Moral Anti-Realism Sequence #3: Against Irreducible Normativity

This is the third post in my sequence on moral anti-realism; it works well as a standalone piece. (See 1 and 2 for my previous posts.)


  • After briefly explaining the concept of irreducible normativity, I delve into a three-tiered argument against the moral realism versions based on it.

  • First, I summarize evolutionary debunking arguments that show that our intuitions about normative bedrock concepts (especially morality) cannot be trusted. Those arguments aim to establish that regardless of whether there are irreducible normative truths, our intuitions about them evolved to track something else. This is problematic both because it means that the search for moral progress is likely doomed and because it calls into question the reasons for taking irreducible normativity seriously in the first place.

  • Secondly, I try to change the perception of normative anti-realism as a self-defeating framework. Through careful consideration of the sources of meaning in our lives, I argue that those sources are compatible with normative anti-realism (at least for most of us). I provide a sketch of what it could look like for anti-realists to reason about ethics, pointing out some ways in which self-determined moral goals can feel more meaningful than externally-imposed ones.

  • Thirdly, I note that the way irreducible normativity is commonly motivated stands in tension with how words obtain their meaning. I then delve into various ways how one could try to make irreducible normativity work as a concept. Some options are too disconnected from what we want to do, and others are too close to it (in the sense that, as far as practical purposes are concerned, they overlap with how anti-realists would also approach normativity). I note that the most attractive way to think about irreducible normativity closely resembles normative naturalism. Finally, I conclude that if the arguments in this post are sound, there’s a tension between moral realism worthy of the name and the notion of open-ended normative uncertainty.

What is irreducible normativity?

In this article, I will discuss examples from morality as an instance of irreducible normativity. As I will explain in the very last section, I think analogous arguments also apply against other forms of normative realism.[1]

Irreducible normativity is the idea that there are facts about what we have reason to do (or believe) that go beyond what’s in line with our subjective evaluation criteria (e.g., our desires, fundamental intuitions, ideals, etc.). These facts would capture that some things qualify as “right” or “good” according to normative standards that apply independently of what we already endorse. Derek Parfit expressed it as follows (Parfit, 2011a):

Like some other fundamental concepts, such as those involved in our thoughts about time, consciousness, and possibility, the concept of a reason is indefinable in the sense that it cannot be helpfully explained merely by using words. We must explain such concepts in a different way, by getting people to think thoughts that use these concepts. One example is the thought that we always have a reason to want to avoid being in agony.

Parfit holds that “reason” is a bedrock concept (Chalmers, 2011)—a concept that is “irreducible” in the sense that we cannot helpfully define it with other words. We can contrast this with the view that “reason” is a “reducible[2] concept. On the reducible interpretation, “having a reason to do X” might mean, for example, something like:

X is a principle we’d endorse if we had all the relevant information and ample time to reflect on it.

Anti-realists about normativity, who interpret all talk about reasons in the reducible way, can point to factors like the following for why “we always have a reason to want to avoid being in agony” is a compelling principle:

  • indifference towards agony is (almost) non-existent among humans,

  • it’s motivationally incongruent[3]

  • empathy toward the experience of moments in tremendous distress compels us to advocate in favor of avoiding agony

Of course, those factors are all subjective. They may not make the principle compelling to absolutely everyone. Certainly, we can imagine alien minds who think differently about agony avoidance. Normative anti-realists have to bite this bullet.

By contrast, Parfit’s stance is that such reductionist accounts are not enough. According to Parfit, “having a reason to do something” captures something more than just the above psychological factors. If “reason” could be defined in terms of psychological factors, the same reasons may not apply to everyone—and some people will have bizarre “reasons.” After all, some individuals could then claim that they have unusual psychologies, senses of morality, or life goals. Irreducible normativity has an aura of particular significance precisely because there are no specifiable requirements needed to buy into it.

On the other hand, that’s also why the concept appears suspect. The fact that we cannot explain what we mean by it should give us pause—perhaps our intuitions are failing to point out something meaningful?

The case against irreducible normativity

The disagreement about irreducible normativity is neither empirical nor about logic. As I argued in my previous post, I think it’s a disagreement about how to do philosophy, specifically about whether or not to incorporate normative bedrock concepts into one’s philosophical repertoire. In the upcoming sections, I will argue that irreducible normativity is philosophically costly (section 1), that we can reason satisfactorily without it (section 2), and that how it is commonly motivated and justified begs the question on whether the concept is even meaningful (section 3). Overall, I will conclude that—except for a specific interpretation that I will address in future posts—irreducible normativity is not worth wanting.

1. Evolutionary debunking arguments

Babies are not objectively cute, hourglass or V-shaped human bodies are not objectively sexy, and honey is not objectively sweet. Those things are cute, sexy, or sweet to us (or “many of us”). Just like our intuitions about what’s cute, sexy, or sweet evolved because viewing the world in those ways proved evolutionarily beneficial in the ancestral environment, our intuitions about morality are also a biological adaptation. The intuition that morality is objective (“speaker-independent”) is a part of this adaptation. The philosopher Michael Ruse (2010) put it as follows:

To be blunt, my Darwinism says that substantive morality is a kind of illusion, put in place by our genes, in order to make us good social cooperators. I would add that the reason why the illusion is such a successful adaptation is that not only do we believe in substantive morality, but we also believe that substantive morality does have an objective foundation. An important part of the phenomenological experience of substantive ethics is not just that we feel that we ought to do the right and proper thing, but that we feel that we ought to do the right and the proper thing because it truly is the right and proper thing.

I don’t fully endorse Ruse’s terminology. As I argued in my previous post, moral anti-realism doesn’t mean that morality isn’t “substantive.” However, I think Ruse is correct about the general point: Our intuitions in favor of moral realism evolved for reasons that have no connection to whether the position is true. That should make us skeptical of those intuitions.

The same style of debunking argument can also be leveled against the content of our moral intuitions, not just whether they reflect an irreducible, speaker-independent reality. In her paper “A Darwinian dilemma for realist theories of value,” Sharon Street (2006) laid out a compelling argument, giving realists about irreducible normativity two hard-to-accept options. The first option is to assume that there’s no connection between our moral intuitions (“evaluative attitudes”) and irreducibly normative moral facts. Accordingly, if our moral intuitions were correct, it would be by sheer luck. The second option is to assume that there is a connection. Street argues that this second option would look implausible on scientific grounds because natural selection favored intuitions that help with survival and reproductive success, not ones that track irreducible normative truths.[4]

For a more rigorous and comprehensive version of the argument, I recommend Street’s paper.

