-Forthcoming in The Journal of Philosophy- This is the pre-print of the text. For the definitive text, please consult the published version. 'Ought' and Error* Christine Tiefensee Abstract The moral error theory generally does not receive good press in metaethics. This paper adds to the bad news. In contrast to other critics, though, I do not attack error theorists' characteristic thesis that no moral assertion is ever true. Instead, I develop a new counter-argument which questions error theorists' ability to defend their claim that moral utterances are (typically) meaningful assertions. More precisely: Moral error theorists lack a convincing account of the meaning of deontic moral assertions, or so I will argue. Keywords Moral error theory  Deontic semantics  Kratzer  Ought  Presupposition failure  Strawson 1 Introduction The moral error theory generally does not receive good press in metaethics.1 This paper adds to the bad news. In contrast to other critics, though, I do not attack error theorists' characteristic thesis that no moral assertion is ever true. Instead, I develop a new counter-argument which questions error theorists' ability to defend their claim that moral utterances are (typically) meaningful assertions. More precisely: Moral error theorists lack a convincing account of the meaning of deontic moral assertions, or so I will argue. Doing so will thus also undermine the tacit metaethical assumption that as representationalists and cognitivists about moral discourse, moral error theorists can help themselves to the same semantic repertoire as other representationalists.2 Rather, we will see that error theorists cannot employ mainstream deontic semantics, as prominently developed by Angelika Kratzer (1981, 2012), as this semantics assigns truth to * I am extremely grateful to Gregory Wheeler, Alessandra Marra and Sebastian Köhler for written comments on an earlier draft and many discussions about deontic semantics. 1 Compare Daly and Liggins' (2010: 209) assessment that "[m]any contemporary philosophers rate error theories poorly", so much so that "[e]rror-theoretic accounts of a discourse are ... commonly dismissed out of hand, as if it were well known that such positions are never the best ones available." For recent defences of the error theory, see Joyce (2001), Pigden (2007), Daly/Liggins (2010), Olson (2014), Streumer (2017) and Kalf (2018). 2 Note that whereas expressivists are generally held to be saddled with the requirement to develop an alternative approach to the logic and semantics of moral claims due to their nonrepresentationalism (Schroeder 2008; Unwin 1999), no such demand is commonly imposed on error theorists. 2 moral assertions when combined with error-theoretic premises and is thus incompatible with the error theory. Similarly, we will find that error-theoretic attempts to avert incompatibility by modifying mainstream deontic semantics are not only semantically unconvincing, but also require error theorists to abandon classical logic, deontic logic or both. Contrary to what appears to be metaethical lore, then, the moral error theory does not have an easy ride with regard to logic and semantics. Rather, it comes with the significant formal cost of having to develop an alternative deontic semantics, a modified deontic logic, a non-classical logic, or all of the above. My strategy, then, will be to expose the error theory's lack of a convincing semantic account for deontic sentences by arguing that error theorists cannot accept mainstream deontic semantics, nor adapt this semantics in such a way as to reach a convincing result. §2 sets the scene for my arguments by providing a brief summary of this mainstream semantics for deontic sentences. §3 will introduce the error theory and explain why this position is incompatible with mainstream deontic semantics. In §4, I will examine if, and if so how, error theorists could seek to revise the mainstream analysis of deontic sentences in such a way as to reach compatibility. Since I will argue that all attempts at such a revision fail, I conclude in §5 that as far as things currently stand, moral error theorists still owe us a persuasive semantics of deontic moral claims. In what follows, I will concentrate exclusively on error theorists' inability to explain the meaning of deontic moral terms, such as 'ought', 'permissible' and 'forbidden'. What about the meaning of other normative and evaluative notions, such as 'good', 'reason' or 'wrong'? Here, two responses are conceivable. Firstly, the semantics of non-deontic and deontic moral notions could be connected, in