In its familiar orthodox form, nonnaturalism is a kind of moral realism. It holds that there are true substantive moral claims, such as, perhaps, that lying is wrong. It holds that there are normative moral properties, such as wrongness, and that these properties are instantiated. Nonnaturalists typically would add that the normativity of these properties is a matter of their being a source of reasons. Perhaps most centrally, nonnaturalists reject the normative naturalist's thesis that moral and other normative properties are natural ones – properties that, roughly speaking, fit within the ontology of science. They hold that these properties are in a fundamentally different metaphysical category from natural properties, such as physical, psychological, or economic ones.
Orthodox nonnaturalism faces familiar challenges (e.g. Enoch Reference Enoch2011, ch 6–9). Recently, some who agree with orthodox nonnaturalists in rejecting normative naturalism have attempted to escape these challenges by abandoning the robust metaphysical commitments of the orthodox view while otherwise remaining orthodox to the extent possible. I will call views of this kind, ‘avant-garde nonnaturalism.’ In this paper, I address one such view.Footnote 1 It agrees with orthodox nonnaturalism that moral and other normative judgements are beliefs like any other beliefs, that moral assertions express such beliefs, and that some such beliefs are true. So it is a version of ‘cognitivism.’ It agrees as well that there are moral properties such as wrongness, that these properties are instantiated, and that they are not natural ones. But unlike the orthodox view, it contends that these claims have no ‘robust’ or ‘heavy-weight’ ontological implications. So it can be described as a version of ‘non-realism.’
Avant-guard views of this kind have been proposed by Derek Parfit (Reference Parfit2011, Reference Parfit2017) and John Skorupski (Reference Skorupski2010), among others, perhaps including Ronald Dworkin (Reference Dworkin1996), Thomas Nagel (Reference Nagel2012) and T.M. Scanlon (Reference Scanlon2014). Parfit initially called his view ‘Non-Metaphysical Non-Naturalism’ (Reference Parfit2011, II, 486) but more recently he has called it ‘Non-Realist Cognitivism’ (Reference Parfit2017, 59). I will use this newer label.
Non-Realist Cognitivism might seem to give both moral naturalists and orthodox moral nonnaturalists all that they have reason to want in a metaethical view. It offers naturalists a view that is cognitivist and that allows there are moral truths. It claims to have no robust ontological implications, and if so, it presumably is compatible with metaphysical naturalism – the view that, roughly, reality is exhausted by the natural (see Railton Reference Railton and Singer2017). It offers nonnaturalists a position according to which moral concepts are nonnatural and irreducible and moral properties are nonnatural even though not metaphysically robust. Accordingly, Non-Realist Cognitivism stakes out an interesting compromise position.
This paper investigates the intelligibility of the view. Section 1 sets out the basic idea and explains how Non-Realist Cognitivism seeks to avoid the standard objections to orthodox nonnaturalism. Section 2 explains a challenge to the view. As it stands, it seems unable to provide a substantive non-trivial account of the meaning and truth conditions of moral claims. There are various strategies Non-Realist Cognitivism might use to address the challenge, including ‘quietist’ strategies. I argue against quietist strategies in Section 2. Section 3 explains the ‘Non-Referential’ strategy taken up by Parfit, as I reconstruct his view, and Section 4 argues that Parfit does not have an adequate response to the challenge. In Section 5, I discuss expressivist versions of the Non-Referential strategy, exemplified by Simon Blackburn's quasi-realism (Reference Blackburn and Copp2006). Section 6 addresses the ‘Meinongian strategy, ’ as found in the work of Skorupski (Reference Skorupski2010). Section 7 briefly discusses the option provided by approaches to semantic theory, such as conceptual role semantics, that are friendly to non-realism about a variety of non-normative discourses. The upshot is skeptical of the prospects for Parfit's version of Non-Realist Cognitivism but it shows there is a rich field of views that are cognitivist and non-realist.
1. Introducing and motivating non-realist cognitivism
To begin, I need to sketch and motivate the basic idea, as I understand it. Only later in the paper will I look in detail at what Parfit and others have said in developing their own versions of the view.
Non-Realist Cognitivism is ‘cognitivist’ and ‘descriptivist.’ It holds that moral judgments are beliefs, literally and strictly speaking, and that they at least purport to describe or represent something. The belief that lying is wrong represents lying as being wrong. Non-Realist Cognitivism holds in addition that some moral beliefs are true. Yet it denies that moral beliefs represent or describe ontologically robust facts or states of affairs that involve ontologically robust moral properties. And it denies that moral and other normative properties are natural ones. Moral truths have no robust ontological implications, says Parfit (Reference Parfit2017, 60). At least, pure moral truths have no such implications.Footnote 2
The view is accordingly committed to distinguishing between ontologically robust facts and ontologically non-robust facts and between ontologically robust properties and ontologically non-robust properties. It is obscure how these distinctions are meant to be understood, but I will propose a reading that I call the base-line reading and that, I believe, captures the basic idea.
Let metaphysical naturalism be the view that ‘reality’ is exhausted by the ‘natural, ’ that all ontologically ‘robust’ properties and facts are natural ones. It would take me too far afield to have a thorough discussion of what is meant by ‘natural’ in this context. In what follows, I will assume an ‘empirical characterization, ’ according to which, roughly, natural properties are those such that any substantive knowledge we can have of them is empirical or a posteriori.Footnote 3 This characterization is more ecumenical than familiar science-based characterizations since it allows us to say that some humdrum properties are natural even if they are not, and perhaps are not reducible to, properties of a kind that would ever be studied in any science. On the empirical characterization, for example, the properties of being a swimming pool and of having been born in September are natural properties. Russ Shafer-Landau opts in the end for an epistemological characterization (Reference Shafer-Landau2003, 61) and Parfit in effect proposes a similar account (Reference Parfit2011, II, 306–307).