Normative realists might argue that our ability to track irreducible normative truths could have been evolutionarily adaptive since this response would circumvent Street’s dilemma. However, nothing about the way irreducible normative truths are usually motivated suggests that they work this way. If it were evolutionarily adaptive to grasp normative truths, these truths would have to directly interact with our cognitive machinery in a way we—presumably—could describe in physical terms. If we can describe the effect those normative truths have on our cognitive machinery, we’d have found a way to describe them in non-normative terminology. On most accounts, this would no longer make them irreducible truths, but naturalist ones.

It’s important to note here that evolutionary debunking arguments only apply against versions of moral realism based on irreducible normativity (“moral non-naturalism”). There are also so-called naturalist versions of moral realism, according to which we can rephrase moral terms like “goodness” or “right” with non-moral terminology. For instance, a naturalist moral realist might say that goodness consists of preference satisfaction or positively valenced states of consciousness. We can explain perfectly well (especially in the personal case) why it might have been evolutionarily adaptive to value those things. Accordingly, naturalist accounts of moral realism are not threatened by the evolutionary debunking arguments.[5] (As I will discuss in the section “Summary, conclusion and open questions,” the distinction between naturalism and non-naturalism can be fuzzy, which makes it difficult to completely shut the door on irreducible normativity.)

Overall, I don’t consider evolutionary debunking arguments to be decisive. Some proponents of irreducible normativity also have interesting replies to them.[6] However, I consider the debunking arguments forceful enough to show that there’s something very strange with the concept of irreducible normativity, and that in order to potentially adopt the concept into one’s philosophical repertoire, one needs to do a great deal of explaining.

2. Normative anti-realism is existentially satisfying (at least it can be)

Many of us want to believe what’s right, pursue our goals rationally, and act morally towards others. Proponents of irreducible normativity may think that if we give up on the idea that right, rational and moral are bedrock concepts, we are accepting that all standards are arbitrary.

In my previous post, I tried to challenge this perception. I argued that giving up on irreducible normativity is perfectly compatible with retaining standards about how to reason, act, or treat others. Anti-realists don’t deny that there is structure to the space of normative considerations—they disagree with the realists only on whether there’s a single true interpretation.

Realists about normativity may interject at this point, saying that it’s bizarre to think that our most basic beliefs are interpretations only, that there’s no fact of the matter about whether and how they are justified.

I want to challenge this sentiment. I think it only seems bizarre because the standards we attach to the expression “no fact of the matter” are unreasonably strong. It’s correct that anti-realism means that none of our beliefs are justified in the realist sense of justification. The same goes for our belief in normative anti-realism itself. According to the realist sense of justification, anti-realism is indeed self-defeating.[7]

However, the entire discussion is about whether the realist way of justification makes any sense in the first place—it would beg the question to postulate that it does. Giving up on realism doesn’t directly change anything about the principles we use to ground our reasoning.[8] For instance, as anti-realists, we are likely to continue to endorse the following principles (among others):

  • Adopt philosophical views that are in reflective equilibrium with the rest of our beliefs.

  • Aspire to hold opinions that follow logically from premises we endorse.

  • Aspire to believe something if we observed it directly or have it from a trustworthy source.

  • Adopt normative principles that strike us as self-evident, or ones that are most in line with our most fundamental normative intuitions (e.g., the preference that we care about others and prefer there to be less involuntary suffering in the world).

Going by those standards of reflectively endorsed belief-formation, anti-realism is not self-defeating at all. Those principles themselves may lack further justification, but that doesn’t have to concern us: they are evaluation criteria. They don’t need further justification because they are the axioms we ground our reasoning on. If these principles strike us as self-evident, that’s all the justification we can get.

Normative realists might say they only want to believe things that are really justified, justified in the sense of normative realism. However, humans already believed things long before we formed an understanding of the difference between realism and anti-realism. Our folk concept about what it means for a belief to be justified is neither (explicitly) realist, nor (explicitly) anti-realist. I concede that many people might say that whether or not a belief is justified seems like a matter of irreducible normativity. Still, that doesn’t settle the question. Our intuitions in favor of realism could be misguided. There’s nothing inconsistent with conceptualizing our realist intuitions as wrong.[9]

I don’t mean to deny that people can commit themselves to the stance that their everyday motivations for believing things are tied inseparably to the truth or falsity of the controversial philosophical theory “realism about irreducible normativity.” I consider this to be a special case rather than the norm, and I will address it in upcoming posts.[10]

For most people, at least, I claim that they already believe all the ingredients needed to reason satisfactorily about normativity, from an anti-realist perspective. I will now sketch what this look like:

Many readers of this post will be familiar with Peter Singer’s famous moral arguments, such as the drowning child argument (Singer, 1972) and the argument from species overlap (Singer, 1975). Singer may have presented these arguments in moral language (e.g., he talked about “moral obligations” to help those in need), but these arguments work independently of any particular metaethical position (Singer, 1973). The drowning child argument appeals to the sentiment that we may want to be the sort of person who saves a child from drowning and connects that sentiment to also wanting to help children overseas through donations. The argument from species overlap consists of appeals to two sentiments: that we don’t want to be the sort of person who mistreats any sentient members of our species, and that we don’t want to adhere to decision principles of discrimination, i.e., treating someone differently solely because of their group membership. The argument then illustrates that for any dimension we may consider to be of significance (e.g., sentience, intelligence, ability to speak, etc.), there is considerable overlap among species.

Singer’s moral arguments are not outliers. When we reframe normative-ethical arguments from an anti-realist perspective, their motivational force doesn’t change. But there’s something about the “place” that normative considerations take up in a person’s thought process that changes.

In his essay “A Critique of Utilitarianism,” Bernard Williams (Williams, 1973) argued that there is something wrong with the utilitarian thought process. If someone believes utilitarianism is the right moral theory, there’s an important sense in which there is no room for the person to choose their life projects. According to utilitarianism, what people ought to spend their time on depends not on what they care about but also on how they can use their abilities to do the most good. What people most want to do only factors into the equation in the form of motivational constraints, constraints about which self-concepts or ambitious career paths would be long-term sustainable. Williams argues that this utilitarian thought process alienates people from their actions since it makes it no longer the case that actions flow from the projects and attitudes with which these people most strongly identify.

