the nature of normative properties cannot depend on which first order normative theory is true. I argue that this premise is false, and that the argument for it does not sit comfortably with (N).

Abstract

Bart Streumer argues that all normative properties are descriptive properties. His first argument is based on the principle that necessarily coextensive predicates ascribe the same property (N), and the claim that there is a descriptive predicate that is necessarily coextensive with normative predicates. From this Streumer concludes that normative properties are identical with descriptive properties. I argue that, even if we accept (N), this conclusion does not follow. Normative properties could only be descriptive properties if there is some descriptive way in which all instances of normative properties are similar. But Streumer does not show that, and the prospects for doing so are, I believe, not good. His second argument rests on the premise that the nature of normative properties cannot depend on which first order normative theory is true. I argue that this premise is false, and that the argument for it does not sit comfortably with (N).

1 Introduction

In his influential book From Metaphysics to Ethics, Frank Jackson offered a sophisticated argument for a reductive account of moral properties. The argument has two steps. The first step aims to tell us something about the general nature of moral properties. The conclusion is that moral properties are descriptive properties. The second step aims to offer a method by which we could determine the particular descriptive nature of moral properties—that is, to tell us which descriptive property each moral property is. The aim was to defend a form of naturalistic moral realism.

Recently, Bart Streumer uses a more wide-ranging version of the first step of Jackson’s argument (although he rejects the second step). He expands this argument to cover not just moral properties, such as rightness and goodness, but all normative properties. So Streumer takes the first step of Jackson’s argument to show that all normative properties are descriptive properties. More precisely, his conclusion is that if there are normative properties, they are identical to descriptive properties (2017: 11).1 Streumer then goes on to argue that if there are normative properties, they are not identical with descriptive properties (42–61). He thus proposes a classic Kantian Antinomy. Kant lists four antinomies, each of which consists of a thesis and an antithesis. Both the thesis and the antithesis has what Kant regards as a compelling argument in its favour. He calls the first two antinomies mathematical and the third and fourth dynamical antinomies. He claims that the thesis and the antithesis of the mathematical antinomies are both false, and that the thesis and antithesis of the dynamical antinomies are both true. He does this using his distinction between the phenomenal and the noumenal. Like Kant’s dynamical antinomies, Streumer claims that the thesis and the antithesis of his antinomy are both true. But without Kant’s transcendental idealism that commits him to saying that normative properties are impossible. They are impossible because if there were such properties, they would be both descriptive and not descriptive (104).

The end result is an error theory about all simple, positive normative judgements.2 We have no reason to do anything, to want anything, or to believe anything, including believing this version of error theory. That makes this error theory literally unbelievable,3 although paradoxically Streumer regards this as a virtue of the theory (170ff). In this paper, I will focus only on his arguments for the reduction of the normative to the descriptive, for if these arguments work, that would be bad news for non-naturalist moral realists like me, independently of whether Streumer can ultimately argue for a general error theory about all normativity. Also, given that the second step of his argument is that moral properties are not descriptive properties, if the first step fails, he will be left with an argument for non-naturalist realism. That is fine by me.

For the sake of simplicity, I will focus on the normative property of rightness in my discussion, and will understand rightness as peremptory rather than merely permissive, i.e., as requiring us to do some act rather than as merely permitting us to do it. It should however be noted that if the reductive argument works against rightness, it will work against all normative properties.

Streumer has three reduction arguments. The first is an expanded version of Jackson’s argument. This is premised on the supervenience of the moral on the descriptive and the principle that necessarily coextensive predicates ascribe the same property—a principle he labels (N). His second argument uses (N) but does not rely on supervenience. It relies simply on the view that the nature of normative properties cannot depend on which normative theory is correct. The third argument is similar to the first, but with a more restricted supervenience base (34ff). I will not consider the third reduction argument separately, as its form makes it susceptible to the same objections as the first reduction argument. So to give it separate treatment would be unnecessarily repetitive. I will argue that these reduction arguments fail in a number of ways, and that this failure leaves us with an argument for non-reductive realism rather than an unbelievable error theory.