Nonnaturalists would not deny that there are natural properties and facts so understood. And nothing in their view commits them to denying that natural properties and facts are metaphysically robust. On the base-line interpretation, Non-Realist Cognitivism agrees that natural properties and facts are metaphysically robust and it adds that moral truths have no implications that are incompatible with metaphysical naturalism.Footnote 4 That is, moral truths have no implications that are incompatible with the view that natural properties and facts are the only ontologically ‘robust’ ones.Footnote 5
On the base-line interpretation, Non-Realist Cognitivism holds that there are moral truths, facts, and properties, but only in ‘minimalist’ senses of the relevant terms. Roughly speaking, in minimalist senses of ‘there is’ and ‘fact, ’ there is a fact that p just in case it is true that p, and in a minimalist sense of ‘true, ’ it is true that p just in case p. Further, in a minimalist sense of ‘property, ’ there is a property F-ness just in case something is or could be F. On the base-line interpretation, Non-Realist Cognitivism holds that talk of moral ‘truths, ’ ‘facts, ’ and ‘properties’ is to be understood in minimalist senses of the terms, such that there is no robust ontological implication (see Beall and Glanzberg Reference Beall, Glanzberg, French and Wettstein2008).Footnote 6
To summarize, on the base-line interpretation, Non-Realist Cognitivism holds that some moral beliefs are true, yet these beliefs do not have ontologically robust truth conditions. There are moral facts and moral properties, but only in ‘minimalist’ senses. Moral truths, facts, and properties are not natural properties nor are they ontologically robust ones. Their existence is compatible with metaphysical naturalism. In Parfit's words, if Non-Realist Cognitivism is correct, then ‘normative truths & do not raise any difficult ontological questions’ (Reference Parfit2017, 62).
Unlike Non-Realist Cognitivism, orthodox nonnaturalism claims that reality includes robust moral properties and facts that are ‘over and above’ those studied in the sciences, those of which we have empirical knowledge, and those that are reducible to properties and facts of the kind just specified.Footnote 7 That is, orthodox nonnaturalism views the existence of moral facts and properties as incompatible with metaphysical naturalism. This, I believe, is the basis of at least many of the familiar metaphysical and epistemological objections to orthodox nonnaturalism.
On the base-line reading, Non-Realist Cognitivism has a bold response to these objections. For, it denies that the existence of moral properties and facts is incompatible with metaphysical naturalism. It claims that ‘there are’ moral ‘properties’ in the minimalist sense. It claims that we can have knowledge of substantive moral truths about how to live our lives. But it holds that these claims are compatible with metaphysical naturalism. Clearly, then, Non-Realist Cognitivism is a striking approach. It sets out a cognitivist position that avoids the standard metaphysical objections to orthodox nonnaturalism, is compatible with metaphysical naturalism, but is neither a form of normative naturalism nor a form of fictionalism or error theory. Non-Realist Cognitivism therefore would appear to offer a promising way of understanding the relation between the moral truths and natural facts about the empirical world.
2. A semantic challenge
The most important worry about Non-Realist Cognitivism is one that I describe as semantic. Orthodox nonnaturalism explains what moral judgments are about, and explains their truth conditions, by postulating robust moral properties, such as wrongness. One cannot simply subtract this robust ontological commitment from the view and expect the result to be intelligible, any more than one can remove one of the legs of a three-legged stool and expect it to remain standing. Some non-trivial adjustment must be made. Otherwise it will be mysterious what a moral judgment could be about, and it will be mysterious what the truth conditions of such a judgment could be. It will be unclear whether anything substantive distinguishes Non-Realist Cognitivism from moral fictionalism, or, indeed, from an error theory. Let me explain.
On a familiar, intuitive, referential or representational semantic view, typical predicates pick out and ascribe properties – their semantic value is, or determines, the property to which the predicate refers. As I will say, they ‘refer’ to properties.Footnote 8 On such a view, the meaning and truth conditions of the sentence, ‘Lying is widespread, ’ is a function of the semantic values of the terms ‘lying’ and ‘widespread, ’ and the predicate ‘widespread’ refers to a familiar property. Orthodox nonnaturalism and normative naturalism, as usually understood, assume such a semantics. They agree that moral predicates refer to moral properties. On the view they share, ‘wrong’ refers to the property of being wrong, and the sentence, ‘Lying is wrong’ is true just in case lying has the property referred to by ‘wrong.’ Naturalists and orthodox nonnaturalists would disagree of course as to whether ‘wrong’ refers to a natural property, but they would agree that its referent is a robust property that is suited to figure in a semantic theory as a relatum of the relation of reference.
What can Non-Realist Cognitivism say about this matter, on the base-line reading? It does not accept the claim, shared by naturalism and orthodox nonnaturalism, that ‘wrong’ refers to a robust property. On the base-line reading, Non-Realist Cognitivism says that wrongness is a property merely in the minimalist sense of ‘property, ’ but to say this is just to say, in other words, that something is or could be wrong. This does not help to explain the semantics of ‘wrong’ since it presupposes that ‘wrong’ is a meaningful predicate. Non-Realist Cognitivism seems, then, to leave us with the mystery of what the semantic value of ‘wrong’ could be. It appears to deny that ‘wrong’ refers to anything that can serve as a relatum of the semantic relation of reference. In a nutshell, it seems to deny that moral predicates refer – except, perhaps, in a minimalist sense of ‘refer, ’ as we will see. If this is right, then Non-Realist Cognitivism owes us some other account of their meaning.
Further, although, on the base line reading, Non-Realist Cognitivism allows that there are moral ‘facts’ in the minimalist sense, the ‘minimalist fact’ that p is not a candidate for something that might make it true that p. This is because, in the minimalist sense of ‘fact, ’ to claim it is a fact that p is just to claim, in other words, that p. So the ‘minimalist fact’ that p is not something logically distinguishable from the claim that p, such that the claim could be about it or that the claim could be true in virtue of its obtaining. Non-Realist Cognitivism owes us an account of what moral claims are about, and of their truth conditions.
One way to appreciate the issue is to ask what distinguishes Non-Realist Cognitivism from an error theory, according to which there are no (pure) moral truths. The error theory and Non-Realist Cognitivism can agree about all the non-moral and non-normative facts. They agree that the moral predicates and moral concepts do not refer to robust properties of any kind. They agree that there are no robust moral facts – certainly there are none that consist in the instantiation of a robust moral property. So they agree that no (pure) moral belief is true in virtue of corresponding to such a robust moral fact. Hence, if we assume a robust account of the meaning of ‘true, ’ the error theory would seem to follow. No pure moral claim is true. The Non-Realist Cognitivist rejects this inference, however, so she presumably must reject a robust account of the meaning of ‘true.’ Yet on a minimalist account, to assert that a moral claim is true is merely to affirm that claim. So, on a minimalist account, the assertion that some moral claims are true is nothing more than a signaling, by the Non-Realist Cognitivist, that she affirms some moral claims. It seems, then, that the key difference between the Non-Realist Cognitivist and the error theorist is that the former affirms certain (pure) moral claims whereas the latter does not.Footnote 9 What explains this disagreement? It does not turn merely on the adoption of a minimalist account of the meaning of the word ‘true, ’ for nothing prevents the error theorist from adopting such an account. It seems that the disagreement must instead depend on a disagreement about the semantics of moral claims. And this disagreement must depend in turn on a disagreement about the semantics of the moral predicates and concepts.
The challenge to Non-Realist Cognitivism, then, is to explain what the moral predicates and moral concepts are about. Or better, it is to provide a semantics of the moral predicates and concepts. Is there a coherent and plausible way to understand their semantics on this view? Is there a coherent and plausible way to understand what moral judgements are about, or to understand their truth conditions? Several strategies are available to Non-Realist Cognitivism.
First is the ‘Non-Referential Strategy.’ This is the strategy of abandoning a robust referential or representational semantics for moral and other normative predicates and providing instead a special doctrine to account for their semantics, one that does not assign them (robust) referents but that nevertheless provides a non-trivial, substantive account of their semantics, while retaining a referential semantics for (most) other predicates. The Non-Referential strategy seems to be the obvious one to take, assuming I am correct to have characterized Non-Realist Cognitivism as committed to denying that moral predicates refer (in a robust sense). As I will explain, there are various ways to take up the Non-Referential strategy, including Parfit's approach, which I will address in sections three and four. Another Non-Referential approach is expressivist, as I will explain in section five.
Second is the ‘Meinongian Strategy, ’ which I will discuss in section six. It proposes that there are special ‘irreal entities’ that serve as the referents of moral predicates but that do not exist in any robust sense. It is not clear whether postulating that there are these things is compatible with metaphysical naturalism. Nevertheless, on a Meinongian reading, Non-Realist Cognitivism postulates ontologically non-robust truth conditions for moral judgments.
Third is the option of advocating or developing some semantic theory that is congenial to non-realist construals of a variety of non-normative constructions and truths, and then applying it to moral and other normative discourse. For want of a better term, I will call this the ‘Wide Non-Realist Strategy.’ There are indeed such theories, including, most importantly, conceptual role or inferential role semantics (Harman Reference Harman1982; Wedgwood Reference Wedgwood2007; Chrisman Reference Chrisman2016). An appraisal of theories of this kind is beyond the scope of this paper, but I will address them briefly in looking at the prospects for Non-Realist Cognitivism.
Finally, there is the strategy of denying that Non-Realist Cognitivism faces a semantic problem at all, perhaps on the basis of a general rejection of semantic theorizing. On the base-line reading, the Non-Realist Cognitivist has adopted a minimalist view regarding the terms ‘true, ’ ‘fact, ’ and ‘property, ’ at least regarding moral truths. ‘Semantic Quietism, ’ as I call the position, adopts a fully minimalist view about all semantic terms and holds that this is all that needs to be said about semantics, in effect denying that the semantic terms have more robust senses. Semantic Quietism might say that, in minimalist senses, the belief that S is ‘about’ whether S; a term ‘N’ ‘refers’ to N; and so on – where we can replace ‘S’ with any meaningful declarative sentence and we can replace ‘N’ with any noun or noun phrase. The belief that Harry Potter is short is ‘about’ whether Harry Potter is short, and ‘Harry’ ‘refers’ to Harry. Semantic Quietism accordingly replaces truth-conditional semantic theory with its minimalist shadow. Yet it does have a response to the semantic challenge. It says that the belief that lying is wrong is about whether lying is wrong; that it is true just in case lying is wrong; and that ‘wrongness’ refers to wrongness – where ‘about, ’ ‘true, ’ and ‘refer, ’ are understood in minimalist senses.
Semantic Quietism renounces the need to provide a general theory of the relation between language and thought and the world. I maintain, however, that there are genuine philosophical puzzles and problems here, and that it is a mistake to ignore them. Obviously this is not the place to argue for this claim. But Semantic Quietism is a radical break with philosophical orthodoxy, and because of this, I think Non-Realist Cognitivism should avoid it. It would be a strike against Non-Realist Cognitivism if it needed to renounce semantic theorizing in order to avoid the semantic challenge.
Moreover, intuitively, it is a mistake to interpret all semantic claims in a minimalist fashion. Consider, for instance, claims in astronomy, such as that the sun is more massive than the moon. Claims of this kind have substantive, non-trivial truth conditions. They are about the stars, where, intuitively, this aboutness relation is a substantive, ‘robust’ relation that, here, takes the stars as one relatum. So, arguably, even if Non-Realist Cognitivism introduces minimalist senses of the semantic terms, it also needs to recognize robust senses of these terms in order to make sense of claims about robust semantic relations between language and the world.
It is important to distinguish Semantic Quietism from ‘Moral Quietism, ’ which we can view as an example of the Non-Referential Strategy. Moral Quietism is, or is a relative of, the view advocated by Ronald Dworkin (Reference Dworkin1996; see Enoch Reference Enoch2011, 121).Footnote 10 It does not reject semantic theorizing in general, but it uses minimalist senses of the semantic terms in accounting for moral discourse and thought, and it marries its minimalist moral semantics to a robust semantics for naturalistic discourse and thought. It says there is not a substantive, non-trivial account of the meaning of any moral term or of the truth conditions of moral claims. It says that there is a property of wrongness (in the minimal sense), where this amounts to saying that some things are or could be wrong. It says that a claim to the effect that a kind of action is wrong is true (in the minimalist sense) just in case that kind of action instantiates wrongness (in the minimalist sense), which it does just in case that kind of action is wrong. Clearly, however, an account of this kind is not explanatory and it does not provide an adequate response to the semantic challenge.Footnote 11 Its claims about the semantics of moral discourse and thought are a sophisticated form of word salad. Moral Quietism does, however, provide a benchmark against which to measure other responses to the semantic challenge. An adequate response must go beyond Moral Quietism.
If I am correct, Non-Realist Cognitivism faces a problem. To account for the semantics of moral predicates – to provide a non-trivial, substantive account of their semantics – it must choose among the Non-Referential strategy, the Meinongian strategy and the Wide Non-Realist strategy. It could instead reject the very idea of semantic theorizing by taking up Semantic Quietism, but this would mean rejecting a whole field of philosophy, and one might hope to defend Non-Realist Cognitivism without having to go this far. The Non-Referential strategy is the most conservative of the approaches, for it seeks to combine an orthodox truth-conditional semantics for non-normative thought and talk with a substantive non-referential semantics for the normative. Moral Quietism is a version of this strategy, but it only gives the appearance of answering the semantic challenge. In what follows, therefore, I turn to other versions of the Non-Referential strategy, beginning with Parfit.
3. The non-referential strategy – Parfit
Parfit holds that normative truths (in the reason-implying sense) have no ‘weighty ontological implications’ (Reference Parfit2017, 60). He acknowledges that the idea of ontological weightiness is unclear. But he claims he does not need to explain it since it is an idea of those who disagree with him and it is up to them to explain what it means (Reference Parfit2017, 60–61). This, I think, is clearly a mistake. Parfit wants to deny that there are moral properties in some ontologically weighty sense. So he cannot plausibly claim that he can ignore questions about what this means.
Parfit tries to explain what he has in mind by reference to mathematics. He says that numbers do not exist in an ontologically weighty sense and he denies that logical and modal truths correctly describe or correspond to how things are in some ‘ontologically weighty part of reality’ (Reference Parfit2017, 59). He says that ‘there is’ can be used in a ‘non-ontological sense’ as when we say there are prime numbers (Reference Parfit2017, 61). But this does not help to explain his view since philosophers of mathematics worry about how to understand its metaphysics. For every metaethical position, except expressivist theories and, perhaps, the error theory, there is a similar position in the philosophy of mathematics. It is not clear that we can understand mathematical truth in a way that has no ‘weighty ontological implications.’
It would help us to understand Parfit if we could assume that he accepts the base-line interpretation. For on this interpretation, Parfit would be saying that normative truths and mathematical truths have no ontological implications that are incompatible with metaphysical naturalism. Since he rejects normative naturalism, according to which moral and other normative predicates refer to natural properties, he would therefore to be committed, on the base-line interpretation, to accounting for the meaning of moral predicates without taking them to refer to properties – except in a minimalist sense of ‘refer’ and ‘property.’ On the base-line interpretation, recall, there are moral truths, moral facts, and moral properties, but only in ‘minimalist’ senses. Parfit would agree. But as we will see, after laying out some of Parfit's central theses and distinctions, he at one point makes a claim that seems incompatible with the base-line interpretation.
The first key to understanding Parfit's view, I believe, is his rejection of ‘Alethic Realism, ’ the thesis that ‘all true claims are made true by the way they correctly describe or correspond to how things are in some part of reality’ (Reference Parfit2017, 58) – that is, in some ontologically weighty part of reality (Reference Parfit2017, 59). As we saw, Parfit thinks that mathematical truths are not made true by correctly describing or corresponding to how things are in an ontologically weighty part of reality, and he has the corresponding view about moral and other normative truths.Footnote 12 If the natural world is all of reality in an ‘ontologically weighty’ sense, he says, then moral claims are not made true by correctly describing how things are in some part of reality so understood (Reference Parfit2017, 62). This is one key to understanding Parfit.
A second key to understanding Parfit is his account of properties in the ‘pleonastic sense’ (Reference Parfit2017, 66). Parfit holds that any (simple, subject-predicate) claim about a thing can be restated as a claim about its ‘properties’ in the pleonastic sense (Reference Parfit2017, 66). This is intended, I think, as a prosaic remark about the use of the term ‘property’ and as such it has no ontological significance in itself. In this sense, a claim about a thing's properties adds nothing to the content of a claim made by using ordinary predication (Reference Parfit2017, 66). Anyone who agrees that lying is wrong should be able to agree that lying has the ‘property’ of being wrong (in this pleonastic sense) without being thereby committed to an ontology that includes wrongness. Accordingly, Parfit's pleonastic sense of ‘property’ is what I earlier called the minimalist sense. Parfit says that he uses the term ‘property’ in this pleonastic sense (Reference Parfit2017, 66). In the pleonastic sense, given that there are simple moral truths, such as that lying is wrong, it follows that there are moral properties, such as the property wrongness. There are also, I assume, normative relations in this sense, such as the relation that holds between a fact, a person, and a kind of action when the fact is a reason for the person to do an action of that kind.
This account leaves it open, for any given predicate, whether it refers to a property in an ontologically robust sense. The claim that the Sun is massive can be restated using the term ‘property’ in the pleonastic sense, but, despite this, the predicate ‘massive’ presumably refers to an ontologically robust property. Parfit agrees that there are ontologically robust properties. He thinks that all robust properties are causal, and he explains that causal properties are ‘the features of concrete objects or events which can have causes and effects’ (Reference Parfit2017, 68). The property of being massive is an example. Parfit denies that moral properties are robust on the ground that they are not causal, but one could contest this claim, and also the conclusion Parfit draws from it that moral properties are not robust. His claim that all robust properties are causal is undefended as far as I can see.
The distinction between the pleonastic use of ‘property’ and its use to refer to ontologically robust qualities is sufficient to put Parfit's position into relief. Unfortunately, Parfit introduces two additional concepts, the concepts of a property in ‘the description-fitting sense’ and of a property in ‘the necessarily co-extensive sense.’ I believe we do best to understand these as two concepts of property individuation rather than as two new concepts of what kind of thing a property is. (Of course, an account of property individuation might have implications for what kind of thing a property is.) The distinction between these two concepts of property individuation seems to cut across the distinction between properties in the pleonastic sense and ontologically robust properties.
In the ‘the necessarily co-extensive sense’ (NCE sense), a property F is identical to a property F* just in case F and F* are necessarily co-extensive (Reference Parfit2017, 68). The NCE notion of property individuation is of doubtful utility for our purposes. Naturalists and nonnaturalists alike, provided they are consequentialists, might agree that the property wrongness is necessarily co-extensive with the property of failing to maximize the general happiness. But the nonnaturalist would insist that these properties are nevertheless numerically distinct since they have different natures. The property wrongness is normative while the property of failing to maximize the general happiness is not normative, she would claim. Parfit would say that the latter is ontologically robust whereas the former is not. To make sense of these claims, Parfit introduces the idea of property individuation in ‘the description-fitting sense’ (DF sense).
In the DF sense, we do not say that a sufficient condition of F and F* being ‘identical’ is that they are necessarily coextensive. Parfit explains that properties ‘fit’ the phrases or terms by which we refer to them and different phrases or terms can refer to the same property (Reference Parfit2017, 66–68). To be identical in the DF sense, F and F* must ‘fit’ exactly the same descriptions. That is, Parfit seems to mean, F and F* must themselves have exactly the same properties. Say that a description ‘fits’ a property just in case it ‘accurately describes’ the property. If so, then Parfit's idea seems to be that, in the DF sense, a property F is identical to a property F* just in case every expression that refers to F also refers to F*, and vice versa, and every expression that accurately describes F also accurately describes F*, and vice versa. For example, in the DF sense, the property of being luminous is identical to the property of radiating light (Reference Parfit2017, 66). Every accurate description of luminosity is also an accurate description of the property of radiating light, and vice versa.
Parfit holds that properties in the pleonastic sense are also, at least often or typically, description-fitting (Reference Parfit2017, 66). I take him to mean by this that properties in the pleonastic sense can often or typically be identified and distinguished using the DF concept of property individuation. How does this work? Note first, that to say that a property ‘is pleonastic’ is an abbreviated way of saying that there is this property in the pleonastic senses of ‘there is’ and ‘property.’ Parfit might claim, for instance, that the property of being an even number ‘is pleonastic, ’ which would be to say that there is this property in the pleonastic senses of ‘there is’ and ‘property.’ And to say this would be to say, in plain terms, merely that something (a number) is or could be even. Now the property of being even is identical in the DF sense to the property of being exactly divisible by 2. That is, every expression that refers to the one property also refers to the other, and vice versa, and every expression that accurately describes the one also accurately describes the other, and vice versa. Since of course, for Parfit, there is the property of being even only in pleonastic senses of ‘there is’ and ‘property, ’ the claim that this property can be ‘referred to’ and ‘accurately described’ presumably must also be understood in pleonastic or minimalist senses of ‘refers’ and ‘accurately describes’ (or ‘fits’). In general, then, if F is a property in the pleonastic sense, then it is identical in the DF sense to a property F* just in case, in pleonastic senses of the quoted terms, every expression that ‘refers to’ F also ‘refers to’ F*, and vice versa, and every expression that ‘accurately describes’ F also ‘accurately describes’ F*, and vice versa.Footnote 13
In denying normative naturalism, Parfit has in mind the DF sense of property individuation. Consider non-analytic naturalism, according to which our normative concepts refer to natural properties even though they cannot be reduced to or analyzed in terms of naturalistic non-normative concepts (Reference Parfit2017, 57, 70). A non-analytic naturalist who is a consequentialist might claim that the concept of wrongness refers to the property of failing to maximize the general happiness. Parfit denies that such a view could be correct.Footnote 14 As we saw, he holds that the property of wrongness is not ontologically robust, so it is not identical (in the DF sense) to any robust naturalistic property (Reference Parfit2017, 71–72).
I am now in a position to return to the question whether Parfit accepts the base-line reading of Non-Realist Cognitivism. There is evidence to the contrary. For Parfit wants to say that some moral claims are true in some more-than-minimal sense, a ‘strong Cognitivist sense’ that would explain how, in making a moral claim, we might be ‘getting it right’ (Reference Parfit2017, 195). We could perhaps interpret ‘getting it right’ in a minimalist sense, but this would not give us a more-than-minimal sense in which moral claims would be true.
I do not see how a more-than-minimal notion of moral truth is compatible with the key features of Parfit's view: his rejection of Alethic Realism for the case of moral claims, his idea that moral properties exist only in a pleonastic sense, and his claim that the existence of moral truths has no robust ontological implications. What, then, might explain Parfit's idea that some moral claims are true in a more-than-minimal sense?
Parfit doesn’t explain his remark but I speculate that it might reflect a confusion between the claim (1) that properties in the pleonastic sense are also description-fitting and the claim (2) that properties in the pleonastic sense exist in some more-than-minimal but less-than-robust sense. On Parfit's account, to say that a property F in the pleonastic sense is description-fitting does not add anything more-than-minimal to the claim that F is a property in the pleonastic sense. For, on his account, to say that a property F in the pleonastic sense is description-fitting is simply to say (a) that some things are or could be F – for this is what the existence of the property comes to, in the pleonastic sense – and (b) there are (or could be) expressions that ‘refer to’ or ‘accurately describe’ F, in pleonastic senses of the terms – for this is what it is for F to be description-fitting. In a case in which F is a property merely in the pleonastic sense, there is no ontological significance to this. So the idea that moral properties are pleonastic and also description fitting is compatible with supposing that Parfit accepts the base-line view.
Given all of this, I think we can conclude, albeit cautiously, that Parfit's view fits the base-line view. There are moral truths, moral facts and moral properties, but only in ‘minimalist’ or ‘pleonastic’ senses of the relevant terms. So understood, the claim that there are moral truths, moral facts, and moral properties, has no ontological implications, so it is compatible with metaphysical naturalism. Yet the moral truths, moral facts, and moral properties are not natural ones.
4. The semantic challenge revisited
Parfit is explicit in denying that a true moral claim is true in virtue of its referring to or correctly describing some (ontologically robust) aspect of reality. And he denies that there are ontologically robust moral properties to which moral predicates or concepts refer. They do ‘refer’ in the pleonastic sense to ‘properties’ in the pleonastic sense but this is verbal legerdemain. It amounts simply to saying that there are true moral claims such as that lying is wrong. It is of no help in explaining what the claim that lying is wrong is about or what could make it true. It is of no help in explaining the semantic value of moral predicates. The non-referential strategy was to abandon a robust referential or representational semantics for moral predicates but to offer instead a substantive, non-trivial account of their meaning and of the truth conditions of moral claims. Parfit does not seem to offer such an account. It is not clear that his account goes beyond Moral Minimalism.
Parfit is clearly committed to abandoning a (robustly) referential account of the semantics of moral predicates. He denies that moral predicates refer to natural properties, and, given his view that moral truths have no ‘weighty ontological implications, ’ he is committed to denying that moral predicates refer to any robust properties. Indeed, on the base-line interpretation, he holds that the only robust properties are natural ones. Accordingly, he is committed to denying that moral predicates refer to ontologically robust properties. And moral properties in the pleonastic sense are not suited to figure as the semantic values or referents of moral predicates, for they are merely shadows of the moral predicates.
Parfit ought to accept the terms of this challenge, for at one point he recognizes that quasi-realist expressivism faces an analogous challenge. He says that expressivism lacks a non-trivial account of the truth conditions of moral claims. It lacks an answer to the question, What would it be for an action to be wrong? (Parfit Reference Parfit2017, 166). Parfit claims that his view can answer this question. In his view, he says, the claim that an act is ‘wrong’ means that everyone has ‘morally decisive reasons not to act in this way’ (Reference Parfit2017, 166–167). But this account merely moves the goal posts without changing the nature of the game. Before we asked, What is it for an action to be wrong? Now we ask, What is it for there to be a morally decisive reason not to do something? In the pleonastic sense, there is a ‘property’ or ‘relation’ of being a morally decisive reason, but this is unhelpful, as we saw in discussing Moral Minimalism.