Williams framed this as an argument against utilitarianism. However, I find that what he was objecting to is primarily the existence of external moral obligations (perhaps in conjunction with consequentialism).[11] Williams’s critique misses the mark for people who think of utilitarianism (or consequentialism more generally) as a personal philosophy. Under anti-realism, the arguments for consequentialist morality don’t disappear—they take on a different, less prominent place in people’s philosophical framework. Instead of “utilitarianism as the One True Theory,” we consider it as “utilitarianism as a personal, morally-inspired life goal.”

Other moral frameworks—such as contractualism or virtue ethics—remain relevant under anti-realism in the same way. Virtue ethics describes the consideration space about what sort of person we want to be, and contractualism the consideration space about how we want to think about the relation between us pursuing our life projects and other people pursuing theirs.

As I will hopefully be able to convey also in future posts of this sequence, and as Luke Muehlhauser has sketched it in his post on Pluralistic Moral Reductionism, the resulting picture of ethics is intellectually satisfying. It conforms to a Wittgensteinian view of philosophy that doesn’t leave us with notions we don’t understand. As it’s summarized in the Stanford Encyclopedia of Philosophy:

[...] Wittgenstein holds [...] that philosophers do notor should notsupply a theory, neither do they provide explanations. “Philosophy just puts everything before us, and neither explains nor deduces anything. Since everything lies open to view there is nothing to explain (PI 126).

All normative-ethical perspectives take on their proper places at the level where the considerations most resonate with us. Anti-realism doesn’t make ethics less serious; nothing about it is watered down. We don’t need external obligations to feel the weight of opportunity costs on our shoulders. Regardless of one’s metaethical leanings, after encountering Singer’s arguments, we can’t help but view the world with different eyes. Baby cows begin to look like differently-shaped human toddlers. The price tags for luxury watches become symbols of the foregone opportunity to save and improve the lives of people in extreme poverty.

Moral realism or not, our choices remain the same. What’s conceptualized differently, under anti-realism, is that we no longer frame them about what’s (externally) moral, but about what sort of person we want to be and what we want to live for. Shouldering the responsibilities of consequentialism—if we decide to go down that road—won’t feel like an attack against our integrity, since we’d be choosing it freely.[12]

Other people’s life choices may differ from ours. In some instances, we might be able to point out that they’re committing an error that they might recognize by their criteria. In that case, normative discussions can remain fruitful. Unfortunately, this won’t work in all instances. There will be cases where no matter how outrageous we find someone’s choices, we cannot say that they are committing an error of reasoning.

While this concession is undoubtedly frustrating, proclaiming others to be objectively wrong rarely accomplished anything anyway. It’s not as though moral disagreements—or disagreements in people’s life choices—would go away if we adopted moral realism.

If it turned out that belief in moral anti-realism made people less moral or inclined to follow the principles of effective altruism, this would pose a dilemma. Of course, whether a position is true is separate from whether it’s beneficial to promote. Moreover, in actuality, I don’t expect anti-realism to lead to decreased moral motivation—not if it’s presented thoughtfully, at least. If the world’s leading philosophers got together tomorrow and announced that moral realism is wrong, what would matter most is what they write afterward.[13] If they write that this means all morality is nonsense, I could imagine that it would have some adverse consequences. By contrast, if they explained how this generally leaves moral arguments intact and gives us the autonomy to choose what sort of people we want to be and what we want to live for, probably not that much would change. (And the things that would change may well be for the better.)[14]

3. Irreducible normativity fails as a concept

Most things don’t change if we abandon normative realism, but some do. In particular, irreducible normativity has no place under anti-realism and no replacement. In this section, I argue that this is okay: irreducible normativity is not worth wanting because it cannot live up to the requirements we associate with it.

I understand the sentiment behind irreducible normativity, but I don’t understand it as a concept. Irreducible normativity looks like a mere intuition to me. For it to be a concept, I need to know something about what it attaches to, how it obtains reference. In the upcoming sections, I will sketch some ways for what this could look like, and why they don’t strike me as compelling.

Consider, first, the option that we don’t know anything at all about how reference is obtained. To illustrate this I’m introducing the concept of super-reasons:


Super-reasons are a made-up concept. They work as follows:

Consider the intuition that something ought to be done. Instead of treating this intuition as subjective “color coding” that our minds attach to (the thought of) specific actions, we stipulate that our intuitions are tracking a real, mind-independent property (anti-realists would point out this is an example of reification). This way, we get the concept of super-reasons: Super-reasons are speaker-independent properties that apply to some actions, making them things we ought to do. By stipulation, we know nothing more about super-reasons, i.e., we have no idea which exact actions are backed by super-reasons. For all we know, we may have a super-reason to clap our hands together three times every Friday.

Should we take super-reasons seriously?

Super-reasons are a weird concept. There’s a sense in which they are “hypothetical only.” Without knowing the conditions under which super-reasons apply, we could envision them as being attached to everything or nothing.

There’s an implied sense in which we are supposed to care about super-reasons. The intuition we attach to super-reasons, that something ought to be done, tends to elicit a desire to act accordingly. In this sense, there is, by definition, something about super-reasons that makes them feel relevant to what we want to do.

However, the way we defined super-reasons made clear that they could be attached to all kinds of actions, including arbitrary ones like clapping one’s hands together, or abhorrent ones such as eating babies. Because super-reasons may not have anything to do with the content our original normative intuitions were based on, we’d be wrong to think of them as related to the familiar normative categories. For instance, our folk concept “morality” has something to do with being kind, but whether or not super-reasons also include being nice to others is left wide open. Whatever super-reasons are about, based on how we defined them, we wouldn’t know.

The concept of super-reasons repurposes a label we’ve initially come to associate with object-level normative principles that resonated with us. These principles include wanting to have beliefs that can generate accurate predictions, or wanting to promote human flourishing. However, instead of staying attached to this familiar content, we removed only the label and transferred it to other things, to principles that may not resonate with us at all. Since we—presumably—care about the content instead of the label, we shouldn’t take super-reasons into account in our decision making. (Of course, based on how we defined super-reasons, we also wouldn’t know how to do that.)

Is irreducible normativity about super-reasons?