2 Streumer’s First Reduction Argument

Streumer does not offer a definition of what a normative or descriptive property is, but instead proposes the following necessary and sufficient conditions for each:

np: a property is normative iff it can be ascribed by a normative predicate.

dp: a property is descriptive iff it can be ascribed by a descriptive predicate. (3)

He argues that normative properties are identical to descriptive properties roughly as follows: Take a particular right act, R1. The rightness of R1 must supervene on some cluster of descriptive properties which are such that if some act has those descriptive properties, it will be right. Following Jackson, Streumer understands the supervenience base in the widest possible sense to include a complete description of the world in which each act is. So the description will include not only features that are non-controversially of the act itself, such as its being the helping of someone in need, but also its being such that every object in that possible world has such and such descriptive properties. We can capture this enormous description with a long conjunctive, descriptive predicate, i.e., is d1, and is d2, and is d3… Call this predicate D1. Since a conjunction of descriptive predicates is a descriptive predicate, D1 is a descriptive predicate. Since D1 is a complete description of the world in which this right act is, the descriptive predicate D1 will entail the moral predicate ‘is right’. This follows from the global supervenience thesis that if two worlds have exactly the same descriptive nature, they will have exactly the same ethical nature. But since different right acts have different supervenience bases, it will not follow that the predicate ‘is right’ entails the predicate D1.

The argument for the right to left entailment proceeds by repeating the first procedure for each and every right act in logical space. That will get a descriptive predicate D2, D3, D4… each of which describes the complete supervenience base for the right acts R2, R3, R4… respectively. We can then form a new predicate which is the disjunction of D1, D2, D3, D4… Streumer calls this predicate D* (10). Since a disjunction of descriptive predicates is itself a descriptive predicate, D* is a descriptive predicate. Because the supervenience base of every possible right act in logical space figures as a disjunct of D*, it follows that if an act is right, then it is D*. Since each disjunct of D* is sufficient to make an act right, it will also follow that the predicate D* entails the predicate ‘is right’. We now have a possibly infinite descriptive predicate that is necessarily coextensive with the normative predicate ‘is right’.

As noted earlier, Streumer endorses Jackson’s claim that necessarily coextensive predicates ascribe the same property (N) (11). Given (N), it follows that the property ascribed by the normative predicate ‘is right’ is the same property as the property ascribed by the predicate D*. This line of argument can be repeated for every normative predicate. So, Streumer concludes, normative properties are all identical to descriptive properties (11). That constitutes the first argument for reduction.

There are a number of points with which we may take issue with this line of argument. Take the notion of ascribing a property. How is the idea of property ascription to be understood? The property ascription claim is not a semantic claim. “Swans are white” does not mean “Swans have the property of being white”.4 If that were true, then realism about colours would be analytically true, assuming at least some simple positive colour statements are true. If true, however, such realism is not analytically true. The same point can be made about moral realism. If “Abortion is wrong” meant that “Acts of abortion have the property of being wrong,” then moral realism would be analytically true (granted some of these claims are true). I think moral realism is true, but this is a substantive metaphysical thesis, rather than an analytical truth.5

I think the idea of property ascription is better understood as a metaphysical claim about truth-makers. If that is right, then the idea is that what makes a proposition of the form “x is D” true, where D is some descriptive predicate, is that x has, or instantiates, a descriptive property—that is, there is some descriptive way x is. Streumer does not tell us what that descriptive way is. We are just told that it is the way that makes a proposition of the form “x is D” true. The notion of a descriptive predicate is left undefined. I think that is okay as we have a decent intuitive grasp of the descriptive. Streumer goes on to say that “the term ‘descriptive’ is just a label. We could instead, he says, use the term ‘non-normative’” (3). That is okay so long as ‘non-normative’ is not understood as ‘not normative’ (3–4). But it is worth noting that he thinks of predicates as labels, as we will come back to that later.

Streumer rejects a kind of minimalism about properties according to which properties are simply the mirror of predicates,6 such that every predicate corresponds to a distinct property. That is shown by his endorsement of N. He also rejects the idea that properties simply mirror concepts. The concepts of water and of H2O are different, but the property of being water and the property of being H2O are the same (11). So there are fewer properties than there are concepts. What are properties if they are not simply the mirror in the world of predicates or concepts? Streumer takes them to be “ways objects can be” (13). But it is not clear that ways things can be are in the actual world. What is in the actual world is ways things are. We can capture that by adding that instances of properties are “ways objects are,” and instances are uncontroversially in the world (although if properties are tropes, then there will be no distinction here, and properties will be ways things are, rather than ways they can be). This is because a way something is cannot be separated from the thing that is in that way, so if the thing is in the world, so are all of the ways it is.

