The Journal of Value Inquiry

, Volume 47, Issue 4, pp 359–374 | Cite as

Ethical Anti-Archimedeanism and Moral Error Theory



Moral Judgment Error Theorist Moral Property Moral Realism Moral Fact 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

1 Introduction

Moral error theory has been criticized from many perspectives. Some argue that it fails to do justice to ordinary moral discourse, because its diagnosis of deep-seated error is misguided.1 Others accept the diagnosis of error but endorse an alternative theory such as moral fictionalism.2 Mackie worried that his theory might be taken to have “pernicious” moral upshots.3 But even the staunchest critics rarely dispute Mackie’s contention that the error theory is a purely second-order metaethical doctrine that does not depend on any substantive moral claims.4 That is so because most philosophers are, like Mackie, ethical Archimedeans.

In recent years, a new challenge to error theory has emerged from an anti-Archimedean perspective that disavows Mackie’s starting point. Anti-Archimedeans believe that all metaethical truths are substantive moral truths. There is nowhere to stand outside of ethics to justify metaethical theses.5 If so, the new worry for error theorists is not that their doctrine is false or pernicious, but the more awkward problem that certain arguments in favor of error theory may be self-contradictory.

The charge of self-contradictoriness has been leveled most forcefully by Ronald Dworkin, who refers to error theory as “external skepticism.” “[M]oral skepticism is itself a moral position…If it is true, then external skepticism defeats itself.”6 Unfortunately, Dworkin has failed to make a sufficiently strong case for these claims. His prose is sometimes imprecise and elliptical, and he never systematized his numerous arguments. His underdeveloped critique has left unanswered questions and resulted in misunderstandings of anti-Archimedean commitments. Nonetheless, Dworkin’s texts contain the basic insights and building blocks for a telling critique of the error theory, centered on the charge of self-contradiction.

Two leading error theorists – Charles Pigden and Jonas Olson – have recently proposed similar rebuttals to Dworkin’s charges.7 Those rebuttals, however, miss their mark. They misinterpret Dworkin’s claims and fail to engage with his real complaints. This article aims to set the record straight in two respects. First, it will seek to correct misapprehensions that arose partly through Dworkin’s imprecisions. Second, it will re-formulate the self-contradictoriness critique in a new and more rigorous way, yet without departing from Dworkin’s core pronouncements. Any fruitful debate between error theorists and anti-Archimedeans must begin with an accurate presentation of the competing positions.

This article discusses self-contradictoriness in relation to just one error-theoretical argument: the metaphysical argument from queerness. To begin with, some ground-clearing is needed. Pigden’s and Olson’s position is summarized in Section 2. Dworkin’s stance is clarified in Section 3; whatever its defects, it is not wedded to the tenets that Pigden and Olson attribute to Dworkin. Taken together, Sections 2 and 3 reveal that the central point of contention identified by Pigden and Olson is in fact a point of convergence. Finally, a series of arguments in support of Dworkin’s critique of the error theory is developed in Sections 48. Although those arguments depart in certain ways from Dworkin’s articulated positions, they hew to his basic theses.

2 Pigden’s and Olson’s Gloss

Pigden and Olson are correct that anti-Archimedeans wish to single out first-order moral theses to which error theorists must commit themselves.8 Both philosophers, however, misapprehend which theses anti-Archimedeans concentrate on. Consider:
  1. (A)

    Acts of torture-for-pleasure are wrong.

  2. (B)

    It is not the case that acts of torture-for-pleasure are wrong.

  3. (C)

    Acts of torture-for-pleasure are permissible.

By Pigden’s and Olson’s lights, anti-Archimedeans affirm an entailment relation: (B) entails (C). In that case, denying this entailment becomes the error theorists’ chief task. For, if they assert that (A) is false and (B) is true, then – if (B) entails (C) – they would also be committed to the truth of (C). Error theorists would thereby contradict themselves, because (C) is a first-order thesis. This is the threat posed by Pigden’s Reinforced Doppelganger Problem, which hinges on two (RD) Principles:9
  • 1. “(RD1) ‘It is not the case that action X is wrong’ entails ‘action X is right [permissible].’”

  • 2. “(RD2) ‘It is not the case that action X is right [permissible]’ entails ‘action X is wrong.’”

Referring directly to Dworkin, Pigden writes: “It is perhaps worth stressing that the RD principles are not analytic since another famous attempt to refute the error theory…rests on the claim that they are.”10
Olson tackles the same entailment relation. If (RD1) and (RD2) were true, then, beyond being committed to (C), error theorists would have to endorse (C′):
  • (A′) Acts of torture-for-pleasure are permissible.

  • (B′) It is not the case that acts of torture-for-pleasure are permissible.

  • (C′) Acts of torture-for-pleasure are impermissible.

Noting that (C) and (C′) are in contradiction, Olson writes: “Ronald Dworkin has argued that this demonstrates the impossibility, indeed the incoherence of” external skepticism.11

After outlining what they see as Dworkin’s challenge, Pigden and Olson argue for what can be called the No Entailment Thesis:

No Entailment Thesis

(RD1) and (RD2) are false.12

Having defended this Thesis, Pigden and Olson take themselves to have defused the anti-Archimedean challenge, which, on their view, depends on the correctness of (RD1) and (RD2).

3 Dworkin’s Position

Pigden and Olson are exactly right to reject (RD1) and (RD2). Those theses are indefensible. As Pigden correctly observes, “the fact that something is not forbidden does not entail that it is permitted.”13 No tenable anti-Archimedean indictment of error theory should draw on (RD1) or (RD2). Alongside error theorists, Anti-Archimedeans can and should affirm the No Entailment Thesis.

If so, has Dworkin’s critique badly misfired? The answer is negative, because Dworkin should not be read as endorsing the Reinforced Doppelganger Principles in the first place. To be sure, Dworkin at times appears to endorse such principles. But – appearances to the contrary notwithstanding – the best interpretation of his position is that he affirms the No Entailment Thesis. The right lesson is not that Dworkin’s argument fails, but that Pigden and Olson have been battling a straw man. To be sure, error theorists can take issue with the dearth of precision and rigor in Dworkin’s work; those defects are remedied in Sections 48 below. But before doing so, a brief exegesis of Dworkin’s texts is warranted to substantiate the preceding claims.

Considerable evidence points away from Dworkin’s acceptance of (RD1) and (RD2). If Dworkin were to affirm those tenets, he would have to interpret the following thesis about indeterminacy as being incoherent: φ-ing is not required nor prohibited nor permissible. Yet, as his writings amply attest, he accepts that such a claim can be coherent in the moral domain. His main message is that indeterminacy is not a default position. It calls for substantive moral backing. Of course, error theorists believe that moral properties are determinately non-existent rather than indeterminate. Still, Dworkin’s stance on indeterminacy is relevant, because it touches on the claim that abortion, for example, is neither prohibited nor permissible. Dworkin emphasizes that this is an intelligible but morally engaged stance:

A belief in indeterminacy is a positive claim, and it needs a positive reason or assumption to support it…If (as a matter of their ordinary, everyday moral convictions) one person holds that abortion is wicked, a second that it is not, and a third that the issue is indeterminate, there are three, not two, substantive positions in the field, and a fourth-party observer needs as much or as little argument for siding with any one of the three as with either of the others.14

Just as the proposition that abortion is neither prohibited nor permissible is morally engaged, thinks Dworkin, so too is the error theorist’s position that countless actions and states of affairs are not endowed with any moral properties whatever.
Pigden errs in attributing (RD1) to Dworkin when paraphrasing the latter’s position:

You can’t be a skeptic about all moral claims, since if you think that abortion is not wrong – or if you think that it is not full-bloodedly true that abortion is wrong – you are committed to the first-order view that abortion is morally permissible. But that only holds if you subscribe to something like (RD1).15

Dworkin actually writes:

If the further claim that abortion is really or objectively wrong means that it is wrong even when and where people do not think it wrong, and the archimedean denies that further claim, he is endorsing the negative moral judgment that there is no moral objection to abortion in societies in which it is approved.16

Everything turns on how the phrase “no moral objection” is understood. As indicated in note 12 above, in everyday usage “not wrong” entails “permissible,” and “permissible” entails “not wrong.” If Dworkin’s phrase is uncharitably construed to mean the equivalent of “not wrong,” it would follow that he endorses (RD1). But there is no good reason to opt for this uncharitable reading, either on narrowly textual grounds or in the wider context of Dworkin’s oeuvre. After all, Dworkin makes no mention of permissibility. Yet he could easily have written: ‘[H]e is endorsing the positive moral judgment that abortion is permissible.’ This formulation would have been precisely in keeping with the views of a proponent of (RD) Principles. What Dworkin actually writes tallies with the No Entailment Thesis, when “no moral objection” is taken to mean: ‘It is not the case that abortion is wrong in Society S.’17 This formulation – as the No Entailment Thesis rightly maintains – does not entail that abortion is permissible in Society S (its moral status might be indeterminate, for example).

A different question now arises: Can the proposition, ‘It is not the case that abortion is wrong in Society S’ be read as anything other than a first-order moral tenet, or what Dworkin calls a “negative moral judgment”? (Obviously, an empirical reading of that statement – which would amount to a report that most members of Society S do not regard abortion as wrong – is set aside here.) This question captures the core dispute between error theorists and anti-Archimedeans. It ultimately rests on a disagreement over the nature of moral properties, discussed in Section 4. What matters here is that – although Dworkin answers the aforementioned question negatively – it fails to follow that he must accept (RD) Principles. The anti-Archimedean complaint against the error theory rests on other grounds.

A couple of Dworkin’s latest statements might be read as supportive of (RD1) and (RD2). The published version of Justice for Hedgehogs, as well as a draft, include such comments.18 Further, in a recent Symposium on that book, Dworkin calls the view that abortion “is neither required nor forbidden nor permissible” “unintelligible.”19 This remark may suggest that he regards claims of indeterminacy as “unintelligible.” But there is good reason to resist this inference. After describing the same proposition about abortion as “mysterious”20 in Justice for Hedgehogs, two pages later Dworkin weighs the possibility that it is a claim of indeterminacy. If so, he writes, the “position is now obviously a substantive moral claim.”21 There is no hint in that discussion that ascriptions of indeterminacy are unintelligible. As an anti-Archimedean, Dworkin has no reason for doubting the intelligibility of the aforementioned claim about abortion. Whether or not that claim is morally tenable is another matter. In light of Dworkin’s wide-ranging remarks across multiple publications, his fleeting comment about unintelligibility may be an oversight. A charitable and plausible interpretation of Dworkin’s overall position is that he accepts the No Entailment Thesis. In any event, Pigden and Olson adduce no evidence to the contrary.

4 The Anti-Archimedean Challenge to Moral Error Theory

If – pace Pigden and Olson – Dworkin accepts the No Entailment Thesis, how can he level the charge of self-contradictoriness without invoking the (RD) Principles?22 To answer this question, the argument from metaphysical queerness is addressed in detail in Sections 48. Most important, what exactly does the charge of self-contradictoriness amount to? The claim here is that error theorists confront the following crux: An argument from metaphysical queerness will violate Hume’s Law and therefore be fallacious, or its conclusion will be inconsistent with at least one of its premises, or it will damagingly beg the question. Because behind every logical inconsistency lies a contradiction, we can continue speaking about a contradiction. The relevant contradictory tenets are as follows:
  • (X) It is not the case that any non-negative moral facts exist.

  • (Y) There exists at least one non-negative moral fact.

The price of making a suitably formulated argument from queerness that has (X) as its conclusion and abides by Hume’s Law is a commitment to (Y), leading to self-contradiction.

Why must error theorists affirm (Y) if their argument is to satisfy Hume’s Law? The answer emerges from a consideration of two related issues: (i) What is the nature of moral properties? (ii) What is the status of one’s answer to (i) – is it an austerely conceptual thesis or a substantively engaged thesis? Anti-Archimedeans and error theorists diverge sharply on these matters. Against the backdrop of dissensus explored below, three points of convergence should be emphasized at the outset: acceptance of the No Entailment Thesis, endorsement of Hume’s Law,23 and rejection of Archimedean varieties of robust, non-naturalistic moral realism.

The Robust Thesis – which encapsulates error theorists’ commitment to a non-minimalistic moral ontology – is introduced in Section 5. The anti-Archimedean perspective on the Robust Thesis is then laid out. It is argued in Section 6 that error theorists beg the question against anti-Archimedeans by insisting on an austerely conceptual reading of that Thesis. Of course, even if error theorists beg the question, it fails to follow that the argument from queerness is self-contradictory. That case is made in Section 7. An additional formulation of the error-theoretic argument that is not discussed elsewhere in the article is explored in Section 8.

5 The Robust Thesis

Whereas anti-Archimedeans opt for a minimalistic account of moral ontology, error theorists reject this account. Developing a full-fledged theory of moral properties is beyond the scope of this article. Instead, a pithy summary by Simon Blackburn suffices for present purposes: “One is talking of moral properties only in a minimalist spirit, of course: the propositional surface of the discourse means that we have moral predicates, and where we have predicates we ascend to properties.”24 Those who consider an account of moral properties along these lines to be inadequate will instead favor some non-minimalistic moral ontology.

Commenting on minimalism about truth, Pigden writes: “I am both a descriptivist and an error theorist. I think moral judgements are truth-apt and that the truth they are apt for is a full-blooded affair[,] not the namby-pamby minimalist property beloved by Horwich (1998) and Blackburn (1993).”25 In light of these and other remarks by Pigden,26 error theorists appear to endorse a subjunctive conditional that shall be dubbed the Robust Thesis:

Robust Thesis

If moral properties were to exist, they would have a more robust metaphysical grounding than is envisaged by minimalism about moral properties and facts.

Is the Robust Thesis true? As a separate matter, is the Robust Thesis anything other than a morally engaged thesis? The anti-Archimedean answer to these questions is first addressed below, followed by a discussion of the error theorists’ contrasting perspective.

On an anti-Archimedean view, the Robust Thesis is best interpreted as a subjunctive version of what Dworkin has derisively called the ‘moral field thesis.’ According to that thesis, there exist “special particles whose configuration might make it true that people should not torture babies and that optional military invasions seeking regime change are immoral.”27 Error theorists, writes Dworkin, “might then declare that because there are no moral particles, it is a mistake to say that torturing babies is wrong or that invading Iraq was immoral.” This characterization reflects quite well how error theorists proceed. Here is how Olson puts the point: “‘Torture is not wrong. But neither is it permissible. There are no moral properties and facts and consequently no action has moral status.’”28 Pigden explains why non-negative atomic moral propositions are all false as follows: “[T]he argument is the standard nihilistic argument that there are no moral properties or relations corresponding to the moral predicates and thus no moral facts.”29

The moral field thesis, writes Dworkin, is “absurd.”30 To claim that acts of torture-for-pleasure would not be categorically prohibited, for example, unless some arcane metaphysical entities were woven into the “fabric of the world” is outlandish for first-order reasons. This view ascribes determinative moral significance to the wrong states of affairs. What could the relevance of those putative metaphysical entities consist in? Why would their existence or nonexistence make any difference to settling the moral question whether A has a duty to refrain from torturing B for pleasure, even when A is inclined to do so and A’s society countenances that practice? The position looks no different from the thesis that the existence of Pluto is a necessary condition for a categorical prohibition on torture-for-pleasure. “[T]he view that the moral wrongness of genocide consists in the field that surrounds its instances…is itself a (preposterous) substantive moral claim.”31 Because of the absurdity of the moral-field thesis, “debunking the moral-field thesis…leaves morality untouched.”32

Officially, Dworkin eschews talk of minimalism (for reasons that are inexplicable).33 Still, it is obvious that Dworkin’s numerous remarks embody the minimalistic spirit. “Value judgments are true, when they are true, not in virtue of any matching [with so-called morons] but in view of the substantive case that can be made for them.”34 Or put differently:

There is no difference in what two people think if one thinks that the only thing that can make an act right is its maximizing power, so that it makes no sense to evaluate rightness in any other way, and the other thinks that the property of rightness and the property of maximizing power are the very same property. The second opinion uses the jargon of metaphysics, but it cannot add any genuine idea to the first, or subtract any from it.35

The phrase “jargon of metaphysics” and the claim that ponderous metaphysical language “cannot add any genuine idea” converges with Matthew Kramer’s ethical case for minimalism. “[A]ll questions directly about the truth of any moral principle are internal to morality tout court – that is…all questions directly about the truth of any moral principle are concerned with the principle’s substance rather than with semantic or alethic considerations that are somehow separate from substantive moral values.”36 Minimalism wins out on first-order grounds because it places the focus where it morally ought to be: on people’s interests, motives, character traits, integrity, dignity, and actions, instead of the existence of mysterious entities. Just as, on a deflationary picture of truth, there is nothing to talk about except the whiteness of snow when one is discussing the truth of the proposition that snow is white, there is nothing to talk about except the contents of moral principles when one is discussing the truth or falsity of any of those principles.37

6 Question-Begging

Error theorists part company with anti-Archimedeans in two respects. First, they affirm the Robust Thesis. Second, they contend that it is not made true by non-negative moral facts. Instead, they regard it as an austerely conceptual thesis grounded in an analysis of the nature of morality and moral discourse. In adopting the latter view, error theorists beg the question against anti-Archimedeans. To see why, two queries should be disentangled: (i) Which presupposition(s) underlie(s) Society S’s moral discourse? (ii) What are the existence conditions for objective moral facts? While the first question is sociological/empirical, the second is philosophical and moral. Presumably, beyond reporting a litany of sociological facts, error theorists wish to advance their own philosophical understanding of the existence conditions for objective moral facts, irrespective of what any particular social group thinks or presupposes. If this presumption is correct, then the Robust Thesis should be construed as a reply to (ii).

But let us suppose that the preceding assumption is false. That is, let us suppose that error theorists flatly refuse to take a stance on (ii). They wish to proceed by ferreting out presuppositions in discrete moral discourses and showing that – no matter which presupposition is unearthed – its truth-maker is non-existent and the discourse is therefore systematically in error. Even if error theorists were to adopt this case-by-case strategy, their austerely conceptual interpretation of the Robust Thesis would still confront the charge of question-begging.

To see why, we should compare two error-theoretic arguments about a society that takes Zeus to be its supreme moral authority. The first one is the Zeus Existence Argument:
  • (ZE-1) In Zeus Society’s moral discourse, propositions affirming the existence of categorical moral norms systematically presuppose that Zeus exists.

  • (ZE-2) It is not the case that Zeus exists.

  • (ZE-3) Therefore, Society Z’s moral discourse is systematically in error.

(ZE-1) holds true on the basis of empirical/conceptual analysis, whereas (ZE-2) is an austerely metaphysical thesis. Anti-Archimedeans do not claim, absurdly, that all arguments relevantly similar to the Zeus Existence Argument must involve substantive moral commitments. Hume’s Law is adhered to in the argument above, because none of its premises is substantively moral.
Other error-theoretic arguments, by contrast, must have recourse to morality. Let us return to the Zeus Society. To give a complete and accurate account of the truth-conditions for claims affirming the existence of categorical moral norms in that discourse, we must include a presupposition about Zeus’s moral authority. We now have the Zeus Authority Argument:
  • (ZA-1) In Zeus Society’s moral discourse, statements affirming the existence of categorical moral norms systematically presuppose that, if Zeus exists, his commands are endowed with moral authority.

  • (ZA-2) It is not the case that, if Zeus exists, his commands are endowed with moral authority.

  • (ZA-3) Therefore, Zeus Society’s moral discourse is systematically in error.

Let us grant that (ZA-1), like (ZE-1), can be established via empirical/conceptual analysis. The presupposition picked out in (ZA-2) is irreducibly moral, however. To comply with Hume’s Law, a refutation of the proposition “Zeus’s commands have moral authority if Zeus exists” must be substantively engaged. Perhaps a being as violent and promiscuous as Zeus lacks moral credibility; perhaps Zeus does not possess a sufficient amount of beneficence or excellence to be endowed with moral authority to impose obligations on human beings. Whatever the argument propounded for (ZA-2), it will have to include substantive claims about the nature of moral authority and an assessment of whether Zeus’s commands would meet the relevant criteria for having such authority. Unlike the justification for (ZE-2) above, the justification for (ZA-2) cannot be austerely metaphysical.

The attraction of the error theorists’ worldview lies partly in its sweeping nature: there exist no objective moral facts, full-stop. But once error theorists turn their gaze on an anti-Archimedean brand of moral realism, the charge of question-begging has bite. After all, what is the subject-matter of their conceptual analysis, in virtue of which the Robust Thesis purportedly holds true? Various kinds of moral realism prevalent in the eighteenth and twentieth centuries, for example? The sheer fact that some moral-realist doctrines in the Western tradition have affirmed or presupposed the truth of the Robust Thesis settles nothing about the correct existence conditions for objective moral facts. Each such theory is open for criticism – including moral criticism. And anti-Archimedeans make the case, summarized above, about which interpretation of moral properties and facts they take to be correct and why. They do not deny that morality has a so-called metaphysical grounding. They merely insist that this Protean phrase should be cashed out in minimalistic terms, in virtue of substantive moral considerations.

An error-theoretic argument directed at the anti-Archimedean sort of moral realism would proceed as follows:
  • (A-1) In anti-Archimedean moral discourse, statements ascribing moral properties to any types or instances of conduct systematically presuppose the existence of minimalistic moral properties and facts.

  • (A-2) It is not the case that minimalistic moral properties and facts exist.

  • (A-3) Therefore, anti-Archimedean moral discourse is systematically in error.

Crucially, (A-2) resembles the second premise in the Zeus Authority Argument, not the Zeus Existence Argument. According to anti-Archimedeans, the only credible basis on which to affirm or deny the existence of a moral property is a moral basis. Their case for a categorical proscription on torture-for-pleasure, for example, relies on considerations about agents’ interests, dignity, and integrity. To deny that a proscription on torture-for-pleasure is categorical, one might ascribe greater normative strength to torturers’ desires than to victims’ interests. If a torturer derives a much higher degree of satisfaction than the degree of disutility experienced by the victim, some consequentialist doctrine might sanction acts of torture-for-pleasure. Perhaps some extreme utilitarians would deny that such a torturer debases himself by undertaking such acts. In any case the relevant truth-makers will be correct principles of morality, not robust non-naturalistic entities, or morons. Claims about morons would be beside the point, because they have no intelligible moral relevance or significance. Put differently, any project of discrediting moral properties by identifying and discrediting some entity or property such as morons will have to explain why that entity or property is of moral relevance. Unless such a feature is morally relevant, the discrediting of it would not discredit categorical prescriptivity. Yet an explanation of the moral relevance of that entity or property is a substantive moral argument rather than an austerely metaphysical argument. It follows that there is no way to ground (A-2), except by taking up a moral stance and contending that every categorically prescriptive norm is substantively mistaken. Insofar as error theorists hope to substantiate (A-2), they will be adopting a first-order moral stance and will thereby be contradicting the conclusion of the argument from queerness.

7 The Error Theorist’s Dilemma

The merits of the Robust Thesis can now be set aside in order to elaborate on the crux outlined in Section 5: In their argument from queerness, error theorists must violate Hume’s Law or damagingly beg the question or propound a self-contradictory line of reasoning.38

A version of the argument from queerness is first presented that obeys Hume’s Law and does not beg the question against anti-Archimedeans. Error theorists cannot sign up to this version of the argument, however, because the first premise states that the subjunctive conditional expressed by the Robust Thesis is made true by a (complex) moral fact:

Version 1
  • (M-1) The Robust Thesis is true in virtue of substantive moral considerations.

  • (M-2) It is not the case that anything in the world can supply the metaphysical basis for categorical moral norms required by the Robust Thesis.

  • (M-3) Therefore, categorical moral norms do not exist.

Whereas (M-2) might express a purely metaphysical truth, premise (M-1) is manifestly a non-negative moral proposition. Given as much, any error theorist who affirms this argument will be committing himself to a contradiction.

In any case, error theorists will wish to reject the first premise in Version 1, because the Robust Thesis is, on their view, a purely conceptual tenet. Accordingly, they could modify the argument as follows:

Version 2
  • (R-1) The Robust Thesis is true in virtue of austerely conceptual facts.

  • (R-2) Nothing in the world can supply the metaphysical basis for categorical moral norms required by the Robust Thesis.

  • (R-3) Therefore, categorical moral norms do not exist.

(R-1) and (R-3) are not in contradiction. Moreover, Version 2 satisfies Pigden’s version of Hume’s Law, which I can happily accept.39 That is because the Robust Thesis is entailed by the argument, and that Thesis contains moral terminology. However, as argued in the preceding Section, this way of establishing Version 2’s compliance with Hume’s Law begs the question. No anti-Archimedean would accept that (R-1) is true.

Error Theorists might reply that anti-Archimedeans are themselves begging the question by insisting that (R-1) is false. Nonetheless, the charge of begging the question is pertinent against them rather than against me. For one thing, whereas Dworkin’s aim in his moral philosophy is to vindicate ordinary ways of thinking about the objectivity of morality, the error theorists are propounding a radically revisionary account of moral discourse as fundamentally mistaken. Thus, the onus is on them to come up with considerations that are convincing on their opponents’ own terms. Error Theorists do not discharge that burden of proof when they persist in asserting (R-1), since their anti-Archimedean opponents on their own terms have an entirely satisfactory account of the truth-value – the falsity – of the Robust Thesis. What is more, the anti-Archimedeans do not accept that the Error Theorists’ terms are in fact fundamentally different from their own. They maintain that any way of cashing out (R-1) or the Robust Thesis can only intelligibly be construed as a substantive moral doctrine: a false substantive moral doctrine.

A transformation of Version 2’s first premise into a conditional proposition yields a new argument, Version 3, that does violate Pigden’s version of Hume’s Law:

Version 3
  • (R-1*) If the Robust Thesis is true, then it is true in virtue of austerely conceptual facts.

  • (R-2) Nothing in the world can supply the metaphysical basis for categorical moral norms required by the Robust Thesis.

  • (R-3) Therefore, categorical moral norms do not exist.

It will be no use pointing out here that the Robust Thesis contains moral terminology. For (R-1*) is phrased as a conditional and, consequently, the Robust Thesis is not entailed by any premise in the argument. Version 3, therefore, runs afoul of Hume’s Law because – whereas its conclusion is substantively moral – none of its premises is substantively engaged. Hence, in addition to begging the question against anti-Archimedeans (in the manner of Version 2), Version 3 contravenes a principle that is accepted by error theorists and anti-Archimedeans alike.

Pigden could object that the anti-Archimedean critique laid out above is inapplicable to his version of error theory, which is restricted to the thesis that “all non-negative atomic moral propositions are false.”40 After all, premise (A-2) in the error-theoretic argument expounded in Section 6 above is governed by a negation operator. And the Robust Thesis – when interpreted as a moral position, as it should be – is a subjunctive conditional, not an atomic moral proposition. Pigden’s imagined reply prompts a helpful clarification: anti-Archimedeans set out to establish that error theorists are committed to some moral claims, not that they are always committed to non-negative atomic moral claims. Given Pigden’s formulation, an anti-Archimedean could rest content with arguing that error theory is false, without also being self-contradictory.

Anti-Archimedeans can pursue a more ambitious retort by arguing that Pigden’s position is ad hoc. According to Pigden, is it the case that – whereas all atomic moral propositions are false – some non-atomic (and non-negative) moral propositions, like conditionals, might be true? If so, this position has no clear rationale. From the error theorist’s perspective, what could be the basis for claiming that the truth-makers for non-atomic moral propositions (complex moral facts) are less metaphysically queer than truth-makers of atomic moral propositions (simple moral facts)?

Let us suppose Pigden contends that complex moral facts do not exist, so that all moral propositions stated as non-negative conditionals are false. Now the anti-Archimedean critique developed above regains relevance: the focus turns back to the status of the subjunctive conditional embodied in the Robust Thesis. Error theorists will insist that that Thesis is made true by a non-moral fact discernible through purely conceptual analysis. By contrast, anti-Archimedeans will maintain that a formulation of the argument from metaphysical queerness that abides by Hume’s Law must present the Robust Thesis as a substantive moral position whose truth-maker would be a complex non-negative moral fact. And there cannot be complex non-negative moral facts without atomic moral facts. If so, error theorists would be committed to affirming the existence of atomic and complex moral facts while denying the existence of any such facts. The charge of self-contradictoriness sticks even to a suitably re-interpreted version of Pigden’s error theory.

8 Yet Another Formulation

Anti-Archimedeans conclude that error theorists have nowhere to stand. Version 1 of the argument from queerness result in contradictions; Versions 2 and 3 damagingly beg the question against anti-Archimedeanism; and Version 3 flouts Hume’s Law. Let us now consider one further version of the argument:41

Version 4
  • (E-T1) If any non-negative atomic moral judgments are to be true, there have to be some moral facts of a non-naturalistic kind.

  • (E-T2) There are no facts of a non-naturalistic kind.

  • (E-T3) No non-negative atomic moral judgments are true.

  • (E-T4) Moral judgments are either true or false.

  • (E-T5) All non-negative atomic moral judgments are false.

Now, if Version 4 is to be sound, each of its premises must be true. Yet the only construal of (E-T1) which renders that opening premise true is a construal that renders it analytically true. On the one hand, if “moral facts of a non-naturalistic kind” is construed to refer to some arcanely robust facts, then (E-T1) is a false substantive moral thesis. As a falsehood, that opening premise would render Version 4 unsound. On the other hand, if “moral facts of a non-naturalistic kind” is construed minimalistically (in line with anti-Archimedeanism) to mean “those things in virtue of which certain moral judgments are true” (E-T1) is true but trivially true. So construed (E-T1) can more perspicuously be formulated as “If any non-negative atomic moral judgment is to be true, there has to be something in virtue of which a moral judgment is true.” (E-T1) as an analytic truth will scarcely be a serviceable premise in an error-theoretical argument.

What is more, “facts of a non-naturalistic kind” will have to be construed minimalistically in (E-T2) if a fallacy of equivocation in Version 4 is to be avoided. When that phrase is so construed, however (E-T2) is a false substantive moral thesis. Though the sub-conclusion (E-T3) and the conclusion (E-T5) are validly derived from (E-T2), the falsity of (E-T2) renders Version 4 unsound afresh.42

9 Conclusion

Anti-Archimedeans believe that all correct metaethical theses must be justified at least in part on substantive moral grounds. Based on this conviction, they bring a unique perspective to analyzing moral error theory. Instead of arguing, like many others, that error theory is merely incorrect or pernicious, anti-Archimedeans advance a more potent criticism concerning self-contradictoriness. This criticism turns out to be more complex and resilient than leading error theorists have initially recognized, and it has nothing to do with Pigden’s Reinforced Doppelganger Principles. The precise charge is best stated as an unpalatable choice: a suitably formulated argument from queerness must transgress Hume’s Law or damagingly beg the question or lead to self-contradiction. This article has aimed to show why this critique has bite and to set the record straight about the burden of proof on both sides in this subtle and underappreciated debate.43


  1. 1.

    See Simon Blackburn, “Quasi-Realism no Fictionalism,” in Fictionalism in Metaphysics, ed. Mark Kalderon (Oxford: Oxford University Press, 2005), pp. 322–338; Blackburn, Ruling Passions: A Theory of Practical Reasoning (Oxford: Clarendon Press, 1998).

  2. 2.

    See Mark E. Kalderon, Moral Fictionalism (New York: Oxford University Press, 2007).

  3. 3.

    John L. Mackie, Ethics: Inventing Right and Wrong (London: Pelican Books, 1977), p. 15.

  4. 4.

    Ibid., p. 16.

  5. 5.

    See Ronald Dworkin, Law’s Empire (Cambridge, MA: Belknap Press of Harvard University Press, 1896); Dworkin, “Objectivity and Truth: You’d Better Believe It,” 25 Philosophy and Public Affairs (1996): pp. 87–139; Dworkin, Justice for Hedgehogs (Cambridge, MA: Harvard University Press, 2011); Matthew H. Kramer, Moral Realism as Moral Doctrine (Oxford: Wiley-Blackwell, 2009); Jeremy Fantl, “Is Metaethics Morally Neutral?” 87 Pacific Philosophical Quarterly (2006): pp. 24–44; Mark Hanin, “Naturalistic Moral Realism and Moral Disagreement: David Copp’s Account,” 18 Res Publica (2012): pp. 283–301.

  6. 6.

    Dworkin, Justice for Hedgehogs, p. 40.

  7. 7.

    See Charles Pigden, “Nihilism, Nietzsche and the Doppelganger Problem,” 10 Ethical Theory and Moral Practice (2007): pp. 441–456; Jonas Olson, “In Defence of Moral Error Theory,” in New Waves in Metaethics, ed. Michael Brady (Basingstoke: Palgrave Macmillan, 2010), pp. 62–84.

  8. 8.

    The anti-Archimedean posture therefore differs from a “Moorean Argument” (Olson, op. cit., p. 66), according to which we should have more confidence in some moral convictions than in the fruits of esoteric philosophizing. While the Moorean accepts error theory at face value without doubting its coherence, the anti-Archimedean does not.

  9. 9.

    Pigden, op. cit., p. 452.

  10. 10.

    Pigden, op. cit., p. 453.

  11. 11.

    Olson, op. cit., p. 69.

  12. 12.
    The placement of the negation operator requires clarification:
    1. (a)

      Acts of torture-for-pleasure are wrong.

    2. (b)

      It is not the case that acts of torture-for-pleasure are wrong.

    3. (c)

      Acts of torture-for-pleasure are not wrong.

    The logical negation of (a) is (b). According to the No Entailment Thesis, (b) does not entail, “Acts of torture-for-pleasure are permissible.” By treating (b) and (c) interchangeably, Pigden and Olson introduce the possibility of confusion. It might be thought that – whereas (b) does not entail the permissibility of torture – (c) does. It might be thought that “not wrong” entails “permissible” and that “not permissible” entails “wrong.” Such entailment would be consistent with the No Entailment Thesis formulated using (b)-type statements. To avoid ambiguity in discussing the Reinforced Doppelganger Problem, the negation applied to (a) should be propositional rather than predicational.
  13. 13.

    Pigden, op. cit., p. 454. For a substantive moral argument in favor of the No Entailment Thesis, see Kramer, op. cit., pp. 109–111.

  14. 14.

    Dworkin, “Objectivity and Truth,” p. 131; see Dworkin, Justice for Hedgehogs, pp. 44, 92.

  15. 15.

    Pigden, op. cit., pp. 453–454.

  16. 16.

    Dworkin, “Objectivity and Truth,” p. 99.

  17. 17.

    For a similar formulation, see Dworkin, Justice for Hedgehogs, p. 176.

  18. 18.
    Michael Smith, in rebutting Dworkin’s critique of external skepticism, quotes a passage from the manuscript of Justice for Hedgehogs that seems to affirm (RD1); see Smith, “Dworkin on External Skepticism,” 90 Boston University Law Review (2010): pp. 509–520, at pp. 511–512. In his book, Dworkin cites Smith’s paper, excises that passage, and makes his familiar case against error theory (Justice for Hedgehogs, pp. 42–44). There remains one questionable feature of Dworkin’s discussion that should be flagged. Consider a debate between two people:
    1. (1)

      “Abortion is never either morally required or morally forbidden. No one has a categorical reason either way. It is always permissible and never mandatory, like cutting your fingernails.”

    2. (2)

      “Abortion is never either morally forbidden or morally required or morally permissible.”

    Dworkin writes that (2) “agrees with (1) and cannot say, without contradiction, that what (1) says is false (or neither true nor false)”; moreover, (2) “makes a much more general claim than (1) does, but his claim includes (1)’s” (Justice for Hedgehogs, p. 43). Obviously, (2) cannot agree with (1) on everything; nor can (2) claim everything that (1) claims. For, Dworkin’s own formulation of (1) and (2) includes a pair of logically inconsistent propositions: abortion is “always permissible,” and abortion is “never…morally permissible.” On a charitable reading of Dworkin’s comments, (2) agrees with (1) on some matters, and (2)’s position includes certain tenets from (1)’s position. This weak reading is all that is required for the anti-Archimedean argument to succeed.
  19. 19.

    Dworkin, “Replies,” Book Symposium: Justice for Hedgehogs, 73 Analysis (2013): pp. 139–146, at p. 143.

  20. 20.

    Dworkin, Justice for Hedgehogs, p. 42.

  21. 21.

    Ibid., p. 44.

  22. 22.

    If Dworkin in fact affirms the Doppelganger Principles, then the rebuttals urged by Pigden and Olson would have merit. But Dworkin has no monopoly on anti-Archimedean views.

  23. 23.

    Pigden has long championed a version of Hume’s Law; see Pigden, “Logic and the Autonomy of Ethics,” 67 Australasian Journal of Philosophy (1989): pp. 127–151. Olson appears to accept Hume’s Law (Olson, op. cit., p. 83 n. 32). Mackie criticized John Searle’s attempt to derive an ‘ought’ from an ‘is’ (Mackie, op. cit., pp. 66–72). Mackie did believe that an ‘ought’ can be derived from an ‘is,’ but “only by speaking within some institution” (Ibid., p. 72). He never said that a non-institutional ‘ought’ can be derived either from an institutional ‘is’ or from a non-institutional ‘is.’

    Unlike the error theorist, however, I concur with Dworkin that Hume’s Law is “itself a moral principle[:]…any argument that either supports or undermines a moral claim must include or presuppose further moral claims or assumptions” (Justice for Hedgehogs, p. 99). Of course, one can ascertain whether Hume’s Law is being complied with in this or that situation without presupposing the truth of any moral principle(s). In this sense, Hume’s Law is a formal doctrine. But the justification and status of Hume’s Law are both substantively engaged. Thus Hume’s Law is a value-neutral thesis and a value-dependent thesis; see Matthew Kramer, “Conceptual Analysis and Distributive Justice,” Oxford Handbook of Distributive Justice (Oxford: Oxford University Press, 2014, forthcoming).

  24. 24.

    Blackburn, “Securing the Nots: Moral Epistemology for the Quasi-Realist,” in New Readings in Moral Epistemology, ed. Walter Sinnott-Armstrong (New York: Oxford University Press, 1996), pp. 82–100, at p. 92.

  25. 25.

    Pigden, “On the Triviality of Hume’s Law: A Reply to Gerhard Schurz,” in Hume on ‘Is’ and ‘Ought, ed. Charles Pigden (Basingstoke: Palgrave Macmillan, 2010), pp. 217–238, at p. 231.

  26. 26.

    I am grateful to Charles Pigden for helpful comments in private correspondence. Naturally, his provision of comments is not to be taken as an endorsement of anything that I have written.

  27. 27.

    Dworkin, Justice for Hedgehogs, p. 32; also see Ibid., pp. 9, 26, 41, 46–48; Law’s Empire, pp. 80–81; “Objectivity and Truth,” pp. 104–105.

  28. 28.

    Olson, op. cit., p. 70.

  29. 29.

    Pigden, “Nihilism, Nietzsche and the Doppelganger Problem,” p. 451.

  30. 30.

    Dworkin, “Objectivity and Truth,” p. 105.

  31. 31.


  32. 32.

    Ibid., p. 120.

  33. 33.

    See Dworkin, “Objectivity and Truth,” p. 103, and Kramer, “Working on the inside: Ronald Dworkin’s moral philosophy,” Book Symposium: Justice for Hedgehogs, 73 Analysis (2013): pp. 118–129, at pp. 121–122.

  34. 34.

    Dworkin, Justice for Hedgehogs, p. 11.

  35. 35.

    Dworkin, “Objectivity and Truth,” p. 101.

  36. 36.

    Kramer, Moral Realism as a Moral Doctrine, pp. 272–273; also see Kramer, “Working on the inside,” pp. 120–122.

  37. 37.

    Error theorists may wish to raise various technical challenges to a minimalist theory of truth. Because I am concentrating on minimalism about properties and facts in the present paper, I leave this matter aside. For extended remarks about formulating a deflationary theory of truth in the context of a moral argument for anti-Archimedeanism, see Kramer, Moral Realism as a Moral Doctrine, pp. 273–287.

  38. 38.

    I am grateful to Matthew Kramer for helpful discussions and for aid in the formulation of some key ideas and paragraphs in Sections 7 and 8 (especially the discussion of Version 4 of the argument from queerness).

  39. 39.

    But see n. 23 above for likely disagreement over the ultimate justification for Hume’s Law.

  40. 40.

    Pigden, “Nihilism, Nietzsche and the Doppelganger Problem,” p. 451. Pigden introduces this restriction to get around the Doppelganger Problem: If, according to error theorists, moral statement M is false, then its logical negation, ~M, must be true. But if ~M is itself a moral statement, then error theory would be self-defeating. And it is highly plausible, says Pigden, that propositions like “It is not the case that we ought to keep our marriage vows” are indeed substantively moral, given their “considerable impact on our conduct” (Ibid.). Olson regards Pigden’s restriction as unnecessary (Olson, op. cit., p. 70).

  41. 41.

    I thank an anonymous referee for the Journal of Value Inquiry for suggesting an approach along these lines.

  42. 42.

    Though a conclusion validly derived from a false premise is not ipso facto itself false, (E-T3) and (E-T5) are indeed both false.

  43. 43.

    For perusing an early draft of this article I would like to thank Hallvard Lillehammer.

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Harvard UniversityCambridgeUSA

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