Irreducible normativity is not about super-reasons. At least, I sense that most proponents of the concept would object to the comparison. They may object that saying, “Imagine that we have a reason to clap into our hands three times every Friday” is like saying, “Imagine that, to be a good friend, you need to like the color purple.” Just because it’s silly to imagine that liking the color purple is an attribute of a good friend, doesn’t mean that “an attribute of a good friend” is a meaningless concept. Just because it’s silly to imagine that clapping one’s hands together three times every Friday is backed by an irreducible normative reason doesn’t mean that no actions are.

That said, the comparison to super-reasons doesn’t seem entirely unfounded. In his writings on metaethics, Parfit quotes criticism by the philosopher Stephen Darwall (Parfit, 2011b, p. 294):

[...] the resulting picture of rational motivation is an alien and unsatisfying one. It fails to make the desire to act for reasons intelligible as one that is central to us and not simply a superadded fascination with a non-natural metaphysical category.

Darwall’s wording suggests that he might interpret irreducible normativity in terms of super-reasons. For instance, what I called “repurposing a label” seems similar to what Darwall calls a “superadded fascination with a non-natural metaphysical category.”

Parfit replied to Darwall as follows:

If Darwall had my concept of a reason, he would not make such claims. When I believe that some fact gives me a decisive reason to do something, it is not unintelligible how I might want to act for this reason.

Question-begging examples

So how is it that irreducible normativity is connected to us wanting to act by it? Unless we have some concrete idea about which principles are backed up by irreducible normativity, the concept is equivalent to super-reasons.

Looking at the examples Parfit and other normative realists use to motivate irreducible normativity, we see something interesting. Unlike the example I used to motivate super-reasons (“you may have a super-reason to clap your hands together three times every Friday”), philosophers tend to motivate irreducible normativity with principles that are as uncontroversial as possible. In Moral Realism: A Defense, Russ Shafer-Landau (2003, pos.178) writes that “At least some moral principles are knowable via self-evidence.” Parfit used the self-evident example “we always have a reason to want to avoid being in agony.” Similarly, in Reasons and Persons (1984), Parfit argued that we have a reason to avoid “Future Tuesday Indifference”—a hypothetical silly disposition where a person generally cares about what happens to their future self except for things that happen on Tuesdays.

Explaining irreducible normativity with self-evident examples makes it apparent how the concept is connected to what we want to do. However, arguably it’s now too connected to that. Self-evident principles are principles that, by definition, (almost) everyone recognizes. (This may not mean that everyone will be motivated to act on them; for instance, amoral psychopaths may not have any intrinsic motivation to act on self-evident moral principles.) If irreducible normativity is meant to be relevantly different from (my conception of) normative anti-realism, then we have to show that irreducible normativity sometimes reaches beyond self-evident principles. Evidently, self-evident examples are fundamentally unsuited for illustrating how that could work.

Readers may object as follows. If we concede that we have an irreducible reason not to stick our hand into a blender without some compensatory gain (a “self-evident principle”), doesn’t that open up the possibility that we also have such a reason to, say, not get an abortion (a “potentially controversial principle”)?

My answer is, “not really.” At least, it depends on what we mean by “irreducible reason.” If—as the example seems to indicate—we think that irreducible reasons can also attach themselves to principles that aren’t self-evident, the question becomes “Which of the not-self-evident principles does it attach itself to?” As long as we don’t know how to think about this, the concept remains under-defined. I may have certain ideas or connotations in my mind that I could use to figure out what principles (other than the self-evident ones) are also backed by irreducible normativity. However, because other people will have in mind subtly different ideas and connotations, those ideas and connotations cannot be the foundation of a speaker-independent concept.

The challenge for normative realists is to explain how irreducible reasons can go beyond self-evident principles and remain well-defined and speaker-independent at the same time.

Is (our knowledge of) irreducible normativity confined to self-evident principles?

One way to address this challenge is by restricting the practical scope of irreducible normativity. One could concede that insofar as irreducible normativity goes beyond self-evident principles, we are forever cognitively closed off to it.

On this view, irreducible reasons are technically different from self-evident principles, but we hope for them to have the same extension. Irreducible reasons would supervene on the self-evident principles, insofar as we are correctly predisposed to find the right principles self-evident. Accordingly, the way in which irreducible reasons differ from self-evident principles, on this view, is only that we allow for the possibility that we could be incorrectly predisposed to ascertain normative truths.[15]

Even though this view is undoubtedly moral realist in spirit, I’d say it makes crucial concessions to anti-realism. (Importantly, I don’t mean the type of “anti-realism” that people associate with the word “nihilism” and the sentiment “anything goes.” I mean the more fruitful version of anti-realism that I characterized in Section 2.)

Compared to the anti-realism I have outlined, a kind of moral realism according to which the only accessible moral truths are self-evident principles is pretty much redundant—at least in practice.[16] I’m more interested in normative realism versions that would actually change the way I think about normativity, i.e., how I reason about ethics, epistemology, or metaphilosophy. If the only implication of normative realism is “all else equal, murder is truly bad” or “all else equal, putting your hand into a blender is truly wrong,” my newfound understanding of that won’t change how I go about pursuing my priorities.

As an anti-realist, I don’t yet call self-evident principles “(probable) normative truths.” However, if I were to start calling them this, it would only make a semantic difference.

Do any prominent moral realists hold the view I just described? I’m not confident, but when I read Russ Shafer-Landau’s account of normativity, I found myself wondering whether my perceived disagreements with his position would go away if I translated my thinking into his philosophical framework.[17] Of course, with the general difficulty of understanding people who think in terms of radically different philosophical frameworks,[18] it’s hard to tell. It might well be that Shafer-Landau would allow no comparison between his view and my anti-realism.

As a side note (even though it doesn’t relate to irreducible normativity), I would “object” in a very similar way to the naturalist version of moral realism Sam Harris argued for in his book The Moral Landscape (Harris, 2010).[19]

Is there a speaker-independent normative reality?

I have argued that, if we assume that we don’t know anything about what irreducible reasons are attached to, the concept becomes vacuous—like super-reasons. I have also argued that if we limit our ability to comprehend irreducible normativity to principles that appear self-evident to us, the resulting concept doesn’t do enough to clearly go beyond moral anti-realism.

In this section, I want to introduce one last option to make irreducible normativity work as a concept.[20] I commonly associate[21] this option with moral naturalism, the view that normative facts are reducible to physical facts. However, as the SEP entry on moral non-naturalism notes, the distinction between naturalism and non-naturalism is complicated:

There may be as much philosophical controversy about how to distinguish naturalism from non-naturalism as there is about which view is correct. [...] Perhaps the most vexing problem for any general characterization of non-naturalism is the bewildering array of ways in which the distinction between natural and non-natural properties has been drawn.

Since I don’t understand this distinction well enough, I intend my arguments from here onwards to apply to both reducible (“naturalist”) and irreducible (“non-naturalist”) versions of speaker-independent normativity.

The last option to make normativity work as a concept is this:

To understand normativity, and to evaluate whether the concept has meaning, we need to look at the space of all possible considerations at the object-level. Normativity is meaningful if there is a single set of principles that sticks out in a sense relevant to us.

On this interpretation, when realist philosophers point toward examples such as “we always have reason to want to avoid being in agony,” they aren’t (just) pointing at the intuition that “some things ought to be done.” Neither are they interested only in what appears to us as self-evident. Instead, they are using a maximally uncontroversial example to get us looking in the right direction. By pointing out salient features of the normative reality, the intention (or hope?) is that with the help of these pointers, we can come to understand what makes some principles normative principles. Because (so goes the assumption) reality “allows for only one interpretation,” the hope is that we’ll learn to extrapolate from the most uncontroversial examples to the more difficult ones, until the entire normative reality is mapped out unambiguously.

If we think about how words obtain their meaning, it should be apparent that in order to defend this type of normative realism, one has to commit to a specific normative-ethical theory. If the claim is that normative reality sticks out at us like Mount Fuji on a clear summer day, we need to be able to describe enough of its primary features to be sure that what we’re seeing really is a mountain. If all we are seeing is some rocks (“self-evident principles”) floating in the clouds, it would be premature to assume that they must somehow be connected and form a full mountain.

Figure 1. Mount Fuji: a metaphor for normative reality. (Public domain)

The next two sections are dedicated to further backing up the claim that to defend this last and—in my view—most attractive version of normative realism, one has to commit to a specific normative theory.

Essences are always subjective

When we see a bunch of similar-looking, similarly-contextualized phenomena, our mind forms a category based on the “essence” (or “archetype”) of the concept in question. For instance, after seeing a bunch of dogs, children form the concept “dog.” There’s a sense in which that concept already came to include chihuahuas even before the children ever encountered a dog that small.

Based on our mind’s readiness to form essences, it’s tempting to assume that after having familiarized ourselves with a bunch of examples of (what we think of as) “speaker-independent normativity,” we know enough to apply this concept to never-before-encountered instances. However, this process (“distilling essences based on central examples”) cannot justify normative realism because it only ever generates subjective concepts.

Wittgenstein pointed out that for terms such as “game” or “language,” we may not be able to give a simple[22] verbal definition, but we can teach them through examples. He coined the term family resemblance (Wittgenstein, 1953) to explain why this works: Even though no characteristics may be present in all the examples, overlapping similarities show up in different combinations—just like members of a family have overlapping similarities in their appearances.

Wittgenstein’s entire point behind family resemblance was that the meaning of a concept is nothing beyond the examples that go into it. Sure, one can extrapolate from old examples to new, never-before-encountered ones. However, whether a never-before-encountered example matches the category in question will always depend on the initial learning process. Concepts built up through family resemblance are not speaker-independent. Whether we come to classify an unusual, never-before-encountered activity as a “game” depends on how it relates to the examples of games we are familiar with, and (presumably) on various weights in our brain’s concept-formation modules. There’s no further fact that determines what’s a game.

If two people learned their “game” concepts through examples that differed along some relevant dimensions, they wouldn’t end up with the same concept. (E.g., consider one child being taught implicitly that games always have a single winner whereas the other child is taught that all the players can win or lose together in many games.)

Crisp reference only works in combination with a compelling theory

There are instances where just a handful of examples or carefully selected “pointers” can convey all the meaning needed for someone to understand a far-reaching and well-specified concept. I will give two cases where this seems to work (at least superficially) to point out how—absent a compelling object-level theory—we cannot say the same about “normativity.”

Example 1 (“H2O”)

Imagine a person who forgot everything they ever knew except for a rudimentary understanding of chemistry. If we gave this person the concept “H2O” (perhaps explained with its chemical formula), this short concept contains enough information to refer successfully to ice cubes, snowflakes, around 60% of the human body, water vapor in the air, and a chemical byproduct of combustion. Simultaneously, “H2O” successfully refers not to similar-seeming things such as dry ice, the “seas” of Titan, or the magnesium compounds in a glass of spring water. Once the person understands “H2O,” they have the requirements needed to sort a wide range of real-world phenomena into “water” and “not water.”

Example 2 (“mathematics”)

Consider an extremely intelligent person who has never encountered mathematics, but is familiar with the basic notion of a formal system. With just a few pointers—syntax and a few axioms—we could give this person the requirements needed to eventually understand all of mathematics (at least for specific axiomatizations of mathematics), opening up an entire realm of well-specified and often useful abstract relations.

These thought experiments illustrate that under the right circumstances, it’s possible for just a few carefully selected examples to successfully pinpoint fruitful and well-specified concepts in their entirety.

There are two crucial differences to the situation we find ourselves in concerning normativity:

  • We don’t have the philosophical equivalent of a background understanding of chemistry or formal systems. Without understanding the basic rules of a domain, our words cannot refer to (aspects of) reality crisply. Normative disagreements are particularly challenging to address precisely because they don’t just concern object-level answers, but also about the methods needed to derive them. Metaphilosophy, the question of how to do philosophy, is itself subject to the disagreement between realists and anti-realists.

  • With the concept of normativity, we can’t know that reference will work successfully. In the above examples, which we looked at from the outside, we were in a position to tell that the chemical formula for water or the syntax and axioms for mathematics would open up novel grounds. However, the hypothetical people in the above thought experiments could not have known this with their limited perspectives. They could not have told the difference if they had instead received randomly drawn chemical formulas or random syntax and axioms.

The above analysis illustrates that to be justified in thinking that a concept successfully refers to a well-specified domain of things outside our head, we need to understand the concept well enough to know its way of referring. If we don’t know how it refers, it doesn’t do so at all.[23] Words can’t have meaning independently of how we use them. We can’t know if there’s a mountain if we don’t already have the means to locate and describe it.