that the former might be in some sense reducible to the latter.3 If so, this study would entail that moral error theorists cannot explain the meaning of any moral assertions, not just that of deontic sentences. Secondly, the semantics of non-deontic and deontic moral notions could be disconnected, in that the meaning of the former might have to receive a different analysis from that of the latter. If so, the current study would have to be supplemented with a further examination of error theorists' ability to explain the meaning of non-deontic moral sentences. Yet, even if this led to results that are more favourable to error theorists, the findings of the present study would stand in their own right: Given the ubiquity and significance of deontic moral assertions within moral discourse, being unable to account for deontic moral claims remains a grave shortcoming of the error theory. 2 Mainstream deontic semantics When asked about the meaning of deontic moral sentences, metaethicists might most obviously appeal to the semantics which has become the mainstream analysis of deon- 3 For more on this idea, see Chrisman (2016: 209-214). 3 tic notions over recent decades.4 Let us have a quick look, then, at how this semantics works and where its advantages lie. Mainstream deontic semantics models deontic notions such as 'ought' and 'permissible' analogously to propositional operators known from modal semantics (Kratzer 1981, 2012).5 To elaborate, take the following two definitions: (1) ⟦Oφ⟧M &,(,) = {w : {v : v ∈ ∩f(w) and there is no v' ∈ ∩ f(w) such that v' <g(w) v } ⊆ ⟦φ⟧M &,(,)}6 (2) ⟦Pφ⟧M &,(,) = {w : {v : v ∈ ∩f(w) and there is no v' ∈ ∩ f(w) such that v'	<g(w) v } ∩ ⟦φ⟧M &,(,) ≠ ∅} Similar to the semantics for the necessity and possibility modals, £ and  , 'ought' and 'permissible' are understood as operations, O and P, on a formula φ, evaluated at a particular world w and context c of a Kripke model M with respect to a set of worlds ∩f(w) accessible from w. As such, (1) and (2) specify the set of worlds, if any at all, in which the respective modal formulae are satisfied, where 'Oφ' and 'Pφ' are interpreted against two conversational backgrounds, f and g. The first, f(w), can be understood as identifying the worlds that are relevant for the interpretation of a deontic sentence. More precisely, let us follow Kratzer (1981: 51) in understanding f(w) as laying out a set of propositions, determined by a sentence's conversational background, and read ∩f(w) as the set of possible worlds in which all of these conversational background propositions are satisfied. This set, ∩f(w), is called the 'modal base' of a sentence evaluated at w. At the same time, (1) and (2) go beyond the standard modal satisfiability conditions of Kripke semantics in that they introduce a second conversational background in the form of an ordering source. More precisely, let us understand g(w) as a set of propositions which specifies a claim's deontic conversational background and ≤g(w) as an ordering induced by g(w), where the best worlds are the lowest elements in the pre-order.7 Intuitively, then, (1) says that the sentence 'Oφ' is true at a world w if and only if φ is satisfied in all worlds of the modal base that are best according to ≤g(w). Otherwise, 'Oφ' is false. With P being the dual of O, (2) says that 'Pφ' is true at 4 Compare Portner (2009: ch. 3.1) and Chrisman (2016: 87-88) for a more detailed introduction to Kratzer semantics. Both agree on the classification of Kratzer's account as mainstream. 5 Some argue that non-agentive and agentive readings of 'ought' must be distinguished, where the former concerns cases in which O operates on propositions, and the latter cases where 'ought' refers to agents and actions (see Schroeder 2011, Chrisman 2016: ch. 5). I will only consider the propositional reading here. 6 This is Portner's (2009: 67) definition (95) with my notation. For ease of exposition, I make the so-called limit assumption, in that (1) and (2) presume that orderings in which worlds become infinitely better are ruled out. None of my arguments hinge on that assumption. See also Silk (2014: 697, Definition 1) for a definition of 'best worlds'. 7 A set of propositions A can induce the ordering ≤A on W as follows (Kratzer 2012: 39): For all worlds w and v ∈ W: w ≤A v iff {p: p ∈ A and v ∈ p} ⊆ {p: p ∈ A and w ∈ p}. 