Parfit could perhaps try to answer the challenge by invoking the idea that a moral claim is ‘non-causally made to be true’ by certain relevant reason-giving natural facts. For an action to be wrong, he might say, is for relevant natural facts to non-causally make it to be true that the action is wrong, or that there are decisive reasons not to do it. For instance, the claim that lying is wrong is non-causally made to be true by the natural facts about lying in virtue of which it is wrong – according to the best moral theory (Reference Parfit2017, 78–79). This non-causal making-true relation is primitive and undefined in Parfit's account, but this is not a problem. Every moral theory needs to postulate this relation. And the fact that it is primitive and undefined does not distinguish it from the relation of reference, which is deployed in truth-conditional semantic theories. It is typically left as primitive and undefined.
The problem, however, is that the non-causal making-true relation is supposed to relate natural facts to normative truths. The natural facts are robust facts or states of affairs such as the fact that hitting you over the head with a crowbar will cause you pain. According to Parfit, however, the normative truths are sentences or propositions that do not refer to or describe any ontologically robust facts, and that are true, if they are true, only in a minimalist sense of ‘true.’ Assuming Parfit is correct about this for the sake of argument, then in what sense could a natural fact make a normative sentence or proposition be true? On a minimalist account of the meaning of ‘true, ’ there is no (robust) property a sentence or proposition can have of being true; to call something true is simply a way of expressing acceptance of it. Consider then the claim that the fact that hitting you over the head will cause you pain makes it be true that it would be wrong to hit you over the head. This claim can only be understood, it seems to me, as a way of expressing acceptance of a claim to the effect that it would be wrong to hit you over the head because doing so would cause you pain. And since this is a normative claim, if it is true, it is true only in a minimalist sense. It seems, then, that invoking the non-causal makes-true relation does not help address the semantic challenge. We can agree with Parfit that there are natural facts about crowbars and human heads that non-causally make it be true that it would be wrong to hit you over the head with a crowbar. What this comes to, on Parfit's account, is that, in light of these facts about crowbars and heads, we are prepared to affirm that it would be wrong to hit you over the head with a crowbar. This does not provide us with an account of what this claim is about. It does not explain what we are affirming.
In short, the non-causal making-true relation is not, and cannot serve as, a semantic relation. This is because the idea that there is this relation presupposes that moral predicates and sentences are meaningful, such that they are candidates for ‘being true, ’ and, such that, when we think a moral sentence stands in the non-causal making-true relation to a natural fact, we can coherently think it is true.Footnote 15 To adequately address the semantic challenge, then, Parfit's story needs to be supplemented. I can see two ways of doing this that appear compatible with Non-Realist Cognitivism.
First, we can introduce a notion of licensing assertions. For instance, we might say, the facts about the crowbar together with the nature of the non-causal making-true relation license asserting the sentence, ‘Hitting you with the crowbar would be wrong.’ The trouble is that the kind of licensing we are looking for is a licensing to assert a sentence in virtue of its truth. There can be things I am licensed to assert in virtue of their being polite, such as ‘I apologize.’ There are things I might be licensed to assert in virtue of being an owner of a boat, such as ‘This boat is now the Santa Maria.’ But Parfit needs an account that elucidates the licensing of a person to assert a sentence due to its truth, not to anything else.
Second, we could perhaps try to use the idea of a concept to leverage an account. We could say that the non-causal making-true relation holds, when it does, in virtue of the nature of the relevant concepts.Footnote 16 On this view, for instance, given the concept of wrongness, and given that lying ‘falls under’ the concept, the sentence ‘Lying is wrong’ is true. The central problem with this move is that Non-Realist Cognitivism gives us no account of what this concept is about. We can say that lying ‘falls under’ the concept wrongness just in case lying is wrong, but this is trivial. That is, the semantic challenge simply reappears as a challenge to explain what the moral concepts are about.
Perhaps it will be useful at this point to compare Non-Realist Cognitivism – assuming the base-line interpretation, and assuming the non-relational strategy for addressing the semantic challenge – with non-analtyic normative naturalism. The non-analytic naturalist agrees with Non-Realist Cognitivism that the concept of wrongness is a concept with a nonnatural content. She holds, however, that this concept and the predicate ‘wrong’ refer to the property of wrongness, which is an ontologically robust natural property. Non-Realist Cognitivism, on the suggested interpretation, denies this. It says that the property of wrongness exists only in a pleonastic sense and it insists that this property is not a natural one. It may seem that Non-Realist Cognitivism is the simpler view since it does not postulate an ontologically robust property of wrongness. Yet, for the naturalist, the property of wrongness is identical to some natural property that Non-Realist Cognitivism would also acknowledge to exist. So there is no gain in simplicity. The advantage of the naturalist view is that it has is a substantive account of the semantics of moral predicates and concepts, of what moral beliefs are about, and of their truth conditions. Non-Realist Cognitivism, if it follows Parfit, has no such account.
5. The non-referential strategy – expressivism
Metaethical expressivism claims to provide exactly what the Non-Referential strategy calls for: a substantive, non-trivial doctrine that purports to account for the meaning of moral and other normative predicates without assigning them referents, except perhaps in a minimalist sense. One might therefore seek to combine Non-Realist Cognitivism with metaethical expressivism. Orthodox, old-fashioned metaethical expressivism is non-cognitivist, of course, but contemporary quasi-realist expressivism seeks to treat moral judgment as a kind of belief, so it is not merely Quixotic to combine quasi-realist expressivism with Non-Realist Cognitivism. Parfit objects at one point that quasi-realist expressivism lacks a non-trivial account of the truth conditions of moral claims (Parfit Reference Parfit2017, 170–171), but he suggests at another point that quasi-realist expressivism could be developed in such a way that the result would be a version of Non-Realist Cognitivism (Parfit Reference Parfit2017, 193).
Expressivism is a theory of both moral thought and discourse. In its account of moral discourse, it treats moral predicates as having the semantic role of expressing motivational states of mind, such as approval or disapproval or the acceptance of a plan, rather than the role of referring to properties (except perhaps in a minimal sense). It treats the meaning of a moral predicate as a function of the kind of state of mind that is its semantic role to express. In its account of moral thought, it holds that moral judgments are at least partly constituted by motivational states of mind. These states of mind might be characterized as beliefs, yet if so, they are beliefs that do not represent states of affairs (Gibbard Reference Gibbard1990, 7–8; Blackburn Reference Blackburn and Copp2006).
We can use Blackburn's ‘quasi-realism’ to illustrate the basic ideas. According to Blackburn, moral judgments are correctly described as beliefs, yet they do not ‘represent’ states of affairs. Since they are non-representational, they are different in nature from ordinary descriptive non-moral beliefs. For example, a moral belief, such as the belief that lying is wrong, does not represent lying as having a property that would be countenanced in a correct ontology. Yet, for Blackburn, there are moral properties in minimal senses of ‘there are’ and ‘property’ (Blackburn Reference Blackburn and Copp2006). And of course anyone engaged in moral thought could properly affirm that there is such a thing as wrongness.
Expressivist theories such as Blackburn's do therefore echo the base-line reading of Non-Realist Cognitivism, but they are not congenial to the picture that seems to be shared by Non-Realist Cognitivists. Blackburn holds, for example, that the meaning of ‘wrong’ is a function of the ‘stance’ of disapproval – or something like disapproval – that is expressed by the assertion of subject-predicate sentences in which a kind of action is said ‘to be wrong.’ Furthermore, Blackburn takes it that moral judgment has a characteristic action-guiding role that ordinary cognitive states of mind do not have. So he sees moral belief as a different kind of belief from ordinary descriptive belief. Non-Realist Cognitivism does not share this picture. It takes from orthodox nonnaturalism an orthodox cognitivist view of moral judgment. It does not view moral belief as partly constituted by motivational states. The problem is that it is completely unclear how a moral judgment, such as the belief that lying is wrong, can be the kind of state that orthodox nonnaturalism takes it to be if there is no property ‘in-the-world’ to which ‘wrong’ refers, such that the belief could represent lying as having that property.
To summarize, quasi-realist expressivism could be developed, or viewed, as a version of Non-Realist Cognitivism. As such it would answer the semantic challenge to Non-Realist Cognitivism by proposing a substantive yet non-referential semantics for moral predicates. The resulting view would be a significant departure from orthodox nonnaturalism, however, one that would go well beyond a simple denial of orthodox nonnaturalism's view that there are ontologically robust, nonnatural moral properties. Because of this, I think it would be confusing to view quasi-realist expressivism as a version of Non-Realist Cognitivism.
6. The Meinongian strategy
The Meinongian strategy is to postulate ‘Meinongian, non-existent’ properties to serve as the referents of moral predicates (Reicher Reference Reicher and Zalta2016). According to this strategy, these properties do not exist in any robust sense of ‘exist, ’ but nevertheless there are these properties in some not-merely-minimal sense of the relevant terms. The Meinongian strategy represents a departure from Non-Realist Cognitivism, on the base-line interpretation. For, on the base-line interpretation, Non-Realist Cognitivism says that it is only in a minimal sense that there are moral properties. Meinongianism denies this. Further, on the base-line interpretation, Non-Realist Cognitivism is compatible with metaphysical naturalism. It is unclear whether Meinongianism is compatible with metaphysical naturalism, for it is unclear what it means for moral properties to have being in some not-merely-minimal sense even though they do not exist. Despite these issues, the strategy arguably remains true to the intent of Non-Realist Cognitivism, for it postulates ontologically non-robust truth conditions for moral judgments.
Parfit can perhaps be interpreted as a Meinongian. He wants to say that some moral claims are true in a more-than-minimal sense, such that a moral claim might be ‘getting it right’ (Reference Parfit2017, 195). On a Meinongian reading, Non-Realist Cognitivism would hold that, although moral properties do not exist, there are these properties in some more-than-minimal sense. There is wrongness, available to be instantiated, even though it does not exist. This claim is undeniably mysterious, but it would apparently allow a Meinongian to hold that moral claims can be true in some more-than-minimal sense.
Skorupski contends that there are moral properties – or ‘reason relations’ – and there are moral truths – or truths about reason relations – but there being such things does not imply that they exist (Reference Skorupski2010, 428).Footnote 17 ‘To exist is to have causal standing, ’ Skorupski says, but there is much in reality that does not exist in this sense (Reference Skorupski2010, 428). There are numbers, for example, and there are fictional people, such as Harry Potter, but neither numbers nor Harry exist. Skorupski insists that he is not merely stipulating that only entities with causal roles shall be said to ‘exist’ (Reference Skorupski2010, 439). Rather, he says, his claim is synthetic (Reference Skorupski2010, 428). There are the things that are referred to by true claims of any kind, but not all things so referred to exist. Fictional entities and numbers do not exist, although there are such things. They are ‘irreal objects’ (Reference Skorupski2010, 137, 423).
Skorupski's position seems to hover uneasily between a view that treats moral properties as having the same ontological status as fictional properties, and a view that treats them as having the same ontological status as (other) existing properties, although they lack a causal role. The former view is a kind of moral fictionalism. The latter view is merely a notational variant of orthodox nonnaturalism. Of course, Skorupski wants to reject both horns of this dilemma.
Metaphysicians and philosophers of language have developed Meinongian theories to address problems that face truth-conditional semantics, such as the problem of negative existence claims and the problem of fictional discourse (Reicher Reference Reicher and Zalta2016). As such, Meinongian theories do not mesh well with the goals of Non-Realist Cognitivism, for Non-Realist Cognitivism does not want to treat wrongness as on a par with fictional properties. Skorupski thinks he can avoid fictionalism since, in his view, fictional truths, such as those having to do with the properties of Harry Potter's wizards, are ‘mind-dependent, ’ whereas moral truths are ‘mind-independent’ (Reference Skorupski2010, 439). Unlike fictional properties, moral properties are ‘objective irreals’ (Reference Skorupski2010, 420). Skorupski seeks to explain this on the basis that fundamental normative principles are synthetic a priori (Reference Skorupski2010, 428, 137). Yet even if we accept this epistemological thesis for the sake of argument, it is not clear how it enables Skorupski to avoid fictionalism, at least if we understand fictionalism as a metaphysical view. For it remains that, on his view, moral properties are metaphysically akin to fictional properties in that they are irreal objects.
Even if Skorupski can avoid fictionalism, it is not clear how he can avoid the charge that his view amounts to a reformulation of orthodox nonnaturalism. The main problem is that it is not clear what difference there is supposed to be between objective irreality and existence. Skorupski holds that only entities with causal roles exist, but he insists that this is neither a stipulation nor an analytic truth (Reference Skorupski2010, 428, 439), so there remains the question what difference there is between objective irreality and existence. Skorupski explains that propositions about objective irreals are not ‘factual’ whereas propositions about existing things are factual (Reference Skorupski2010, 8, 137). But even if the non-factuality of propositions about objective irreals follows from the latter's non-existence, this does not explain what it is for these things to be objectively irreal. Skorupski holds, as we saw, that propositions about objective irreals are synthetic a priori (Reference Skorupski2010, 137). But even if this explains the difference between objective irreals and mind-dependent irreals, it does not explain in what sense something that does not exist can have being. So it is not clear how Skorupski can avoid the charge that, if his view is not a form of fictionalism, it is merely a notational variant of orthodox nonnaturalism.
Even if we waive these worries, it is not clear how, on a Meinongian reading, Non-Realist Cognitivism avoids the familiar objections to orthodox nonnaturalism. These objections seem to have nothing to do with whether moral properties exist or instead are merely ‘objectively irreal.’
The fundamental problem with the Meinongian strategy is that it is unclear what distinguishes things that exist from things that do not exist but are. If Non-Realist Cognitivism is going to help itself to the Meinongian strategy, it will need to explain this, and explain how it avoids fictionalism, while at the same time avoiding the familiar objections to orthodox nonnaturalism.Footnote 18
7. Conclusion
Avant-garde nonnaturalism attempts to avoid the familiar challenges to orthodox nonnaturalism by eschewing robust metaphysical commitments. Non-Realist Cognitivism is one such position. It holds that there are moral truths, properties, and facts, but only in minimalist senses of the relevant terms. I contend that this view faces the challenge of explaining both what moral judgments are about, and what their truth conditions are. On a familiar intuitive referential or representational semantics, the semantic value of a predicate is, or determines, the property to which the predicate refers. According to Non-Realist Cognitivism on the base-line reading, however, moral predicates do not have robust referents. Non-Realist Cognitivism says that ‘wrong’ refers to a property in the minimalist sense, but this is just to say that some things are or might be wrong. It presupposes that ‘wrong’ is a meaningful predicate without telling us anything about its meaning.
I have considered a number of strategies that Non-Realist Cognitivism might pursue in an attempt to address this challenge. I focused mainly on Parfit's version of the Non-Referential Strategy and I argued that Parfit's view is unable to account for the meaning of moral predicates and moral sentences. I briefly considered an expressivist variant of the Non-Referential strategy, as illustrated by quasi-realist expressivism. The trouble is that expressivist accounts of moral judgment sit uneasily with Non-Realist Cognitivism. I also considered a Meinongian strategy, according to which there are special non-existent Meinongian entities that serve as the referents of moral predicates. The central weakness of this approach is the obscurity of its basic idea.
There remains one option that I identified early in the paper but have not yet discussed, the so-called Wide Non-Realist Strategy. This is the strategy of proposing or developing a semantic theory that is congenial to non-realist construals of a variety of non-normative constructions and truths, and then applying it to moral and other normative discourse. Consider, for example, conceptual role semantics (Harman Reference Harman1982; Wedgwood Reference Wedgwood2007; Chrisman Reference Chrisman2016). Obviously I cannot go into detail here, but the central idea, crudely, is that the ‘role’ of a concept in our thought and talk determines its semantic content as well as the semantic content of the term that expresses the concept. The import of such a view for metaethics depends crucially, of course, on what one takes to be the relevant conceptual roles. As Matthew Chrisman points out, conceptual role semantics is compatible with expressivism, but it is also compatible with moral naturalism as well as orthodox nonnaturalism (Chrisman Reference Chrisman, McPherson and Plunkett2017; see Loewer Reference Loewer1982; Wedgwood Reference Wedgwood2007). Further, it is compatible with the kind of hybrid moral naturalism that I have proposed. In my view, if it is read as a version of conceptual role theory, the fundamental characteristic role of moral and other normative concepts determines that these concepts, and the predicates that we use to express them, refer to robust natural properties while also figuring in judgments that characteristically motivate action (Copp Reference Copp2017b). For present purposes, however, the important point is that conceptual role semantics might be able to support a non-realist view that is congenial to Non-Realist Cognitivism. For instance, Chrisman (Reference Chrisman2016) proposes that ‘ought’ plays the role of a sentential operator, as in the sentence, ‘It ought to be that I tell the truth.’ And he suggests that ‘ought’ in such contexts neither refers to a property of actions, nor to a relation between actions and agents, nor does it express a motivating attitude. So his approach seems to mesh nicely with a non-realist yet cognitivist view. As Chrisman concedes, however, it is unclear whether this approach can be extended to all moral terms (Chrisman Reference Chrisman, McPherson and Plunkett2017). I mention it as an example of a way in which the Wide Non-Realist Strategy could be pursued.
The fundamental problem is to explain the semantics of moral terms and concepts – what moral talk and thought are about – while denying that there are any robust moral properties, and without compromising the goal of avant-garde nonnaturalism, which is to retain an orthodox cognitivist position while rejecting orthodox nonnaturalism, normative naturalism, fictionalism, and the error theory. Non-Realist Cognitivism can explain what moral thought and talk are about in a minimalist sense of ‘about.’ It can say, for example, that the claim that lying is wrong is about whether lying is wrong. But this is trivial when understood in a minimalist sense. What we need, and what Non-Realist Cognitivism may be unable to deliver, is a substantive, non-trivial, and philosophically interesting account. The best chance of achieving this, in my view, is to pursue the Wide Non-Realist Strategy, yet it remains to be seen where this approach will lead.
Disclosure statement
No potential conflict of interest was reported by the author.
Acknowledgement
A version of this paper was presented to the 2017 Vancouver conference on Representation and Evaluation, and I am grateful to all the participants for their helpful comments and suggestions. Mark van Roojen presented enormously helpful comments to the conference. I am also very grateful for extended conversations and, in some cases, written comments, with and from Matt Bedke, Matthew Chrisman, Jamie Dreier, Tyrus Fischer, Josh Gert, Anandi Hattiangati, Diego Machuca, Kian Mintz-Woo, Laura Schroeter, François Schroeter and Stefan Sciaraffa. I apologize to those I have forgotten to mention.