Streumer claims that if properties are ways objects can be (and by extension, instances are ways things are), then (N) is the correct criterion of property identity (11). It is worth noting that Jackson was not quite so confident. When he proposed (N) he denied that necessary coextension entailed identity. He wrote: “I think the necessary co-extension of ethical and natural properties provides a strong reason to identify them, strong but not apodictic” (2017: 201). I think that if Jackson thought that this principle led to the sort of paradoxical error theory Streumer proposes, he would regard this strong reason as overridden. Streumer would claim that that is just because the error theory is literally unbelievable,7 so any alternative is more plausible (ch. 11). But this point does not depend on the implausibility of a general error theory. All it requires is some moral proposition that we may, without arrogance, claim to know. Take some simple uncontroversial moral proposition, e.g., “Rape is wrong.” If we know anything in morality we know this. Grant Streumer the truth of all the premises of his argument except (N), and grant that his argument is valid, or at least provides a compelling case for a general normative error theory if (N) is true. We then have a choice between (1) and (2):

  1. (1)Accept that (N) is true, and reject our belief that rape is wrong.
  2. (2)Retain our belief that rape is wrong, and reject (N).

Even if we agree with Jackson that we have very good reason to accept (N), the sensible thing to do here would, I propose, be to reject (N).8 But let us put that point aside. Even if (N) is granted, and even if it is granted that we can invent a descriptive predicate that is necessarily coextensive with rightness, it would not follow that rightness is a descriptive property.

According to Streumer and Jackson, (N) is supposed to enable us to learn something about how the world is. It supposedly enables us to know that moral properties are descriptive properties. It only tells us something about the general nature of the moral, as it does not tell us what specific descriptive property any moral property is. But learning something about the general nature of some property, i.e., what class of property it is, is still learning something about its nature. But learning that two predicates are necessarily co-extensive does not tell us anything about the single property they ascribe. Remember, according to Streumer predicates are simply labels or names for certain properties (3). But if that is right, then all we learn from the fact that the predicates ‘is right’ and D* are necessarily coextensive is that they both refer to the same property. Learning this does not tell us anything about the general nature of that property. That these two names are names for the same thing only tells us something about the English language. It does not tell us anything about the thing referred to other than that there is one thing rather than two. It is like learning that the label ‘Hesperus’ and ‘Phosphorus’ refer to the same thing. We learn something about the world when we learn this—namely, that there is one planet rather than two. But we do not learn anything about the general nature of that planet. The same is true of the labels ‘is right’ and D*. We may learn that there is one property rather than two if we grant (N), but in learning that, we do not learn anything about the general nature of that property.

It may seem that the case of water and H2O provides a counterexample to my claim that learning that two terms are necessarily coextensive tells us something about the nature of the thing to which they refer. For when we learnt that the predicate ‘is water’ and ‘is H2O’ are necessarily coextensive, we did learn something about the nature of water—namely, that it is essentially composed of two gasses in a certain ratio. But the order of knowledge is quite different in this case than it is in the reduction argument. We did not learn that water is H2O by first establishing that the predicates ‘is water’ and ‘is H2O’ are necessarily coextensive. Rather we learnt that these two predicates are necessarily coextensive by investigating the substance picked out by the predicate ‘is water’ and learning something about the essential nature of that substance. What we learnt by investigating this substance is that there is some way in which all water is similar, namely by the combination of these two gasses in the right ratio.

The reduction argument works, or is supposed to work, in a quite different way. It does not work to necessary coextension, but from it. It is supposed to tell us something about the general nature of normative properties by constructing some predicate that is necessarily coextensive with normative predicates. It is this methodology of which I am sceptical, for the reasons mentioned above. If I am right, then Streumer and Jackson make an illegitimate leap from the fact that these two predicates refer to the same property, to the conclusion that this property is descriptive. Of course, given dp, this conclusion comes out as true by definition. But for reasons I will now outline we should reject dp.

To learn something about the nature of the single property ascribed by the predicates ‘is right’ and D* we would have to consider the nature of various instances of that property, with a view to seeing in what way they are all similar. If there is a descriptive way in which they are all similar, however descriptiveness is to be understood, then we could conclude that the single property ascribed by the necessarily co-extensive predicates is a descriptive property. But if there is no descriptive way in which all instances of the relevant normative property are similar, then that property could not be a descriptive property. If that property could not be a descriptive property, that would falsify dp, i.e., the claim that a property is descriptive iff it can be ascribed with a descriptive predicate.

Take rightness. If there is no descriptive way in which all possible right acts are similar, then rightness cannot be a descriptive property.9 That is compatible with N, for it is compatible with the idea that the predicates ‘is right’ and ‘is D*’ ascribe the same property. If there is no descriptive way in which all right acts are similar, then the property ascribed by ‘is right’ and D* could not be a descriptive property, and so dp would turn out false. That is compatible with the view that these predicates ascribe the same property, and so does not entail that N is false. But one cannot leap straight from the view that there is a single property, rather than two, to any conclusion about the general nature of that property without first ensuring that there is a descriptive way in which all right acts are similar.

Why is it so tempting to think that if there is a single property ascribed by the normative predicate ‘is right’ and the descriptive predicate D*, then that property must be descriptive? One reason why it seems so natural to move from (N), and the necessary co-extensiveness of ‘is right’ and D*, to the claim that these predicates ascribe a descriptive property may be because normative properties supervene on descriptive properties, and so the descriptive property is explanatorily more fundamental. If, therefore, there is a single property here, it seems it must be the more fundamental descriptive one.

But supervenience is an asymmetric relation. The ethical supervenes on the descriptive, not vice versa. If this relation becomes one of identity, i.e., rightness is identical with the descriptive property, that asymmetry is lost, as identity is symmetrical. So if the property of being right is identical with some descriptive property, no side would have explanatory priority over the other.10 Actually, if the identity claim is true, then neither property can supervene on the other, or result from, or ground the other, as there would not be two properties—the supervening one and the one supervened upon—but one property.11 Neither could one sentence have priority over the other, although we may think that one does if we think that they are ascribing different properties. If the disjunctive descriptive predicate and the normative predicate are just different names for the same property, then saying that the sentence “Act x is right” is true because it is true that “Act x is either D1 or D2 or D3…” would be like saying “Planet y is Hesperus” is true because it is true that “Planet Y is Phosphorus,” or that it is true that “Person Z is Superman” because it is true that “Person Z is Clarke Kent.” If the reductive claim were true, these predicates would be merely different names for the same thing and neither would have priority over the other. So one cannot support the conclusion that the single property ascribed is a descriptive property from the explanatory priority of the descriptive. Once we have identity, we lose all asymmetries including that of explanatory priority.

Furthermore, there are possible instances where a descriptive and a normative predicate are necessarily coextensive, but the single property ascribed would have to be the normative property. Sidgwick rejected a simple sensation account of pleasure on the ground that there is no way in which the very different pleasant experiences we enjoy, such as gustatory, aesthetic, philosophical, or social pleasure, are similar at the level of sensation. He writes:

[W]hen I reflect on the notion of pleasure,—using the term in the comprehensive sense which I have adopted, to include the most refined and subtle intellectual and emotional gratifications, no less than the coarser and more definite sensual enjoyments,—the only common quality that I can find in the feelings so designated seems to be that relation to desire and volition expressed by the general term “desirable,” in the sense previously explained. I propose therefore to define Pleasure—when we are considering its “strict value” for purposes of quantitative comparison—as a feeling which, when experienced by intelligent beings, is at least implicitly apprehended as desirable .... (1963: 127)

Suppose something like Sidgwick’s definition of pleasure as a desirable feeling is correct. It would follow that the descriptive predicate ‘is pleasant’ is necessarily coextensive with the evaluative/normative predicate ‘is a desirable feeling’, and so this evaluative predicate would ascribe the same property as this descriptive predicate. But if the only way in which all pleasant feelings are similar is by being desirable, the single property ascribed by the evaluative and the descriptive predicate would be an evaluative property, falsifying dp.

This example is further evidence that it is a mistake to assume that if a descriptive and a normative predicate are necessarily coextensive, they ascribe a descriptive property, even if (N) is true. Even if we accept (N), we can only move from the co-extensiveness of a descriptive and a normative predicate to the view that the property ascribed by these predicates is a descriptive property if there is some descriptive way in which each instance of this property is similar. The Sidgwick example shows, I think, that this may not always be true. In such cases, the property ascribed may well be a normative property, and since there is no descriptive way in which all pleasures are similar, this will be an irreducibly normative property. Since a necessarily coextensive ethical and descriptive predicate may ascribe a single ethical property, this could be true of ‘is right’ and D*. It could well be that the case that the only way in which all right acts are similar is by being right, and so the single property ascribed by the predicates ‘is right’ and D* must be the non-descriptive property of rightness itself.

I say it could well be the case that the only way in which all right acts are similar is by being right. That is because, as Streumer notes in his second argument for reduction, if some simple first-order normative theory were correct, such as a simple form of utilitarianism, then there would be a descriptive predicate that is necessarily coextensive with ‘is right’, namely, the predicate ‘maximises happiness’ (30). We can add that if that is true, then there would be a descriptive way in which all right acts are similar, and so rightness could be identified with that descriptive property. If we thought that right acts are right because they maximise happiness, that would be lost with this supposed identity, as right-making is an explanatory, and so asymmetric relation, and asymmetry would be lost with identity. So such a theorist would have to find some other right-making property. That would not be a problem for such a simple form of utilitarianism, for if maximising happiness and rightness were identical, then the utilitarian could just sum all the things that would make these people happy as the right-maker. But the main point is that simple utilitarianism would have a contender property with which to identify rightness. This would not, however, be an option if a pluralist normative theory, such as Rossian pluralism, were true, for then different right acts would be made right by different properties, and there would be no guarantee that there is some descriptive way in which all right acts are similar, and so no guarantee that there is some shared descriptive property with which rightness could be identified.

The above point would make the prospects for reduction depend to some degree on whether a simple first-order normative theory is true. Streumer rejects that dependence, and I will discuss his view about that below. But even if that dependence were allowed, one would only be able to find descriptive similarity by defending a very crude first-order ethical theory, and the prospects for that are not in my view good. In any case, neither Jackson nor Streumer provide such a defence. Jackson suggests that the descriptive property which is rightness may be the property of maximising happiness (1998: 142), but given his methodology there is no guarantee about that, and there are plenty of very good and familiar reasons to suppose that such a simple theory is false.12

Could the descriptive way in which all right acts are similar be by having in common the disjunctive property that mirrors the predicate D*?13 Jackson is willing to fall back on this position, if the method he outlines based on Ramsifying mature folk psychology doesn’t come up with something simpler. It should be noted that Streumer’s argument does not rely on disjunctive properties, since the job of the first step of the argument is to establish that normative properties are descriptive properties, not to tell us what descriptive property they are. But since the second step of his argument tries to show the failure of various attempts to specify what that descriptive property is, it is worth considering, albeit rather briefly, whether the descriptive property ascribed by the disjunctive predicate simply mirrors that predicate. We would then have at least one descriptive way in which all right acts are similar, and so it could be true that rightness is a descriptive property.

I do not, however, think that a disjunctive ‘property’ would be able to do what is required, for a disjunctive property could not capture a respect in which things that have that property are similar.14 So disjunctive properties could not be genuine properties. To see this, take the simple disjunctive predicate ‘is either green or square’. Take two objects to which this predicate may truly be applied—a red square and a green circle. We can truly say that each object is either green or square, since only one disjunct of a disjunction needs to be true for the disjunctive claim to be true. How do we decide whether these two things are similar in the respect of being either green or square? That will depend on how we understand ‘being similar in a respect’. As Paul Audi has pointed out on one account of this idea, such similarity follows trivially. Consider the following definition:

For x to be similar to y in respect of having some property F, is just for x to be F and y to be F.

All there is to similarity-in-a-respect, on this understanding, is property-sharing, so one could only deny that our two objects are similar in a disjunctive respect by denying that they share the same disjunctive property, which is clearly question-begging (Audi 2013: 750). Audi offers a better alternative:

For x to be similar to y in respect of being F will be for x insofar as x is F to resemble y insofar as y is F. (2013: 758)15

Disjunctive ‘properties’ do not satisfy this criterion. A green circle, in so far as it is green or square is simply green with no trace of squareness, and a red square, in so far as it is green or square, is simply square with no trace of greenness, and greenness does not in any way resemble squareness (Audi 2013: 760). If this simple disjunctive ‘property’ cannot capture any similarity between the things that are supposed to have it, then there is no hope for a property that combines (in the disjunctive way) many more properties.

Not all disjuncts of putative disjunctive properties are dissimilar. One could capture all determinate shades of red with a long disjunctive predicate = ‘is either scarlet, or imperial red, or Indian red, …’ One could not deny this disjunctive property on the ground that there is no way in which all things that have it are similar, for they are all similar in respect of being red. But this is a problem for the view that there are disjunctive properties rather than an advantage. For the way in which all of the disjuncts are similar is not disjunctive. They are all similar in respect of being red, and that is not disjunctive. Similarly, every triangular thing is either equilateral, or isosceles, or scalene, but that does not mean that triangularity is a disjunctive property. That is because there is a non-disjunctive thread of similarity running through all triangles in so far as they are triangular.

Another reason to reject the idea that there are genuine disjunctive properties is simply that they are redundant. All that is needed to make a disjunctive statement true is one of the properties ascribed by one of its disjuncts. So if a property ascription is understood metaphysically, we need not assume that disjunctive predicates ascribe disjunctive properties. Take the predicate ‘is either green or square’. What makes it true that a green circle is either green or square is its greenness (a non-disjunctive property), and what makes it true that a red square is either green or square is its squareness—once again, a non-disjunctive property. We do not need to suppose that, in addition to these non-disjunctive properties, these objects also have a disjunctive property of being either green or square in order to make the disjunctive proposition that they are either green or square true. That work is done by each of the properties disjoined.

The same is true for determinate forms of determinable properties, say the property of being red. All that is needed to make it true that something is red is an instance of one determinate shade of red that would figure in a disjunct of the putative disjunctive property of being either scarlet, or imperial red, or Indian red, or… Similarly all that is needed to make it true that something is either scarlet, or is imperial red, or is Indian red, or… is an instance of the determinate shade. The disjunctive property is completely redundant as a truth-maker for either determinable propositions or disjunctive propositions. Once the redundancy of disjunctive properties is noted, there is absolutely no pressure to include disjunctive properties into our ontology, and for reasons that have nothing to do with similarity.

To summarise: we cannot conclude that rightness is a descriptive property from (N), and the necessary co-extension of the predicate ‘is right’ and the descriptive predicate D*, unless there is some descriptive way in which all right acts resemble each other. If there is no descriptive way in which they all resemble each other, then the property ascribed by the predicates ‘is right’ and D* cannot be a descriptive property. It could however be the (irreducible) property of being right, for the property of being right may well be the only way in which all right acts are similar, just as the only way in which all pleasant feelings might be similar is, as Sidgwick thought, in an evaluative way.

3 Streumer’s Second Reduction Argument

Streumer’s second argument for reduction is novel. He notes, as we have already seen, that if some simple first-order normative theory were correct, then we would have a descriptive predicate that is necessarily coextensive with a normative predicate. In conjunction with (N) it would follow that:

  1. (1)If simple first-order normative views are correct, normative properties are identical to descriptive properties. (32)

Streumer also endorses

(W) Whether normative properties are identical to descriptive properties cannot depend on which first-order normative view is correct. (31)

In defence of (W) Streumer plausibly says that “whether normative properties are identical to descriptive properties seems to depend on the nature of these properties rather than on” which objects have those properties, and which descriptive properties these objects have (31).

If (1) and (W) are true, it must be true that “normative properties are identical to descriptive properties whether or not simple first-order normative views are correct” (32). Otherwise, (1) would contradict (W). So the following must be true:

  1. (2)If some non-simple first-order normative view is correct, normative properties are identical with descriptive properties.

(1) and (2) together entail:

  1. (3)If any first-order normative view is correct, normative properties are identical with descriptive properties.

This is an ingenious argument, but at least one of its premises, (W), can be challenged. I agree that there is something wrong about arguing from some first-order normative theory about what is right to some claim about the nature of rightness, although Scanlon maintained that the best way to think about debates about fundamental normative principles was as a debate about the nature of wrongness (1998: 11–12). But one need not start from the normative theory to get dependence. One might have an argument for the nature of rightness, which is such that if rightness has that nature then a certain normative theory must be true, or certain normative theories must be false. Moore seemed to argue in this way in Principia Ethica. There he argued that rightness is the property of maximising intrinsic goodness. His argument runs as follows:

  1. (1)Right acts are unique in respect of value.
  2. (2)But no right action can possibly have unique value in the sense that it is the sole thing of value in the world.
  3. (3)Its value cannot be unique in the sense that it has more intrinsic value than anything else in the world

Therefore

  1. (4)It can be unique only in the sense that it produces the best outcome.

Therefore:

  1. (5)The property an act has of being right is the property that act has of producing the best outcome. (1993: 197)

This argument for a definition of rightness in terms of goodness does not start from any normative theory, but from what Moore takes to be a distinctive feature of the nature of rightness—its being unique in respect of value. But if Moore is right to define the property of being right as he does, then any first-order normative theory that claims that an act can be right even though it does not produce the best outcome, such as a Kantian or Rossian theory, must be false. If the property of being right and the property of producing the best outcome are identical, it is not possible for some act to be right yet not produce the best outcome. So Moore’s account of the nature of rightness would depend upon which first-order normative theory is true in the sense that, if some non-consequentialist theory were true, then rightness could not be as Moore argued it is. So an account of the nature of rightness could depend on whether a simple first-order normative theory is true not because its nature is inferred from that theory, but because the theory follows from its nature. The same would be true if some naturalist theory of rightness were true. That might well constrain which normative theories could be true, and in that sense depend on whether they are true.

I do not think Moore’s argument is very persuasive, and Moore himself quickly abandoned that definition of rightness, but that is beside the point. It is a perfectly legitimate way to argue, and it does make the nature of moral properties depend upon which first-order normative theory is true. Moore’s view does not identify a moral property with a descriptive property, but defines it with reference to causality and intrinsic goodness. But it does show that the nature of some normative property can depend on which first-order normative theory is true, and that casts doubt on (W).

Another way one could legitimately argue from the nature of rightness to the truth of a simple first-order normative theory would be along the lines mentioned earlier from (N). One might argue that there is some descriptive way in which all right acts are similar. So there is a descriptive property that all right acts have, such that if an act has the property of being right it has this descriptive property, and vice versa. If all acts that have this descriptive property are also right, one will have a necessarily coextensive predicate. One might then argue using (N) that rightness is identical to that descriptive property. If that descriptive property is the property of maximising happiness, it would follow that the property of being right is identical with the property of maximising happiness. But if this is the nature of rightness, it would imply that a simple form of utilitarianism must be true, and whether rightness is identical with this descriptive property would depend on the truth of a first-order normative theory and (W) would be false. Once again, it does not matter whether this is a compelling argument. All that matters is that this is a perfectly legitimate way to argue, which I think it is.

In addition to the above concerns, I do not think that Streumer’s argument for (W) sits comfortably with (N). According to (N), whether normative properties are identical with descriptive properties depends (supposedly) on whether we can construct a necessarily co-extensive descriptive predicate. That doesn’t look like it has anything to do with the nature of these properties. (N) just tells us that two predicates always pick out the same property. It does not suppose that they do this because of the general nature of that property. Rather, things are the other way round. That argument reaches a conclusion about the general nature of the property (its being descriptive in nature) because we can construct a predicate that necessarily co-refers. This presents Streumer with a dilemma:

Either the argument for (W) is good or it is not.

If it is a good argument, it will work against (N) so undermining the argument for (1). If it is not good, we can reject (W) and then there is no argument for (2).

Either way, Streumer’s second reduction argument fails.

4 Conclusion

Both Jackson’s and Streumer’s reduction argument fails because it fails to show that there is some descriptive way in which all right acts are similar. If there is no descriptive thread of similarity running through all right acts, then rightness could not be a descriptive property. And if the only way in which all right acts resemble each other is by being right, then that would have to be the single property ascribed by the predicate ‘is right’ and D*. These predicates would ascribe the single, non-descriptive property of being right. This conclusion sits perfectly with the second strand of Streumer’s argument that rightness, or any other normative property, is not identical with a descriptive property. So unlike Kant’s antinomy, Streumer’s antinomy ends up, I maintain, rejecting the thesis (reduction) and endorsing the antithesis (non-reduction). There is no argument from queerness in Streumer, so as far as that goes he has no reason not to accept this conclusion, which at least has the advantage of being credible, and so allowing him to believe his own view.

References

  • Armstrong D.M. 1978. A Theory of Universals: Universals and Scientific Realism, volume 2. Cambridge: Cambridge University Press.

  • Audi P. 2013. “How to Rule Out Disjunctive Properties,” Noûs 47: 748766.

  • Bader R. 2017. “The Grounding Argument against Nonreductive Moral Realism,” Oxford Studies in Metaethics 12: 106134.

  • Enoch D. 2011. Taking Morality Seriously: A Defence of Robust Realism. Oxford: Oxford University Press.

  • Heil J. 2005. “Dispositions,” Synthese 144: 343346.

  • Jackson F. 1998. From Metaphysics to Ethics: A Defence of Conceptual Analysis. Oxford: Oxford University Press.

  • Jackson F. 2017. “In Defence of Reductionism in Ethics.” In Singer P. (ed.), Does Anything Really Matter?: Essays on Parfit on Objectivity, 195212. Oxford: Oxford University Press.

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  • Majors B. 2005. “Moral Discourse and Descriptive Properties,” The Philosophical Quarterly 55: 475494.

  • Moore G.E. 1993. Principia Ethica. Edited by Baldwin T. . Cambridge: Cambridge University Press.

  • Ross W.D. 2002. The Right and the Good. Edited by Stratton-Lake P. . Oxford: Oxford University Press.

  • Scanlon T.M. 1998. What We Owe to Each Other. Cambridge, MA: Harvard University Press.

  • Scheffler S. 1982. The Rejection of Consequentialism. Oxford: Oxford University Press.

  • Sidgwick H. 1963. The Methods of Ethics. London: MacMillan.

  • Shafer Landau R. 2003. Moral Realism: A Defence. Oxford: Oxford University Press.

  • Streumer B. 2017. Unbelievable Errors: An Error Theory about All Normative Judgements. Oxford: Oxford University Press.

  • Williams B. 1985. Ethics and the Limits of Philosophy. London: Fontana.

1

Unless otherwise stated, all references to Streumer will be to his 2017 book.

2

Not all normative judgements come out false according to error theory. Conditional normative judgements come out true, e.g., the transitivity of ‘better than’.

3

This is because, Streumer argues, we cannot believe that P whilst believing that we have no reason to believe that P: “A person believes that p only if this person does not believe that there is no reason to believe that p, unless the belief that p is compulsive or deluded” (140).

4

Jackson looks like he thinks that this is a semantic claim when he says that “to believe that X is right is to believe that X has the property of being right” (2017: 196).

5

It is standard to claim that realism is built into the practice of moral discourse. I take that to be weaker than claiming that it is analytical.

6

In correspondence, he said that he rejects this for dialectical reasons, and that he does not deny that there are also properties in the minimal sense.

7

This is because we cannot believe something we think we have no reason to believe. My own view is that his error theory is believable, so if unbelievability is a benefit of such a theory, it is not a benefit he can enjoy. But I will not argue for that position here.

8

This is in part because N is a controversial theory about property identities, which seems vulnerable to counter-examples (see Shafer Landau 2003: 91; Enoch 2011: 138–139; Bader 2017), whereas “Rape is wrong” is in no way controversial, or vulnerable to counter-examples. There may be cases where it is unclear whether consent was given, either because of the age of the woman, or because she was drunk. But what is controversial here is just whether some specific case is one of rape, not about the general proposition that rape is wrong.

9

For a similar argument for why ethical properties cannot be descriptive properties, see Majors (2005). He rests his argument on the following principle:

Kind Constraint – Property Formulation: if a property is of a kind K, then the members of its extension must have something in common which is visible from level K. (2005: 485).

Bradford, however, supposes that the supposed descriptive property referred to by D* is disjunctive (2005: 486). First, I don’t think that is true, and second, his way of putting the point still links to the sort of predicates that can be used to pick out this property rather than on the basis of something in the nature of the property itself. He also goes on to criticise N. But as I note, one can grant N, as the best it can do is show that some ethical predicate and D* refer to a single property. It does not follow from this that the single property is descriptive.

10

Schroeder (2007: 63–64) makes this point about property identity claims. He prefers to talk of constitutive explanations rather than property identity, as the notion of explanation is asymmetric, so captures better the idea, say, that figures are triangles by having three sides and do not have three sides because they are triangles (2007: 63). But this is not how Streumer thinks of his reductive claim. I think, however, that Schroeder goes too far when he says that this sort of reductive thesis tells “us more about English than about, for example, reasons” (2007: 64). If the reduction were successful, this would tell us that we need only postulate one truth-maker for two different types of sentence. That would be a metaphysical claim. See also Bader (2017: 122).

11

Bader (2017) argues that a distinctive type of grounding, normative grounding, is incompatible with identity. If this were true, and if similar grounding is required in addition to necessary coextensiveness for identity, then Jackson’s argument would fail. But it seems to me that, to deal with this objection, Jackson could simply deny that there are different sorts of grounding, rather than different types of things grounded.

12

See, for example, Ross (2002), Williams (1985), Scheffler (1982), and Scanlon (1998), although there are many others.

13

The idea of a disjunctive property is tricky, as disjunction is a truth-function and properties disjoined are not truth-valued. Audi suggests a way round this problem. He writes:

So the notion of a disjunctive property appears to depend on a different sort of disjunction, a manner of combining properties. The notion is not unintuitive, especially if it is understood by analogy with conjunction. The idea that properties can be combined by conjunction, though not uncontroversial, is at least straightforward. One way to get a handle on what disjunctive properties are supposed to be, then, is to say that they are the complex properties that result from combining simpler properties in this disjunctive manner. (2013: 751)

14

This point and the argument in its favour are familiar in the literature. See, for instance, Armstrong (1978: 20), Heil (2005: 347), and Audi (2013).

15
Audi claims that this presupposes what he calls inheritance realism according to which properties are immanent to their bearers. This is an Aristotelian realist view rather than a Platonic one. But I do not see why one must assume inherence realism to use this definition. Audi writes:

The inherence realist insists that the distinction we make in thought between, say, a insofar as it is F and a insofar as it is G corresponds to a distinction in the thing itself. The inherence realist differs, then, from both the nominalist and the Platonist. The nominalist insists that the distinction between a insofar as it is F and a insofar as it is G is merely a distinction of reason. The Platonist allows that there is a real ­distinction here, but denies that it corresponds to any divisions within a itself between non-mereological constituents of a. (2013: 753–754)

But if the Platonist understands instances as actual ways things are (and universals as possible ways things might be), then the distinction between a insofar as it instantiates F and a in so far as it instantiates G will correspond to a real difference in a itself, for the instance of F and of G will be different ways in which a is. I will however put aside this point in what follows as it will overcomplicate things.

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