4 w just in case there is at least one highest-ranked world of the modal base at which φ is satisfied. Otherwise, 'Pφ' is false. This semantics offers crucial advantages for the interpretation of deontic sentences (see Chrisman 2016: 87-88). Firstly, inclusion of conversational backgrounds enables Kratzer semantics to provide definitions of modals that are both unified across different uses of modals and flexible in accounting for these different uses. For instance, if we are assessing moral deontic sentences, the pre-order must be generated by a moral standard which evaluates worlds in terms of their comparable moral value. Were the sentence epistemological or prudential, say, g(w) would have to be filled in by a respective epistemological or prudential norm, yielding an order in terms of their comparative epistemic or prudential value. Crucially, then, mainstream deontic semantics can explain why words such as 'must' and 'ought' "generate a diversity of 'flavors'" (Chrisman 2016: 33) across different languages without having to postulate a plethora of separate meanings for epistemic, teleological, prudential or moral modals. Secondly, by basing semantic analyses of deontic sentences not on morally ideal worlds, but on modal bases which allow room for moral deficiencies, mainstream deontic semantics enables us to deal with deontic sentences that concern non-ideal contexts. For instance, assume that we are assessing the sentence 'The poor ought to be helped'. Since this sentence's conversational background concerns cases of poverty, this means that the worlds which are relevant for the assessment of this sentence, and thus included in ∩f(w), are those in which poverty exists. By inducing an ordering ≤g(w) on this modal base, we can accordingly account for sentences that assert what we ought or are permitted to do with regard to poverty although worlds in which we find poverty are hardly morally ideal. Thirdly, the fact that ≤g(w) is required to be only a pre-order-i.e., a ranking that permits non-identical worlds to have the same rank, rather than induce a partial order-expands (1)'s and (2)'s semantic scope considerably by making it possible to analyse deontic sentences even if they are relativised to partially inconsistent standards. For instance, assume that one moral ideal ranked worlds highest which satisfy the propositions 'The poor are helped' ('r') and 'Somebody works for charity' ('s'), whereas another relevant moral standard considered those worlds best in which the poor are helped but nobody works for charity. Then the current proposal would still make it possible to account for the truth of an assertion such as 'The poor ought to be helped' by placing (r ∩ s)-worlds and (r ∩ ¬s)-worlds both on top of the moral ranking. Consequently, mainstream deontic semantics pays heed to the intimate link between deontic moral terms and other modals, provides a unified definition of deontic notions whilst catering for different modal uses, is structurally comparably simple and deals with tricky cases such as non-ideal contexts and partially inconsistent standards. As such, it comes as no surprise that it has garnered much support amongst metaethicists, logicians, semanticists and linguists alike. 3 The error theory's incompatibility with mainstream deontic semantics Given the attractiveness of mainstream deontic semantics, then, we might think that error theorists too would want to employ it in order to explain the meaning of deontic 5 sentences. Why they cannot do so, contrary to expectations, will be explained next. Before I make my case for its incompatibility with mainstream deontic semantics, though, I need to say a few more words about the error theory. Moral error theorists hold that all moral assertions are untrue because there is nothing that could make them true. Thus formulated, the error theory is a local theory about moral discourse and its assertions. Most error theorists defend this local version, with only a few seeking to extend it so as to encompass normative discourse in general (Streumer 2017). In what follows, I will focus exclusively on local error theories about moral discourse. At the same time, this definition of the error theory is neutral towards different versions thereof. According to what Olson (2014: 4) calls the "standard version", the thesis that all moral assertions are untrue is to be read as stating that all moral assertions are false (Mackie 1977, Olson 2014, Streumer 2017),8 whilst the "non-standard version" interprets it as claiming that all moral assertions are neither true nor false (Joyce 2001). Whereas I will remain neutral towards these different readings in this section, they will become relevant for the arguments presented in the next. Why all moral assertions are untrue is, in turn, explained differently by different error