Summary, conclusion, and open questions

To maintain that normativity—reducible or not—is knowable at least in theory, and to separate it from merely subjective reasons, we have to be able to make direct claims about the structure of normative reality, explaining how the concept unambiguously targets salient features in the space of possible considerations. It is only in this way that the ambitious concept of normativity could attain successful reference. As I have shown in previous sections, absent such an account, we are dealing with a concept that is under-defined, meaningless, or forever unknowable.[24]

Normative realism is the view that questions about normativity have a speaker-independent solution. It is commonly argued normative realism enables us to be morally uncertain (whereas this is less clear for anti-realism).[25] I disagree. In this piece, I have put forward the argument that to be a normative realist worthy of the term, one has to provide that solution already. Or, at least, one has to provide the requirements needed to unambiguously derive it—just like the syntax and axiomatization of mathematics specifies what constitutes the solutions to mathematical questions.

Curiously enough, I believe that if the arguments in this post are sound, moral realism worthy of the name is incompatible with open-ended notions of moral uncertainty.[26]

Some moral realist philosophers have indeed advanced confidently-endorsed proposals for solutions to normative ethics. I’d say this includes Derek Parfit.[27] Besides Parfit, I’m also thinking about accounts that aim to ground moral realism in the “intrinsic value” of some conscious experiences, and the view that we can quantify it and turn morality into a calculus (e.g., de Lazari-Radek & Singer, 2014).

I titled this post “Against Irreducible Normativity.” However, I believe that I have not yet refuted all versions of irreducible normativity. Despite the similarity Parfit’s ethical views share with moral naturalism, Parfit was a proponent of irreducible normativity. Judging by his “climbing the same mountain” analogy, it seems plausible to me that his account of moral realism escapes the main force of my criticism thus far. In addition, I’m generally unsure whether I understand the distinction between naturalism and non-naturalism well enough to claim that there are no other conceptions of irreducible normativity that can withstand my arguments.

For these reasons, I have to end this article with a somewhat unsatisfactory conclusion. If my arguments here are sound, then either irreducible normativity is not worth wanting (i.e., it’s either vacuous, trivial, or meaningless), or it stands and falls together with the case for moral naturalism.[28] I will argue against moral naturalism in upcoming posts.

Appendix: Morality versus other types of normativity

Moral realists (e.g., Shafer-Landau, 2003; Cuneo, 2007) have advanced so-called “partners-in-crime arguments.” These arguments say that if we are realists about at least one normative domain, there’s no good reason why we shouldn’t also adopt moral realism.

In the section “Normative anti-realism is existentially satisfying (at least it can be),” I focused primarily on examples from ethics. However, I think the same arguments apply analogously to all the versions of irreducible normativity.

For versions of irreducible normativity where we don’t or can’t know to which principles normativity is attached, the partners-in-crime arguments cut both ways. All subtypes of normativity fail for the same reasons.

By contrast, for versions of normativity that depend on claims about a normative domain’s structure, the partners-in-crime arguments don’t even apply. After all, just because philosophers might—hypothetically, under idealized circumstances—agree on the answers to all (e.g.) decision-theoretic questions doesn’t mean that they would automatically also find agreement on moral questions.[29] On this interpretation of realism, all domains have to be evaluated separately.


Many people helped me with this post, but I want to especially thank Elijah Armstrong for his helpful suggestions and advice on how to better explain opposing philosophical views, and Sofia Davis-Fogel for her her comments and help with making my writing more intelligible.

My work on this post was funded by the Center on Long-Term Risk.


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Cuneo, T. (2007). The Normative Web: An Argument for Moral Realism. Oxford: Oxford University Press.

De Lazari-Radek, K. & P. Singer. (2014). The Point of View of the Universe. Oxford: Oxford University Press.

Dennett, D. C. (2008). Some Observations on the Psychology of Thinking about Free Will. In J. Baer, J. C. Kaufman, & R. F. Baumeister (eds.), Are we free? Psychology and free will. Oxford: Oxford University Press. 248–259.

Harris, S. (2010). The Moral Landscape: How Science Can Determine Human Values. New York: Free Press.

Parfit, D. (1984). Reasons and Persons. Oxford: Oxford University Press.

Parfit, D. (2011a). On What Matters, Volume I. Oxford: Oxford University Press.

Parfit, D. (2011b). On What Matters, Volume II. Oxford: Oxford University Press.

Plantinga, A. (1993). Warrant and Proper Function. Oxford: Oxford University Press.

Ruse, M. (2010). The Biological Sciences Can Act as a Ground for Ethics. In Ayala, F. and R. Harp (eds.), Contemporary Debates in Philosophy of Biology. New York: Wiley-Blackwell. 297–315.

Schroeder, M. (2011). Derek Parfit: On What Matters, Volumes 1 and 2. Notre Dame Philosophical Reviews. <ndpr.nd(.)edu/​news/​on-what-matters-volumes-1-and-2/​>.

Shafer-Landau, R. (2003). Moral Realism: A Defense [Kindle version]. Oxford: Oxford University Press. Retrieved from Amazon(.)com.

Singer, P. (1972). Famine, Affluence and Morality. Philosophy and Public Affairs, 1(3):229–243.

Singer, P. (1973). The Triviality of the Debate over “Is-Ought” and the Definition of “Moral”. American Philosophical Quarterly, 10(1):51–56.

Singer, P. (2009 [1975]). Animal liberation. New York: Harper Perennial Modern Classics.

Street, S. (2006). A Darwinian Dilemma for Realist Theories of Value. Philosophical Studies,127 (1):109–166.

Williams, B. (1973). A Critique of Utilitarianism. In J.J.C. Smart and B. Williams (eds.), Utilitarianism: For and Against. Cambridge: Cambridge University Press.

Williams, B. (1979). Internal and External Reasons. In R. Harrison (ed.), Rational Action. Cambridge: Cambridge University Press. 101–113.

Wittgenstein, L. (2010(1953)). Philosophische Untersuchungen. Frankfurt am Main: Suhrkamp.

Yetter-Chappell, R. (2017). Knowing What Matters. In P. Singer (ed.), Does Anything Really Matter? Parfit on Objectivity. Oxford: Oxford University Press. 149–167.

  1. For instance, epistemology, decision theory, science (realism about the corrective of scientific explanations or theories), metaphilosophy (realism about the proper way to do philosophy), etc. ↩︎

  2. The more common terminology is “internal reasons” or “instrumental reasons.” See Williams (1979). ↩︎

  3. In moments of agony, we, by definition, wish to be free from suffering. Not wanting to avoid being in agony is not quite motivationally impossible (especially because one can steer toward sources of agony during times when one isn’t yet subject to them). Still, it represents a state where one part of one’s motivational system conflicts with another part. ↩︎

  4. Moral realists might argue that this argument is weaker against versions of moral realism built around intrinsic (dis)value tied directly to positively or negatively valenced states of conscious experience. I will argue against these versions of moral realism in a future post. ↩︎

  5. Alvin Plantinga’s evolutionary argument against naturalism (Plantinga, 1993, ch.12) fails for the same reasons. Plantinga, a theist philosopher, advanced an evolutionary debunking argument against the coherence of the reductionist worldview held by atheists. As noted in the linked Wikipedia article, some components of Plantinga’s original argument—particularly related to his understanding of evolution—appear to have been of dubious quality. However, it seems that a steelmanned version of Plantinga’s argument would work analogously to Street’s argument. Instead of calling into question our ability to grasp moral truths, Plantinga’s argument attacks our ability to understand empirical truths. The best reply to this type of debunking argument is to drop the idea that “truth” is a bedrock concept. If we subscribe to the conception of truth popular on LessWrong (i,e., “truth” as a naturalist and reducible concept), the evolutionary origin of our belief-forming mechanisms poses no threat. According to this conception of truth, having a true belief means nothing more than that there is an in-theory-observable correspondence between our beliefs (“map”) and the world (“territory”). It’s no mystery then that evolution would have equipped us with the ability to form such territory-corresponding beliefs: An organism is usually better off meeting its goals or drives if it can develop accurate beliefs about the world. (Of course, in many instances, it was beneficial to have self-serving but false beliefs, or to bet on crude heuristics even though they may lead us astray under changed circumstances—that’s why we have biases.) ↩︎

  6. Richard Yetter-Chappell provided a particularly interesting reply. In his essay “Knowing What Matters” (Yetter-Chappell, 2017) he argued that to circumvent the evolutionary debunking arguments, we need to assume that we can only acquire moral knowledge if we are equipped with the right psychological dispositions. He further argued that we have to accept that there is no way to reliably tell whether our dispositions are correct. One might be inclined to reject this position outright because it sounds as though having the right dispositions is based on sheer luck.
    However, Yetter-Chappell replies that while luck is indeed involved, this doesn’t mean that our chances for being correctly predisposed are tiny. Unlike with lottery numbers, which all have the same prior probability of winning, he argues that we should not assign the same prior probability for every possible psychology. From our present vantage point, introspecting on how our minds are equipped to accept induction and to enable (some of) us to hold nuanced views and change our minds in reaction to new evidence, we can safely assume that things could look a lot worse. Compared to most conceivable psychologies, ours seems like it would be more likely correct than the average.
    In many ways, Yetter-Chappell’s arguments remind me of arguments against modest epistemology. People who excel at autonomous thinking may occasionally feel that they are justified to disagree confidently with a particular expert, even in the absence of an outside-view justification for this confidence. On inside-view grounds, their beliefs will appear to be more nuanced and more coherent than (their model of) the expert’s inside view. Of course, many reasoners who reject modest epistemology will crash and burn. Still, those who are actually skilled at inside-view reasoning will often get things right, for the right reasons. As someone who agrees with the arguments against modest epistemology, I can’t help but find Yetter-Chappell’s argument intriguing. At the same time, I don’t think his reply takes all the force out of the evolutionary debunking arguments. Sure, Yetter-Chappell correctly notes that we shouldn’t feel threatened by the possibility of aliens who don’t accept induction or are otherwise incapable of forming nuanced thoughts. But what about the conceivability of aliens who reason about everything the same way as we do, except that they start from different ethical premises? Reasoning about morality not only requires generally-useful reasoning skills, but also some fundamental intuitions about what matters—those intuitions could have evolved in different ways based on contingent directions of the selection pressures in one’s ancestral environment.
    (Admittedly, this somewhat merges the evolutionary debunking argument with the argument from widespread moral disagreement. In future posts, I will argue that we don’t need to envision aliens. Even among humans, we can observe unbridgeable disagreements between reasoners whose thinking is—as far as we can tell—maximally nuanced and versatile.) ↩︎

  7. As Ben Garfinkel describes it in his LessWrong article Realism and Rationality:
    [...] if anti-realism is true, then it can’t also be true that we should believe that anti-realism is true. Belief in anti-realism seems to undermine itself.↩︎

  8. It can change something indirectly. E.g., an anti-realist is more likely to give up parsimony to save some moral intuition that they really like. ↩︎

  9. People with strong views about norms in the context of interpersonal relationships have to do this all the time or risk becoming impossible to work or live with. For example, I may have a strong intuition that it’s objectively wrong for my co-workers to do things in their preferred way, as opposed to my preferred way. Still, I have a choice: I can treat this normatively valenced intuition as a personal belief and (try to) agree to disagree, or I can reify the intuition and treat it as my judgment about a speaker-independent fact. In the latter case, I can’t agree to disagree (at least not without some degree of condescension). ↩︎

  10. I plan to address this option in the upcoming posts “4. Why the Wager for Moral Realism Fails” and “5. Metaethical Fanaticism (Dialogue).” ↩︎

  11. As Williams emphasizes in his critique, he doesn’t necessarily (or primarily) disagree with the conclusions of utilitarianism, but with the way they are derived. In particular, he does not like the idea that utilitarian considerations are the only (or the primary) moral considerations for a person to consider. ↩︎

  12. If this sentiment doesn’t quite resonate with some readers, but they would like to read more about it, I recommend two blog posts by Nate Soares: “On caring” and “Altruistic motivations”. ↩︎

  13. For example, I was inspired by the essay “Some observations on the psychology of thinking about free will” (Dennett, 2008). Dennett’s paper might be interesting because of the parallelism between anti-realism about metaethics and compatibilism about free will (both of them arguably being more palatable than one may at first think). ↩︎

  14. For instance, moral uncertainty works very differently under normative anti-realism. I consider this to be a benefit instead of a drawback because the option space for moral anti-realists is more nuanced. There are strong arguments in favor of valuing reflection, but also arguments to trust at least some of one’s object-level normative intuitions more than one’s instincts on how to set up a safe reflection process. Peer disagreement also functions differently under normative anti-realism. While realists should only consider someone’s philosophical expertise before deciding how much to update on the other person’s views, normative anti-realists would do well to also assess that person’s most fundamental intuitions to see whether these are sufficiently compatible with theirs to warrant updating. ↩︎

  15. “Incorrectly predisposed” is an under-defined term in this context, which makes this version of irreducible normativity is not fully specified either. ↩︎

  16. Arguably, the described notion of irreducible normativity still differs from my anti-realism in an important sense. At least in theory, irreducible normativity postulates a single correct way to “fill in the gaps,” once we go beyond self-evident principles. However, on close inspection, that seems to be little more than a trick of words. Only very few philosophical principles are universally considered self-evident. Everything else would remain under-determined as far as our attainable knowledge of normativity is concerned. If we are forever closed off to the correct solution, it is of no use to even believe that there’s a “single correct way to fill in the blanks.” Since we can’t make any progress toward the correct solution, we’ll have to use other decision criteria. In practice, moral realists of this kind will have to resort to subjective reasons—just like the anti-realists. ↩︎

  17. For instance, Shafer-Landau puts a lot of emphasis on self-evidence as the means to obtain moral knowledge (Shafer-Landau, 2003, pos. 1374):
    We would go far in responding to sceptical worries if we could defend the existence of self-evident moral principles. I believe that we can.” As a moral particularist, he also doesn’t see the need to connect self-evident principles into an overarching and complete moral theory. About the content of moral principles (“moral laws”), he writes the following (pos.1494–1496):
    I think it likely that every one of them will incorporate a ceteris paribus clause, though establishing that point is extremely difficult and a matter of fundamental normative ethical theory, and so beyond our present [s]cope.↩︎

  18. I’m echoing a sentiment expressed in Mark Schroeder’s (2011) review of Parfit’s On What Matters (1&2):
    [A]ccording to [Parfit], few people who have ever contributed to the literature on metaethics even have the conceptual resources required to disagree with him.
    Bernard Williams, for example, turns out to lack the concept of a reason. John Mackie turns out to fail to have thoughts about morality, rather than to believe that nothing is wrong. Christine Korsgaard lacks normative concepts. Simon Blackburn and Allan Gibbard’s disagreement with Parfit? That’s superficial, too – they don’t have normative concepts either. I’m flattered to report that I am among the few metaethicists whom Parfit credits as sharing the required conceptual repertoire to disagree with him.↩︎

  19. In particular, my critique of Harris’ moral realism version is that it doesn’t quite seem worthy of the name (according to my terminology), because I felt that all he’s argued for in his otherwise excellent book is that some moral principles are self-evident. (And also that morality is importantly connected to consciousness and well-being.) From this, we cannot yet infer the existence of a uniquely correct and complete normative theory. ↩︎

  20. Perhaps there are options I am missing. It is difficult to comprehensively argue against the merits of a concept that cannot be crisply defined. ↩︎

  21. The reasons I primarily associated this way of thinking about normativity with moral naturalism are best described in this quote by Russ Shafer-Landau (2003, pos. 1260–1262):
    [N]aturalists might defend a particular model of moral theorizing (e.g. Pettit and Jackson’s moral functionalism, or Harsanyi’s utilitarianism, or Harman’s relativism), and claim that the correct application of such a theory yields the surprising conclusion that, for every moral property, there is a non-gerrymandered descriptive property that is identical to it.
    It is particularly the part about locating a “non-gerrymandered descriptive property” that captures how I’m thinking about it. ↩︎

  22. Concepts such as “game” or “language” may seem impossible to define with words in practice, but they are definable in theory. We could construct satisfactory verbal definitions of these concepts if we could use disjunctions and as many words as there are atoms in our local galaxy cluster. Consider cat pictures: Modern image-classification algorithms trained for cat detection successfully quantified “catness.” The evaluation criteria behind these algorithms might be enormously demanding to spell out. Still, at its core, a fully trained image-classification algorithm does little more than transforming image data into a giant matrix of possible attributes to evaluate those attributes according to whether they score sufficiently high to pass the threshold on “catness.” That metric was trained from human-labeled examples—arguably not too different from the way babies pick up language from their parents. (There’s also no single best way to extract features from examples—hyperparameter tuning illustrates how machine learning is a bit of an art, with a degree of arbitrariness.) ↩︎

  23. There are limited exceptions, of course. For instance, if a trustworthy teacher guaranteed us that a given concept successfully refers to a speaker-independent property, we could start using it in meaningful ways even before fully understanding the concept’s meaning. However, in this example, it’s crucial that at least the trustworthy teacher thoroughly understands the concept. If said teacher were also deferring to someone else, and that person were to defer to others yet again, then the concept may turn out to be ill-grounded after all. ↩︎

  24. One might argue that “meaningless” and “forever unknowable even in theory” sound like the same thing. Even if these two notions are somehow different, I’d say we can ignore things that are forever unknowable. ↩︎

  25. See, e.g., this section in Ben Garfinkel’s LessWrong post “Realism and Rationality.” ↩︎

  26. Normative realism remains compatible with narrower notions of uncertainty, such as uncertainty about what follows from axiomatic principles. Similarly, giving up on realism still allows the option of valuing further moral reflection. There are strong arguments for this on anti-realist grounds, though the specifics work differently from the way moral realists think about moral uncertainty (see also my comments in endnote 14). I plan to address moral reflection from an anti-realist perspective in a future post. ↩︎

  27. Parfit considered it vital to his philosophical project to show that disagreement among ethicists is not as wide-reaching as it’s commonly described. He argued that Kantianism, consequentialism, and contractualism are three different ways of “climbing the same mountain” (Parfit, 2011a). I don’t know Parfit’s work deeply enough to know his thoughts on normative uncertainty. Still, I’d say there’s a plausible reading of his “climbing the same mountain” analogy, and the importance he attaches to it in the context of his life’s work, that stands in some tension with open-ended notions of moral uncertainty. ↩︎

  28. As I have outlined my first post, I am particularly interested in versions of moral naturalism that, should they prove correct, will be highly relevant to people’s lives and life projects. I have tried to sum up the desiderata for this with the concept One Compelling Axiology. As I envision, this would combine a specific, complete theory about what objectively is in someone’s interest, or is good or bad for them, with a specific, complete theory of what it means to do good for others from a kind of “impartial perspective.” ↩︎

  29. I expect that many deep-seated disagreements in epistemology or decision theory won’t go away even under the perfect conditions for philosophical reflection. However, I’m not particularly attached to that claim. In the course of this sequence, I only want to argue for anti-realism about morality. ↩︎