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Author: Mark Schroeder1
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  • 1 University of Southern California
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In Unbelievable Errors, Bart Streumer offers resourceful arguments against each of non-reductive realism, reductive realism, and non-cognitivism, in order to motivate his version of the normative error theory, according to which normative predicates ascribe properties that do not exist. In this contribution, I argue that none of the steps of this master argument succeed, and that Streumer’s arguments leave puzzles about what it means to ascribe a property at all.

Abstract

In Unbelievable Errors, Bart Streumer offers resourceful arguments against each of non-reductive realism, reductive realism, and non-cognitivism, in order to motivate his version of the normative error theory, according to which normative predicates ascribe properties that do not exist. In this contribution, I argue that none of the steps of this master argument succeed, and that Streumer’s arguments leave puzzles about what it means to ascribe a property at all.

1 Introduction

Bart Streumer’s book, Unbelievable Errors, is jam-packed with arguments and careful engagement with the philosophical literature at every turn. There is a great deal to be learned from it, both about its subject matter and about the philosophical virtues of both tenacity and care. Nevertheless, despite having read it and come to appreciate these virtues, I find myself unable to believe its conclusion. Cleverly, Streumer anticipates precisely this, going so far as to warn me of it in his title. Even he, he argues, does not fully believe his own conclusion. Yet the reasons for our unbelief are not the same. Streumer finds himself unable to believe his conclusion, and argues that this is because his conclusion is a blind spot for belief—no one can believe what they believe they have no reason to believe, and so you cannot rationally and with full understanding believe that there are no reasons at all. I don’t doubt that this is so. Yet I find myself unable to believe Streumer’s conclusion for the much more mundane reason that I find his arguments for it to be unconvincing.

In essence, Streumer’s argument for the error theory is an argument by elimination. He argues, against non-reductive realism, that if normative properties exist, they are identical to descriptive properties. Then he argues, against reductive realism, that normative properties are not identical to descriptive properties. And finally, he argues that non-cognitivism is false. Importantly, arguing by elimination puts the error theorist in a position of dialectical weakness, rather than strength—all it takes to fail is one uneliminated alternative, or one false step in any one of the arguments. But despite its cleverness, Streumer’s argument by elimination is particularly weak; as I’ll suggest in what follows, all three of his arguments against competing views fail—in each case, I believe, because he is not sufficiently sympathetic with the perspective of proponents of these views. Moreover, I find his positive picture—the kind of error theory for which he means to have argued, even though he cannot quite bring himself to actually believe it—puzzling in ways that go beyond its occupation of a blind spot for rational belief.

In what follows I’ll take these four issues in order: in Sections 2, 3, and 4, Streumer’s arguments against non-reductive realism, reductive realism, and non-cognitivism, respectively, and in Section 5, the further puzzles that remain concerning Streumer’s own version of the error theory.

2 The Reduction Argument

Streumer’s argument against non-reductive realism is a variant on familiar arguments from the supervenience of the normative to the constructability of properties that are necessarily coextensive with normative properties.1 The key feature of all such arguments is that they rely on an extremely coarse-grained criterion for property identity, and in addition to relying on such a conception, Streumer’s argument relies on a very relaxed sufficient condition for a property to count as ‘descriptive’. I’ll take issue with each of these commitments, in order.

At issue in all direct supervenience arguments for property identity is the right standard for individuation of properties. According to the most coarse-grained possible conception, properties are equivalent to sets of possible individuals. This thesis has two components, existence, which says that for every set of possible individuals there is a property, and uniqueness, which says that there is at most one property shared by any set of possible individuals. Direct supervenience arguments for property identity are typically naturally interpreted as motivated against the background of both existence and uniqueness. They appeal to existence in order to construct a descriptive property that is shared by exactly the same set of possible individuals as a given normative property, allowing them to appeal to uniqueness in order to prove that the normative property and the descriptive property are the same property. Then they do this for every other normative property, hence establishing that every normative property is a descriptive property.

Together, however, existence and uniqueness are incompatible with one of the most central traditional theoretical roles that properties have been held to play—that of what things have in common. This is because every two possible individuals share membership in exactly the same number of sets of possible individuals. So given existence and uniqueness, it follows that every pair of possible individuals shares exactly as many properties as every other set of possible individuals, and hence, if properties tell us what things have in common, that no pair of possible individuals has more in common than any other pair of possible individuals. So together, existence and uniqueness give us at best a vacuous sense in which properties tell us what anything has in common. Since this is a central theoretical role for properties, I infer that properties cannot obey both existence and uniqueness. Hence, something must be wrong with the style of supervenience argument that I sketched in the last paragraph.

Now, to avoid this conclusion, we can give up existence, we can give up uniqueness, or we can give up both. My own recommendation is to give up both, essentially on the grounds that the stock of basic properties is so limited that we need more complex properties to characterize other ways that things can have things in common. For example, suppose that A and B are red squares, C a blue square, and D a red circle. A, B, and C share in common that they are squares, A, B, and D share in common that they are red, and A and B have more in common than the others. One way that A and B could have more in common is simply that there are more things that they have in common. But another way is that there is something else—something distinctive—that they have in common, the property of being red squares. If we accept this—that being a red square is a property—then we should surely not think that this is a coincidence. For every other pair of compossible properties we will be able to construct similar cases. And so if we go in for such properties at all, we should say that they somehow arise from or depend on their conjuncts. Indeed, this can explain why A and B are red squares in part because they are red, and because they are square (cf. Schroeder 2005; 2007: Ch. 4).

A very simple picture of how this could be, and how it could be ontologically innocuous, is that conjunctive properties are complex, sharing their conjuncts as parts. It is a small step from this to the conclusion to the rejection of uniqueness—for once we acknowledge complex properties, we can structure them in different ways that are nevertheless guaranteed to pick out the same individuals. This is my own view—a view that rejects both existence and uniqueness, and hence on which the reduction argument fails in multiple places—and it is not motivated in any way by the idea that properties are the shadows of concepts or predicates, which I wholeheartedly reject along with Streumer.

Now, as I understand Streumer’s version of the supervenience argument, he means to rely on uniqueness without relying on existence.2 This idea has some promise, in that it is both the more natural way of giving up on one of existence or uniqueness without giving up on both, and in that it keeps the principle that does more work in the supervenience argument for reduction. But it means that since existence is not what guarantees that the construction of a complex descriptive predicate in his argument picks out a property, something else must guarantee it.

Streumer’s answer to this, I take it, is simple and natural. It is that we don’t need existence to guarantee that the complex descriptive predicate that Streumer’s argument constructs picks out a property, because by construction, it is necessarily coextensive with—and hence satisfied by the same set of possible individuals as—the normative property with which we started. So by Streumer’s reasoning, the assumption that the normative predicate expresses a property is enough to guarantee that the descriptive predicate expresses a property, without any need to appeal to existence.

This is why Streumer articulates his version of the assumption of the coarse-grainedness of properties with principle (N):

(N) Two predicates ascribe the same property if and only if they are necessarily coextensive.

If principle (N) is true, then if the constructive part of Streumer’s argument works at finding a complex descriptive predicate that is necessarily coextensive with a normative predicate, it follows that those two predicates express the same property, and hence that normative properties really are descriptive properties, in Streumer’s sense. Yet since (N) is formulated in terms of predicates, rather than in terms of properties, it is actually consistent with denying existence, so long as there are some sets of individuals that do not correspond to the intension of any predicate.

But the logical space between (N) and existence is too small, given Streumer’s other commitments. In particular, in a later part of the argument, in order to make sure that there are enough descriptive predicates for his argument to work, he assumes that every property can serve as a name for itself. This assumption makes it too easy to construct a descriptive predicate corresponding to any set of possible individuals. For any given set of possible individuals o1 in w1, o2 in w2, and so on, you take the disjunction of being identical to o1 in w1 or identical to o2 in w2 … If there are no names for these individuals or these worlds, then we just let them serve as names for themselves, as Streumer allows elsewhere. So given this incredibly relaxed conception of how to construct descriptive predicates, it follows from (N) as stated that there is a property corresponding to every possible set of individuals. This is particularly bad for Streumer, because it then turns out that his own form of the error theory is provably wrong, because if necessarily nothing is wrong, then ‘wrong’ is equivalent to ‘round square’, and hence both express the null property.

So it is no surprise that in a footnote Streumer tries to qualify principle (N) further.3 On his preferred, careful, version of principle (N), what it says is that:

(N*) Two predicates that both ascribe a property ascribe the same property if and only if they are necessarily coextensive.

Yet when we replace (N) with (N*) in the argument, the reduction argument no longer goes through. Just because Streumer has a way of constructing a complex descriptive predicate that is necessarily coextensive with any given normative predicate, it doesn’t follow that if the normative predicate ascribes a property the descriptive predicate does, too. Maybe the descriptive predicate does not ascribe a property at all.

Streumer might fix this problem by appealing to a principle of intermediate strength between (N) and (N*)—I’ll call it (N&):

(N&) If a predicate ascribes a property, then it and any other predicate with which it is necessarily coextensive ascribe the same property.

(N&) does not entail existence, even in the company of Streumer’s extremely relaxed view of how to construct descriptive predicates. And it is enough to establish that if moral predicates ever ascribe properties at all, those properties are identical to descriptive properties, given Streumer’s very relaxed conception of what makes something a descriptive property. I’m not clear on why anyone would think that (N&) is true without deriving it from existence, however, and I’m particularly not sure on what grounds Streumer could think it to be true, because I am not particularly clear on what property ascription amounts to, for Streumer—I’ll return to this question in Section 5.

Yet even if we grant Streumer (N&), I believe that this merely shows that something has gone deeply wrong somewhere with the argument. This is because it is consistent with (N&)—indeed, it is a commitment of taking (N&) not to be explained by the truth of existence—that the complex descriptive predicate constructed by Streumer’s argument only counts as expressing a property at all because it is coextensive with a normative property. Yet if that is so, then there is a very natural sense in which normative predicates are joint-carving predicates in a way that is not indebted in any way to the fact that there are complex descriptive ways of picking out the individuals with the very same properties. Indeed, this is very close to the version of non-reductive realism defended by Graham Oddie (2005), one of the authors Streumer cites, in Chapter 2.

This leads me to the diagnosis that in addition to relying on false premises, something is flawed about Streumer’s setup of the problem, in the first place. Indeed, I think it is not hard to see that his conditions on what it takes for something to count as a ‘descriptive’ predicate are far too weak to be interesting.

The problem is that we can reductio Streumer’s characterization of descriptive properties by showing their consequences even without the assumption of supervenience. There are a variety of ways to do so. In order for his argument to work, Streumer needs to adopt a very weak sufficient condition on what it takes for a property to count as ‘descriptive’. All it takes, is that it must be expressible by a complex predicate formed out of descriptive terms, and the logical connectives ‘and’, ‘or’, and ‘not’. But Streumer weakens this condition even further. Worried that there will not be enough descriptive terms to go around, in order to construct the complex descriptive predicate that he needs, he proposes that it does not need to be expressible in any actual or even possible natural language, but could instead be composed out of terms in a ‘lagadonian’ language, in which the objects or properties that are not named by any natural language are their own names instead. Streumer holds that if a predicate can be constructed in such a lagadonian language, then the condition of satisfying that predicate is a descriptive predicate. But we can exploit this fact to construct a complex predicate that is necessarily coextensive with any property D—without assuming supervenience at all.4

We do it by noting that any property D corresponds to a set of possible individuals—the individuals o11,…o1n who satisfy D at world w1, the individuals o21,…o2m who satisfy D at world w2, and so on, for every possible world. So trivially, necessarily, something satisfies D just in case it is identical to o11 at w1 or o12 at w1 or … or o1n at w1 or o21 at w2 or o22 at w2 or … or o2m at w2 or o31 at w3 or … and so on. Clearly this complex descriptive predicate does not involve any tricks that Streumer does not allow—it is a very long disjunction, of course—too long, in fact, to even be an infinite list, because it will have uncountably many disjuncts—but of course Streumer’s own disjunctive predicates can also be uncountably long. It is constructed only out of the logical connective ‘or’, identity, and it uses individuals for which we lack names as names for themselves in a lagadonian language. And we can perform this construction for any property D—without making any assumptions about supervenience at all.

Indeed, we can run restricted versions of this argument without the Lagadonian names at all. Let m be any normative property that has ever been entertained in thought by a human, and om the very first occasion on which it was so entertained. Then consider the predicate, ‘satisfies the property actually entertained on occasion om’. This predicate is necessarily coextensive with m, so by (N&), it expresses the property m. Yet all of the terms in this complex predicate are clearly descriptive. So by parity of reasoning, every normative property that has ever been entertained in thought by a human is a descriptive property.

These arguments show, I think, more about the unhelpful liberality of the notion of ‘descriptive property’ in this argument, than about the reductive consequences of supervenience. Such a notion of ‘descriptive property’ is far too liberal to helpfully characterize what could possibly be at stake between reductive and non-reductive realists. Of course, since Streumer’s ultimate goal is to argue for the error theory, rather than for reductive realism, perhaps that is no obstacle—it just places more weight on his argument against reductive realism. So let us turn to that, next.

3 Reductive Realism

In the last section, I have argued that Streumer’s argument against non-reductive realism is flawed—relying on insufficiently sympathetic engagement with the plausible commitments of his interlocutors. But let us suppose, for the sake of argument, that those arguments are instead successful. That would bring us to his arguments against reductive realism in chapters 4 and 5. The structure of these arguments is supposed to be a dilemma—or perhaps a trilemma. The dilemma arises because the reductive realist owes us an answer to the question of what makes it the case that a certain normative predicate ascribes a certain descriptive property. The problem for reductive realism is supposed to be that there is some dilemma about being able to give an adequate account of content-determination that will apply to normative predicates.

This is not a terribly surprising place to look for an argument against reductive realism, given the sociology of the last thirty years of metaethics; as Streumer acknowledges, this is precisely how Terry Horgan and Mark Timmons have famously proposed to argue against reductive realism in their moral twin earth thought experiment and accompanying arguments.5 Yet as I’ll explain in a moment, the holes in Horgan and Timmons’ argumentative strategy are very large, and so it is also not surprising that Streumer’s argument inherits similar holes, despite differing in substantial ways from Horgan and Timmons over the construction of the details.

According to Streumer, there are only three possible answers to the question of what makes it the case that normative predicates ascribe the properties that they do. The first is that users would ascribe the property under certain descriptively specified conditions. The second is that users would ascribe the property under certain normatively specified conditions. And the third is that the true first-order normative theory applies this predicate to things that have this property.

To see what is so strange about trying to make a dilemma out of this, all that is required is to observe how little of the logical space of possible answers to the question of what makes it the case that normative predicates ascribe the properties that they do these answers take up. And to see that, all it takes is to observe that both of Streumer’s first two answers attempt to answer what makes it the case that a predicate ascribes the property that it does in subjunctive terms. So in order for his trilemma of options to be exhaustive, the third answer has to be general enough to include every possible non-subjunctive theory about in virtue of what words means what they do. (It is also worth noting that the first two answers do not exhaust the space of subjunctive answers, since not all subjunctive accounts are accounts about subjunctive conditions of use.) But far from encompassing every possible non-subjunctive answer to this question, the third answer that Streumer considers is actually incredibly specific.

Indeed, the third answer does not, at a first pass, even have the right form to answer the question at all—for example, the true first-order normative theory is true quite independently of any facts about natural language. For example, Google translate tells me that the word for ‘wrong’ in Western Frisian is ‘ferkeard’ and in Albanian is ‘i gabuar’. But if this is correct, then ‘ferkeard’ would have ascribed the property of being ‘wrong’ even if ‘i gabuar’ meant something different in Albanian, and similarly in reverse. But according to Streumer’s third possible answer to what makes it the case that normative predicates ascribe the properties that they do, these can’t differ, because they are both explained by facts about what the true first-order normative theory ascribes the predicate to.

I infer that Streumer’s statement of this theory is overly casual. Presumably what he must mean is that according to this answer, what explains why normative words ascribe the properties that they do is that the statement of the true first-order normative theory in that language ascribes those predicates to things just in case they have those properties. This rescues the theory from the charge of absurdity, but not in a way that helps it to answer the question with which we started. For in order for any sentence of the language to be a statement of part of the true first-order normative theory, the terms in that sentence must first ascribe normative properties. So this still isn’t even the right kind of thing to answer in virtue of what those terms come to count as ascribing the properties that they do. Since it doesn’t even count as answering the question, therefore, it can’t possibly represent the space of all possible non-subjunctive answers to the question, unless we could somehow know a priori that there could be no possible non-subjunctive answer to the question.6

Yet plausibly, any reasonable metasemantic theory is going to be non-subjunctive in nature. There are familiar, obvious, obstacles to subjunctive theories of content determination that resemble conditional fallacy counterexamples to subjunctive theories of many other things: cases in which the closest world in which the subjunctive condition is satisfied is one that is relevantly different, and the term actually means something else in that world (see Shope 1978). So whether the correct metasemantic theory appeals to linguistic conventions, causal covariation, informational or teleological semantics, inferential roles, interpretability, or something else, all of the most defensible accounts of the nature of linguistic meaning are categorical, rather than subjunctive, in nature.

Since Streumer does not survey the vast space of possible views about what makes normative predicates come to pick out the properties that they do, it is very hard to see how it even has the right structure to constitute prima facie evidence against reductive realism. In this, it has much in common with Horgan and Timmons’ moral twin earth argument. Horgan and Timmons’ argument works by proposing an intuitive counterexample to a theory of content determination for normative terms, and then asserting that there will be similar intuitive counterexamples to any other possible theory. They are confident that there will be counterexamples to every other possible theory because they know which sorts of features of cases tend to prompt the relevant intuitions about what words mean, but somehow, as they conceive of the dialectic, the reductive realist is not allowed to use these same features of cases in order to construct their theory of in virtue of what normative words come to mean what they do, and Horgan and Timmons never explain why not.

We might hope that Streumer’s argument puts us in a stronger position than Horgan and Timmons’ does to consider what the problems might be with alternative views. But it does not even do that. Streumer’s argument does not even work against one of the horns of the dilemma that he does consider—the answer on which what explains why normative predicates ascribe the properties that they do the fact that they would be ascribed to things that have this property under some subjunctive normative condition. Streumer’s objection to this view is what he calls the regress objection. To see why the regress objection fails, it helps to see why there is a possible view against which it is a good objection. According to this possible view, when thinkers use normative terms, as in thinking ‘stealing is wrong’, they are really having a complex thought of the form, ‘stealing has the property that I would ascribe using the word ‘wrong’ under subjunctive condition C’, where ‘C’ is itself specified in normative terms. This is of course absurd. The normative condition in C, because it is also deployed in the speaker’s own thoughts, needs to ascribe a normative property, and by the same theory, it can only do so if the speaker intends it to ascribe whatever property she would ascribe using that term in C—and so the regress (or at least a vicious kind of circularity—it’s a regress proper only if there are different normative conditions, which of course the view needn’t hold) is off and running.

Of course that view is absurd. But it doesn’t follow that the true view of content determination is not normative—just that it doesn’t work by deploying a normative word or concept in thought. Indeed, it is not hard to see that the true general view of content determination cannot require that its key concepts be deployed in thought by thinkers, on pain of exactly this sort of regress. Even if some terms come to refer to what they do by being associated with descriptions in thinkers’ minds, not all can. And so there must be an explanation of why some terms come to refer to what they do that does not appeal to terms that must also independently have reference in speakers’ minds.

But Streumer holds that this is not the only worrisome kind of potential regress in the neighborhood. He reasons that we can also secure a regress as follows: if ‘right’ picks out the property of rightness in virtue of the fact that, for example, we would judge that a certain action, A, is right after maximum rational reflection, then whether action A is right must depend on whether the judgment that A is right is such that we would make it after maximum rational reflection. This is supposed to be the input to a regress, because in turn, whether some condition is a condition of maximum rational reflection must in turn depend on whether we would judge it to be after maximum rational reflection.

The problem with this argument is that even views on which ‘right’ picks out the property of rightness in part because of what we would apply it to after maximum rational reflection do not have this consequence. They do, of course, entail that whether the sentence ‘A is right’ is true depends on whether the judgment that A is right is such that we would make it after maximum rational reflection. But it should be agreed on all hands that ‘A is right’ is true just in case the proposition that it expresses is true. The metasemantic view under consideration says that which proposition it expresses depends on what we would apply ‘right’ to after maximum rational reflection, but it does not say that whether that proposition is true depends on this.

Streumer’s regress argument is therefore a bit like arguing that ‘use’ cannot pick out any relation, because something must make it the case that ‘use’ picks out the relation that it does, and it cannot be that speakers would use ‘use’ to ascribe that relation under certain descriptive circumstances because that would entail a kind of guarantee of not being in error about what is a use or not, and it cannot be that speakers would use ‘use’ to ascribe that relation under certain conditions of use, because that appeals to ‘use’ and hence generates a regress. I contend that this conclusion is no less likely to be true than Streumer’s.

So I conclude that not only does Streumer’s argument fail to exhaust any reasonable conception of the logical space for his opponent, it doesn’t even offer forceful general criticisms of the possibilities that it does consider, even when those views are as deeply implausible as I believe this one to be. And this, I think, should not be surprising. If there is any reasonable answer as to what properties normative predicates ascribe, it is hard to see how there could not be a theory of content determination according to which they ascribe those properties. On the contrary, the fact that any theory of content determination fails to explain why normative terms ascribe that property would be evidence against that theory of content determination (cf. Schroeder ms).

4 Non-Cognitivism and the Symmetry Objection

So far I’ve been arguing that Streumer’s arguments against non-reductive realism and reductive realism are both flawed. Indeed, I have been arguing that these arguments not only have false premises, but are deeply unsuited to carrying the kind of dialectical weight which Streumer requires. But let us suppose for the sake of argument that Streumer’s arguments against non-reductive realism and reductive realism are successful, and hence that he has shown that there are no moral properties. In Chapter 6, Streumer argues that non-cognitivism cannot be true, either. I’ll set aside whether Streumer has successfully characterized non-cognitivism in such a way that eliminating it leaves us with the error theory, and just focus on whether his argument against it is successful at showing what it is supposed to show.

Streumer’s argument against non-cognitivism turns on assumption (A):

(A) When two people make conflicting normative judgements, at most one of these judgements is correct. (71)

Streumer further explains what he means by this:

For example, suppose that Fred thinks euthanasia is permissible but Susan thinks it is impermissible. We may then think that Fred’s judgement is correct, or we may think that Susan’s judgement is correct, or we may think that neither judgement is correct. But we will not think that both judgements are correct: we take conflicts between normative judgements to be what I will call asymmetrical. (71)

Set aside, for the moment, that neither principle (A) nor this gloss on it establishes anything like asymmetry, in the normal meaning of that word—and that this is a good thing for Streumer, since by his own account, his own error theory takes a symmetric stance toward all pairs of conflicting normative judgments, holding neither to be correct.7 Whether he has mis-named the problem or not, what Streumer intends to argue is that principle (A), so understood, is incompatible with non-cognitivism.

On the face of it, this is a very surprising claim indeed—and I say this even as someone who has written and published scores of thousands of words about the difficulties that non-cognitivists have in correctly capturing what is going on with inconsistent pairs of normative judgments (Schroeder 2008a, 2008b). What is so surprising about it is that only two principles are required in order to explain principle (A).

The first principle is a disquotation principle for ‘correct’. According to this principle, ‘X’s judgment that P is correct’ entails ‘P’. Given this principle, if we think that Fred’s judgment that euthanasia is permissible is correct, then we must infer that euthanasia is permissible, and if we think that Susan’s judgment that euthanasia is impermissible is correct, then we must infer that euthanasia is impermissible. But by ‘conflicting normative judgments’, Streumer means judgments that are logically incompatible—so in using ‘euthanasia is permissible’ and ‘euthanasia is impermissible’ as an example to illustrate this principle, he is taking for granted the plausible assumption that ‘impermissible’ entails ‘not permissible’. So if we think that Susan’s judgment that euthanasia is impermissible is correct, we must infer that euthanasia is not permissible. And so consequently, if we think both that Fred’s judgment that euthanasia is permissible is correct and that Susan’s judgment that euthanasia is impermissible is correct, then we must infer that euthanasia is permissible and euthanasia is not permissible.

The only other principle that is required, therefore, in order to explain why we will not think that both judgments are correct, is the principle that we do not, at least rationally, believe logical contradictions—since ‘euthanasia is permissible and euthanasia is not permissible’ is a logical contradiction. Since we do not rationally believe contradictions, we will not rationally jointly believe things that jointly commit us to contradictions. And so, as Streumer says, though we may think that Fred’s judgment is correct and though we may think that Susan’s judgment is correct, we will not think that both judgments are correct.

As we’ve seen, it takes only two very simple principles to dismiss Streumer’s charge that non-cognitivism is inconsistent with (A). So Streumer cannot be right unless non-cognitivism is either inconsistent with one of these principles, or inconsistent with their conjunction. So let’s take a look at whether this could be right.

The second principle is that we don’t believe—or it is not rational to believe—outright contradictions. This seems like a pretty obvious principle. Indeed, it is so obvious that if we were somehow able to establish that this principle was inconsistent with non-cognitivism, that would look like a more forceful objection to non-cognitivism. So it would be terribly dialectically weird if, having some secret reason to be confident that this principle is inconsistent with non-cognitivism, Streumer concealed it to give an argument about principle (A), rather than simply pointing out that non-cognitivism is inconsistent with the claim that it is irrational to believe contradictions. So I infer that Streumer has no reasons for thinking that non-cognitivism is inconsistent with this second principle.

A much more plausible construal of his argument is that Streumer thinks that non-cognitivism is inconsistent with the disquotational principle for ‘correct’. Indeed, this is what he goes on to gesture at on the next page. According to Streumer, claim (L) is not true:

(L) When two people have conflicting likes or dislikes, at most one of these likes or dislikes is correct.

The fact that (A) is true but (L) is not, Streumer contends, is some evidence against non-cognitivism. And it is natural to think this, because it is natural to construe non-cognitivism, at a first pass, as saying that normative judgments are just a matter of liking or disliking something (I’ll come back to this characterization in a moment—it is not in fact the characterization that Streumer actually gives of non-cognitivism in the book, and for good reason, given his argumentative aims).

More to the point, we might think that the contrast between principles (A) and (L) gives us a clue as to why Streumer might think that non-cognitivism is incompatible with the disquotational principle for correctness. The naïve version of this thought would go like this: since principle (L) is not true, there is no corresponding disquotational principle for correctness. But since non-cognitivists are committed to thinking that normative judgments are relevantly similar to likes or dislikes, non-cognitivists must be committed to thinking that there is no true disquotational principle for correctness, either.

All of this is speculative—Streumer doesn’t actually tell us very clearly what is wrong with the disquotational principle, despite its naturalness and almost immediate link with accounting for the point of principle (A) as he describes it. But in any case, we can see directly that it is a mistake to assume that non-cognitivists will not be able to explain the relevant difference between principle (A) and principle (L). The general form of an answer to what distinguishes these two principles is simple: normative judgments are beliefs, but likes and dislikes are not—or at any rate, not all—beliefs.

In general, different kinds of attitudes can be correct or incorrect. Just as it can be correct to believe that Catelyn won’t fall, it can be correct to hope that Catelyn won’t fall. But the conditions under which each of these are correct are different. It is correct to believe that Catelyn won’t fall only if she won’t fall, but it can be correct to hope that she won’t fall even if she does turn out to fall. It is correct to hope that she won’t not because she won’t, but because it would be unfortunate, if she does. So there is no general disquotational principle for ‘correct’ which says that ‘X’s φ that P is correct’ entails that P. Though ‘X’s belief that P’ entails that P, ‘X’s hope that P is correct’ does not entail that P.

Given this, it is no wonder that attitudes that are not cases of belief—attitudes like liking or disliking something—will not obey any disquotational principle for correctness. Non-cognitivists worth their salt should say that not all likings are cases of belief. Indeed, they need to say this for many other reasons—for example, in order to explain why we do not call likings ‘true’ or ‘false’, in order to explain why likings are not expressible by complex sentences, and so on.8 The fact that non-cognitivists say that normative beliefs are in some ways like likings—for example, in their motivational structure, or in their lack of representational content about the world—undermines in no way their claim that not all likings are beliefs.

In general, the proper non-cognitivist perspective on the relationship between normative judgments and ordinary descriptive beliefs about the world is often deeply misunderstood. It is commonly assumed—even by many non-cognitivists themselves—that the relationship is that normative and descriptive judgments are simply very different kinds of things—things that might in principle have very different properties, including, as Streumer believes, properties with respect to how correctness can be predicated of them. But this is a mistake. Non-cognitivists should not say that normative and descriptive belief are deeply different kinds of thing, but rather that they are two special cases of the same kind of thing: belief.9

On this picture, although ordinary cognitivists have been right that when an agent has an ordinary descriptive belief—for example, that grass is green—they stand in some psychological relationship to something that determines the set of worlds in which grass is green—and although they are right that belief consists in a psychological relationship to a proposition, they have mis-identified which psychological relationship belief is, and they have mis-identified what sort of thing propositions are. The mistake that ordinary cognitivists have made, according to the non-cognitivists, is precisely analogous to noting that the state of being about to go to Paris consists in a relationship of being about to do something, noting that you are about to go to Paris just in case you are about to go someplace, and the place where you are about to go is Paris, and inferred that the relationship of being about to do something consists in the relation of being about to go somewhere, and that actions are places.

Of course this reasoning is absurd, and if non-cognitivists are right, then the analogous reasoning about belief and propositions is equally absurd. According to the picture of non-cognitivists, belief is a general relationship toward propositions, just as being about to is a general relationship to actions. But just as some actions are the act of going someplace, some propositions consist in relations to an intrinsic representation that determines a set of worlds. So for the non-cognitivist, normative beliefs are not something totally different from ordinary descriptive beliefs; they are just the more general case—just as being about to brush your teeth is not a totally different kind of thing from being about to go to Paris—it is just being about to do a different thing, a thing that is not a matter of going to a place.10

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Of course, it may turn out that non-cognitivists’ picture is false. If so, their view is false. But it would not do to argue against their view without understanding what it says. The non-cognitivist who has fully thought through their own picture should not get nervous when Streumer points out that the analogue of principle (A) holds for ordinary descriptive beliefs about the world, but principle (L) is not true. Rather than constituting evidence that they are in trouble, this constitutes evidence that they are on the right track—for it is evidence that the disquotational principle for correctness applies to beliefs, and according to the non-cognitivist, normative judgments are beliefs.

5 The Error Theory

After arguing for the error theory, Streumer attempts to defend it. There are many general puzzles about how to best formulate the error theory, and Streumer’s defense is constrained by the structure of his argument, which is an argument against the existence of normative properties. This constrains his development of his positive account of the error theory, and leads to some particularly distinctive puzzles in his case.11

The central puzzle is why Streumer counts as denying the existence of normative properties at all, rather than affirming their existence and claiming that they are all identical with the property of being a round square. This is closely connected to the issue of whether Streumer accepts the principle of existence from Section 2, because Streumer’s error theory does entail that necessarily, something is wrong just in case it is a round square. So if ‘round square’ expresses a property, then by principle (N&), it is the same as the property of being wrong. Yet Streumer describes his error theory as the view that there are no moral properties—not as the view that the only moral property is the property of being a round square.

On the one hand, I think that I know why Streumer wants to describe his view in this way—it sounds more like a metaethical error theory and less like a first-order theory or a peculiar version of reductive realism, for example. Another problem is that it is incompatible with principle (D) (for difference):

(D) At least one normative property is not identical to the property of being a round square.

I contend that principle (D) is more compelling than any of the three principles—(S), (G), and (A)—which underwrite Streumer’s arguments against non-reductive realism, reductive realism, and non-cognitivism, respectively. And if this is right, then that would be another problematic feature if it turned out that this was the right way to describe Streumer’s form of error theory. So I guess I understand why he does not want to describe his form of the error theory in this way.

What is less clear to me, is why this is not a good description of his view. After all, Streumer claims that many sentences containing normative words are true. For example, he thinks that it is true that stealing is not wrong. The view that he defends holds that it is true that Hitler was not evil, and true that it is not a good idea to look both ways before you cross the street. It also entails that it is true that there is no reason for him to believe the error theory. Most of these things sound bad, though of course the view also entails that it is true that stealing is not permissible, that it is true that Hitler was not admirable, and true that it is not a bad idea to look both ways before you cross the street.

The view on which normative predicates ascribe the null-intension property makes excellent sense of all of these claims. But the view on which there are no normative properties at all makes them extremely puzzling. Take, for example, the English adjective ‘mugenheh’, which I just made up Let’s just stipulate that it expresses the propery of being mugenheh. Since I haven’t decided what it means, yet, there is no property that it ascribes. And that, of course, makes sense of why nothing counts as ‘mugenheh’. But it doesn’t make sense of why nothing is mugenheh, because it is no more clear what it would take to not be mugenheh than it is what it would take to be mugenheh. This is because the logical form of the sentence ‘x is mugenheh’ is mugenheh(x), and the logical form of the sentence ‘x is not mugenheh’ is ~mugenheh(x). So since there is no property of being mugenheh, the logical form of the first sentence is ???(x) and the logical form of the second sentence is ~???(x). If you can spot which of these is more likely to be true based on your understanding of first-order logic, please help me out.

Streumer assumes, in contrast, without argument so far as I can tell and without any explanation of what he has in mind, that since the properties ascribed by normative terms do not exist, every negation of a simple subject-predicate sentence involving a normative predicate is true. The most natural conjecture as to what he has in mind, is that he thinks that the logical form of simple subject-predicate sentences like ‘x is wrong’ is ‘$P:P is the property of wrongness & instantiates(x,P)’. If there is no property of wrongness, then this logical form will be false and its negation will therefore be straightforwardly true. So one might conjecture that Streumer is thinking that ordinary, apparently simple, predication in natural language in fact needs to be understood in terms of higher-order quantification over properties.

One clue that this is what Streumer is thinking is that he says that

A belief ascribes a property if and only if it conceptually entails that something has this property. (107)

If my conjecture about how Streumer is thinking about the logical form of simple subject-predicate sentences with normative predicates is correct, then this claim is true in a very straightforward way. Beliefs that ascribe properties are just beliefs whose logical forms say something quite explicitly about something having (instantiating) a property. In contrast, if the more obvious logical form for ‘x is wrong’ is true, this logical form does not mention wrongness—it just predicates wrongness. So it does not entail anything at all about the existence or instantiation of properties, absent appeal to some general principles from higher-order logic.

Indeed, what I suspect is actually true is that there are no claims at all in natural language that ascribe properties in the sense that Streumer stipulates in this passage. ‘Stealing is wrong’ does not conceptually entail that something has the property of being wrong, because it does not entail that there is a property of being wrong—it only entails that if there is a property of being wrong, then something has it. But this is not something special about ‘wrong’; it is true of every other predicate. ‘Grass is green’ is true, in part, because there is a property of being green, but it does not say that there is such a property.

Streumer tells me (in correspondence) that my conjecture is not correct, and that his view is compatible with the thesis that sentences like ‘grass is green’ and ‘murder is wrong’ ascribe properties without saying that there are properties. But this puts us back to square one in trying to understand why it follows from the fact that the property ascribed by some predicate R does not exist, that it is true that nothing is R. It leaves open, of course, the possibility that property talk is just a sort of epiphenomenon on an underlying intensional semantics on which every set of possible individuals counts as a property—except for the empty set. Since having the empty set for its intension is the only way of ascribing a property that does not exist, on this view, it does follow that if R expresses a property that does not exist, then it is true that nothing is R. So this alternative interpretation makes sense of much of what Streumer says in the book.

But on this alternative interpretation, Streumer’s rejection of the principle of existence for properties is trivial. This means that it can no longer be availed to, in order to explain why properties can play the role of making sense of why some pairs of possible individuals count as having more in common than other pairs of possible individuals—because no pairs of possible individuals each belong to the empty set, anyway. So this brings back my argument from the role of properties in telling us what things have in common in its full force.

Moreover, this interpretation makes even more puzzling how the argument for the error theory is supposed to go. If properties are something substantive in virtue of which claims get to be true or false, then I can see how an argument that there is no property of wrongness could lead us to conclude that ‘stealing is wrong’ is in error. But if there is no more to talk about properties than claims about what is possible and what is not, then I don’t see how we can argue directly that there are no moral properties or even that there are no moral descriptive properties, without arguing directly about what is wrong. But that, of course, is how I’ve suggested elsewhere that we should be arguing for the error theory, anyway (see Schroeder 2007: Ch. 7; Perl and Schroeder, forthcoming).

6 Unwilling Disbelief

The point that I have been endeavoring to make, here, is that the problem that Streumer’s unbelievability thesis is intended to solve is a non-problem. There can’t be a deep puzzle about why we don’t all come to believe Streumer’s conclusion when presented with his arguments, because the arguments are simply not that good. Drawing out this point has required me to focus on the many weaknesses that I see in the arguments, especially when interpreted as aspiring to this very high standard.

This can sound harsh, out of context. But it is worth reminding ourselves of just how high this standard is. Normally, when we see an author present an argument for a philosophical conclusion, we do not expect them to also offer a debunking explanation for why not everyone accepts their conclusion. And it is no slight to Streumer, I think, to note that far more forceful arguments have been given for many other conclusions that have not convinced everyone but for which we need no special debunking explanation of why not everyone is convinced. To say that Streumer’s argument is simply not this good is not, I think, to say anything surprising, when we reflect on the number and diversity of views that it is intended to rule out or on the complexity of the theoretical resources that it is required to call upon. The argument may still tell us much about the attractions of the error theory—and it does—and help us to understand a new and resourceful form that the error theory may take—which again, it does.

Of course, things may look different from the inside. Streumer, obviously, by his own testimony does find his arguments convincing when he takes them one by one. And again by his own testimony, he struggles to accept the conclusion that they drive him to. This, indeed, may deserve some explanation. But my suggestion is that we should not confuse Streumer’s self-therapy with our own resistance to his conclusion.12

References

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1

The original such argument comes from Kim (1984), but one of its key steps is anticipated in Blackburn (1973). Streumer’s version of the argument owes the most to Jackson (1998). Another prominent recent variant is Brown (2011).

2

Thanks to correspondence with Streumer for clarification of this point.

3

Page 11, note 6. Note that ‘N*’ is my name for this revised principle; Streumer doesn’t name it.

4

I first offered a version of the following argument as a reductio of Frank Jackson’s (1998) supervenience argument in an unpublished paper in 2002. Billy Dunaway (2015) has published a more sophisticated version of the argument, from which he draws a slightly different conclusion. Streumer comments on Dunaway’s argument on page 32, in note 1 to chapter three.

5

See Horgan and Timmons (1990), (1992), (1996a), (1996b), (2000), and (2009).

6

In essence, these are Streumer’s own reasons for rejecting the third possibility, and we differ only over whether it is a possibility worth taking seriously. And of course, his own reasons for taking it seriously are dialectical.

7

This is slightly complicated, because Streumer does not think that negative judgments like ‘stealing is not wrong’ are normative at all, but he does defend the view that ‘euthanasia is permissible’ and ‘euthanasia is impermissible’ are conflicting normative judgments, rejecting the claim that ‘impermissible’ means simply ‘not permissible’.

8

Compare especially Dreier (1996) and the reply in Gibbard (2003).

9

Horgan and Timmons (2004), Schroeder (2013, 2015).

10

The following diagram is from Schroeder (2013).

11

For comparison, many other defenses of the error theory do not work by arguing against the existence of normative properties, but directly argue that nothing is wrong, or that moral discourse is based on a mistaken presupposition, from which it may or may not follow that there are no moral properties. Compare Joyce (2001), Olson (2014), Finlay (2008), and Perl and Schroeder (forthcoming). It is therefore consistent with some of these other ways of formulating the error theory that moral properties do exist.

12

Special thanks to Diego Machuca, Nick Laskowski, and particularly to Bart Streumer.

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