theorists. Some maintain that whilst moral assertions would be true only if there were categorical reasons or objective moral properties,9 such reasons and properties are metaphysically too queer to exist (Mackie 1977, Olson 2014); others suggest that the very idea of a moral property is straightforwardly inconsistent (Streumer 2017). These argumentative differences do not matter for my purposes. However, I will consider shortly how this error-theoretic rejection of categorical reasons and objective moral properties can be captured within the framework of deontic semantics. Finally, error theorists are representationalists and cognitivists about moral discourse. As such, they hold that moral utterances are meaningful assertions that purport to represent moral reality and express moral beliefs (Joyce 2001: 8)10-which brings us back to the meaning of deontic moral sentences. As I have indicated above, it does not seem far-fetched to assume that just like other metaethicists, error theorists too would want to explain the meaning of deontic moral assertions on the basis of mainstream deontic semantics. And indeed, since error theorists seek to agree with other representationalists about the meaning of moral assertions, albeit not about the existence of moral truths, we might even expect them not to encounter any problems when doing so. In this vein, Schroeter and Schroeter (2018: 13) submit that "[e]ven ... error theorists can accept Kratzer's compositional semantics: they can simply take the standard of evaluation for the moral 'must' to be context invariant and the mental states expressed [by deontic sentences] to be repre- 8 Declaring that all moral assertions are false might raise worries about the error theory's consistency. For more on this worry, see Olson (2014: 11-15), Streumer (2017: 124-128), Pigden (2007: 450-454), Sinnott-Armstrong (2006: 32-37) and Joyce (2001: 6-9). 9 I will follow Olson (2014: ch. 6) in understanding categorical reasons as concerning favouring relations that cannot be reduced to an agent's desires, aims, roles or rule-governed activities. Moral properties will be taken to be objective in the sense of being mindindependent. 10 I ignore here how representationalism and cognitivism can be distinguished from nonrepresentationalism against the background of creeping minimalism (Dreier 2004). 6 sentational."11 Evers (2014: 294) appears to agree when suggesting "that moral error theorists accept The truth of moral claims requires the existence of absolute standards and There are no absolute standards in reality, and goes on to explain that "[f]rom the combination of these claims, it ... does follow that no first-order moral claims are true" (Evers 2014: 294)-just, we may add, as the error theory maintains. However, any such hopes for an easy combination of the error theory with mainstream deontic semantics are quickly frustrated. For, contrary to Evers' contention, combining error-theoretic premises with mainstream deontic semantics does not entail that all moral assertions are untrue, but that some moral sentences are indeed true. To explain why, I will first examine how the error-theoretic position can be simulated within mainstream deontic semantics and suggest that there are two natural ways of doing so. Then I will argue that combining either way with mainstream deontic semantics returns the truth-value true for certain deontic sentences, and thus directly contradicts the error theory. Starting with step one, then, I believe that both Schroeter/Schroeter (2018) and Evers (2014, 2016) are absolutely right in two respects. Firstly, they correctly suggest that it is deontic semantics' appeal to ordering sources which enables us to capture the error theory within deontic semantics. For, rather than stating that the error theory proclaims that the truth of moral assertions depends on the existence of categorical reasons or objective moral properties, we can now translate this thesis into the claim that the truth of deontic moral claims depends on there being objective moral standards which induce an ordering of categorical, objective, or absolute moral value on the modal base.12 To abbreviate, let us call this assumption (P): (P) There are objective moral standards. According to error theorists, (P) is a "non-negotiable" part of moral deontic concepts' meaning (Joyce 2001: 6, Olson 2014: ch. 6). That is, they believe that anybody who uses the word 'ought', say, but denies that this word commits her to there being objective moral standards, is not talking about the moral concept 'ought', but some nonmoral term 'schmought'. Secondly, Evers rightly observes that error theorists believe (P) to be false. However, this observation is not sufficient to assess moral error theory's combination with deontic semantics. Rather, we also need to consider how error theorists' rejection of (P) can be modelled within deontic semantics. There are two natural ways of doing so. According to the first, rejecting (P) should be simulated in terms of an empty set of best worlds: 11 Regrettably, this passage did not make it into the final version of their article published in McPherson/Plunkett's (2018) The Routledge Handbook of Metaethics. 12 Compare Evers (2014: 294) for more on the relation between reasons and objective moral standards. 7 (E1) {v : v ∈ ∩f(w) and there is no v' ∈ ∩f(w) such that v' <g(w) v}= ∅ More intuitively, the idea behind (E1) is that if error theorists are right in claiming that there is no such thing as an objective moral standard, worlds cannot be ranked in terms of objective moral value. But if so, there cannot be any worlds of highest moral value either; rather, the set of best worlds must be empty. Alternatively, rejecting (P) could be modelled in terms of an empty ordering source g(w). Empty ordering sources, in turn, entail that no order of the modal base can be generated, which means that all worlds within the modal base are equivalent: (E2) {v : v ∈ ∩f(w) and there is no v' ∈ ∩f(w) such that v' <g(w) v}= ∩f(w) More intuitively, the motivation behind (E2) is that if we are to believe error theorists that there is no such thing as an objective moral ordering, then all possible worlds must be morally indistinguishable. (E2) seeks to capture exactly this position by taking all worlds in the modal base to be equivalent. In the next section, I will argue that (E2) is a much more plausible interpretation of the error theory than (E1). For now, though, let us move on to step two and show that plugging either simulation of the error theory into mainstream deontic semantics leads to their incompatibility. This point is easily made with regard to (E1) and its implications for oughtsentences. For, remember that (1) says in effect that 'Oφ' is satisfied if and only if the set of best worlds in ∩f(w) is a subset of the set of worlds in which 'φ' is satisfied. At the same time, we now assume with (E1) that the set of best worlds is empty. Yet, the empty set is a subset of every set, and thus also of ⟦φ⟧M &,(,). (1) together with (E1) entail, therefore, that all sentences of the form 'Oφ' are trivially true. Accordingly, coupling (E1) with mainstream deontic semantics straightforwardly refutes the errortheoretic thesis that all moral sentences are untrue. (E2)'s semantic implications, in turn, require slightly more comprehensive explanations. Let us start with the observation that since (E2) takes all worlds in the modal base to be equivalent, (E2) entails that (1) and (2) no longer quantify over a subset of the modal base, but over all possible worlds that are compatible with f(w). As such, (1) and (2) respectively become equivalent with necessity and possibility in standard modal logic (Portner 2009: 69): (1*) ⟦Oφ⟧M &,(,) = {w : {v : v ∈ ∩f(w)} ⊆ ⟦φ⟧M &,(,)} (2*) ⟦Pφ⟧M &,(,) = {w : {v : v ∈ ∩f(w)} ∩ ⟦φ⟧M &,(,) ≠ ∅} Next, let us look specifically at (2*) and permissibility-claims. (2*) will assign falsity to 'Pφ' only if the prejacent proposition 'φ' failed to be satisfied in all worlds in ∩f(w). Now, admittedly we can construct models in which this is indeed the case. However, these will not be models that are deontically relevant. To elaborate, when modelling moral discourse, we are interested in deontically pertinent circumstances, which are those in which we deliberate about what to do and what not do to, which alternative 8 courses of actions are open to us and which of these alternative actions to choose. For instance, we might consider whether we ought to help the poor or are permitted to increase our own welfare, whether it is obligatory to follow veganism or permissible to eat meat, etc. In order to capture this nature of moral deliberation, then, our models must be such that the prejacent proposition 'φ' of a deontic sentence-e.g. 'The poor are helped', 'Meat is eaten', etc.-is contingent in the model, in that the modal base must contain both φ-worlds and ¬φ-worlds. But if so, in all deontically relevant models, it will be the case that 'φ' is satisfied in at least one world in ∩f(w). And this entails that for these models, (2) combined with (E2) implies that all sentences of the form 'Pφ' are true-again contrary to what error theorists claim. