Why formal objections to the error theory fail


 Many philosophers argue that the error theory should be rejected because it is incompatible with standard deontic logic and semantics. We argue that such formal objections to the theory fail. Our discussion has two upshots. First, it increases the dialectical weight that must be borne by objections to the error theory that target its content rather than its form. Second, it shows that standard deontic logic and semantics should be revised.


Introduction
Many philosophers argue that the error theory should be rejected because it is incompatible with standard deontic logic and semantics. We argue that such formal objections to the theory fail. Our discussion has two upshots. First, it increases the dialectical weight that must be borne by objections to the error theory that target its content rather than its form. Second, it shows that standard deontic logic and semantics should be revised.

The objection
There are different versions of the error theory. We will initially focus on the standard version, which says that normative judgements are beliefs that ascribe normative properties, but that these properties do not exist and that all normative judgements are therefore false. There is also a presuppositional version that we will discuss in §3. Everything we will say about the normative error theory carries over to the moral error theory. 1 The objection that we will discuss relies on two assumptions that are built into standard deontic logic and semantics. 2 The first is the law of excluded middle, according to which (L) For every proposition p, either p or not p.
The second is the duality of permissibility and impermissibility, according to which (D) Every action is either permissible or impermissible.
(D) follows from (L) if 'im-F' means 'not F', but can be retained as a separate assumption by those who reject (L). Moreover, as Perl and Schroeder note, 'duality is not just a feature of moral uses of possibility and necessity modals; it is a feature that is encoded into our best semantic theories about the meanings of possibility and necessity, in general ' (2019: 1458). 3 To bring out the objection to the error theory that these assumptions give rise to, consider the following sentence: (1) Lying is impermissible.
According to the error theory, (1) ascribes the property of being impermissible to lying, but this property does not exist and (1) is therefore is false. If we assume (L), the falsity of (1) entails that (1) Lying is not impermissible.
But (2) itself ascribes a normative property: the property of being permissible! This means that if we assume (L) and (D), the error theory says that (2) is both true and false. And it says the same about (1), since if we assume (L) and (D), the falsity of (2) similarly entails (1). These seemingly innocuous assumptions therefore lead to a reductio of the error theory. 4

Existing responses
Error theorists could block the objection by endorsing the presuppositional version of the theory, which says that normative judgements are beliefs that presuppose the existence of normative properties. Since presupposition projects through negation, this version of the theory entails that (1) and (1) are both defective in the same way. Presuppositional error theorists can therefore reject (L): they can say that (1) and (1) are both neither true nor false (Kalf 2018). 5 But this comes with two costs. The first is that rejecting (L) is controversial. The second is that rejecting (L) is especially problematic when it comes to (1) and (1). Compare the following two sentences: (3) Barack Obama has supernatural powers.
Are (3) and (3) both defective in the same way? We doubt it: since Barack Obama does not have supernatural powers, there is a good case for saying that (3) is false and (3) is true. And just as supernatural powers do not exist, the error theory says that normative properties do not exist. This means that if the error theory is true, (1) and (1) are analogous to (3) and (3). There is therefore a good case for saying that error theorists should take (1) to be false and (1) to be true.
Note that there is an important difference between (1) and (3) and the following standard example of a sentence with a false presupposition: (4) The present king of France is bald.
Since there is no present king of France, (4) ascribes an existing property to a non-existent object. This makes it plausible that (4) and its negation are both defective in the same way. By contrast, (3) ascribes a non-existent property to an existing object. Since this existing object does not have this property, there is a good case for saying that (3) is false and (3) is true. And if the error theory is true, the same applies to (1) and (1). 6 These considerations against the presuppositional error theory may not be decisive. 7 But we think they make it worth exploring whether error theorists can instead block the objection without rejecting (L). Some standard error theorists have tried to do this by denying that the sentence (1) Lying is not impermissible entails that (2) Lying is permissible.
For whereas (2) ascribes the property of being permissible to lying, they say, (1) merely denies that lying has the property of being impermissible. And they similarly deny that the claim that (2) Lying is not permissible entails that (1) Lying is impermissible.
For whereas (1) ascribes the property of being impermissible to lying, they say, (2) merely denies that lying has the property of being permissible. If so, the standard error theory says that (1) and (2) are false and (1) and (2) are true. This blocks the objection by rejecting (D) rather than (L) (Pigden 2007: 450-54, Olson 2014: 11-15, Streumer 2017 Error theorists who block the objection in this way recognize that when we utter (1) we convey that we accept (2), and that when we utter (2) we convey that we accept (1). But they think this is because (1) conversationally implicates (2) and (2) conversationally implicates (1). These sentences implicate this, they think, because we normally assume that every action is either permissible or impermissible. We can cancel these implicatures by denying (D): in other words, by saying that lying is neither permissible nor impermissible.
But this way to block the objection may also seem to come with a cost. As we said, (D) follows from (L) if 'im-F' means 'not F'. Error theorists who block the objection in this way must therefore deny that 'im-F' means 'not F'. Is this plausible?

The purity analogy
We think it is. To see why, consider the following analogy. Richard Joyce notes that some communities used to engage in discourse about spiritual purity and impurity, which implicates a kind of uncleanliness or pollution that may reside in objects, may pass to humans through contact, may be transmitted to others like a contagion, and which may be cancelled through certain ritual activities, usually involving washing. (Joyce 2001: 1) 9 Such discourse classifies certain objects as spiritually pure and other objects as spiritually impure. Consider the following sentence: (1*) This house is spiritually impure.
According to what we can call the purity error theory, (1*) expresses a belief that ascribes a non-existent property and is therefore false. If we assume (L), the falsity of (1*) entails that (1*) This house is not spiritually impure.
Suppose that those who make purity judgements take spiritual purity and impurity to be duals: that is, suppose they think that (D*) Every object is either spiritually pure or spiritually impure. Like (D), (D*) follows from (L) if 'im-F' means 'not F'. If those who make purity judgements endorse (D*), they will take (1*) to entail that does not instead consist in the absence of permissibility (Streumer 2017: 125). Moreover, some uses of 'permission' in ethics transparently do not denote the absence of impermissibility: see, for example, Hurka and Shubert 2012. 9 Joyce focuses on one specific instance of such discourse (involving the word 'tapu', the basis for the English word 'taboo'), but there are plenty of similar examples.
But (2*) ascribes the property of being spiritually pure! This means that if we assume (L) and (D*), the purity error theory says that (2*) is both true and false. And it says the same about (1*), since if we assume (L) and (D*), the falsity of (2*) similarly entails (1*). Those who make purity judgements may take this to be a reductio of the purity error theory. But it clearly is not! Something has gone wrong.

What the purity analogy shows
We want to be clear about what we take this analogy to show. We do not take it to show that (D) is false. Instead, we take it to show two things. The first is that any formal objection to the normative error theory will fail, since it will overgeneralize to the purity error theory. The purity error theory and the normative error theory have the same form: both say that x judgements are beliefs that ascribe x properties, but that these properties do not exist and that all x judgements are therefore false. These theories only differ in their content: one concerns spiritual purity and impurity, the other concerns permissibility and impermissibility. Since the purity error theory is very plausibly true, it cannot be false in virtue of its form. This means that the normative error theory cannot be false in virtue of its form either! The second thing we take the analogy to show is that (D) is not an innocuous formal assumption. (D) may look like a formal assumption because it does not take a stand on the permissibility or impermissibility of any particular action and is therefore neutral between different first-order normative views. But (D*) may similarly look like a formal assumption to those who make purity judgements, since it similarly does not take a stand on the spiritual purity or impurity of any particular object. And just as (D*) entails that objects have purity properties and is therefore incompatible with the purity error theory, (D) entails that actions have normative properties and is therefore incompatible with the normative error theory. We think that (D) is a substantive normative claim rather than a formal assumption, though an extremely general one that is compatible with any first-order normative view. If so, this also explains why the error theory is incompatible with (D): because the theory entails that all substantive normative claims are false.
Of course, it is psychologically much easier for us to reject (D*) than to reject (D). But this may simply be because we are unlikely to reject (D) unless we believe the normative error theory. Most error theorists recognize that the theory is difficult for us to believe (Olson 2014: 143-44) and one of us has even argued that a general normative error theory is impossible to believe (Streumer 2017). The purity error theory is much easier for us to believe, which makes it much easier for us to reject (D*).
why formal objections to the error theory fail | 5 Opponents of the error theory may reply that since 'im-F' means 'not F', error theorists who endorse (L) are committed to endorsing (D). We think the purity analogy undermines this reply, since we take it to show that 'spiritually impure' does not merely mean 'not spiritually pure' and that 'im-F' therefore does not merely mean 'not F'. But we also have three others ways to bolster our case. One is to consider other examples in which 'im-F' is not equivalent to 'not F': for instance, 'x is immortal' is clearly not equivalent to 'x is not mortal', since otherwise all inanimate things would be immortal. More generally, if we accepted (L) and thought that 'x is immortal' is equivalent to 'x is not mortal', we could derive a deeply implausible analogue of (D): that everything is either mortal or immortal! A second way to show that 'im-F' does not merely mean 'not F' is to consider examples in which we distinguish 'im-F' from 'non-F': for instance, whereas 'non-moral' merely means 'not moral', 'immoral' clearly means more than this: it means something like 'contrary to morality' (compare 'Genocide is immoral' and 'Genocide is non-moral'). In the same way, 'impermissible' may mean something like 'contrary to permissibility'.
A third way to show that 'im-F' does not merely mean 'not F' is to consider category mistakes. Take the sentence (5) The number 157 is permissible, where this does not mean that a certain action (such as answering '157' in response to a certain question) is permissible, but that the number 157 itself is permissible. We think there is a good case for saying that this sentence is false, since it ascribes a property to the number 157 that this number does not have. 10 If we assume (L), the falsity of (5) entails that (5) The number 157 is not permissible.
But this clearly does not entail that (6) The number 157 is impermissible.
Of course, ascribing permissibility or impermissibility to an action is not a category mistake. But if we are right that (5) is true and (6) is false, category mistakes do show that 'im-F' does not merely mean 'not F'. 11 Opponents of the error theory could also reply that the duality of modals is encoded into our best semantic theories of necessity and possibility irrespectively of whether 'im-F' means 'not F': standard deontic semantics takes obligation and permission to be deontic necessity and possibility, which makes obligation and permission inherit this duality. The problem with this reply, however, is that we can always define bogus modalities: for example, we can define spiritual necessity and spiritual possibility by defining the spiritually possible worlds in terms of the logically possible worlds and some set of spiritual laws. 12 If it is a general feature of necessity and possibility that they are duals, and if this feature is inherited by more specific modals, then it will be inherited by spiritual necessity and possibility. But we should clearly be error theorists about spiritual necessity and possibility. And if we should reject duality in the case of spiritual modality, we can also reject it in the case of deontic modality.
Moreover, error theories about spiritual purity and spiritual modality are not isolated cases. We can make the same point with other bogus modalities and other erroneous discourses. This stacks the deck against opponents who are tempted to bite the bullet and insist that (D) and (D*) are both innocuous formal assumptions. We think this is an implausible response to the purity analogy, since it commits these opponents to acribing purity properties. But more importantly, there is no end to the number of bogus modalities that can be defined using the recipe we provided above. For each bogus modality, these opponents will have to endorse a claim that is analogous to (D*). That is an unsavoury quantity of bullets to bite.

Conclusion
Nothing we have said shows that the error theory is true. It just shows that a common objection to the error theory fails and that other formal objections to the theory will fail as well. Does that matter? Yes. For one thing, it increases the dialectical weight that must be borne by objections to the error theory that target its content rather than its form. For another, it suggests that standard deontic logic and semantics should be revised to make them compatible with the error theory, by dropping either (L) or (D). As we said, it is possible to drop (L), but we think the best option is to drop (D). 13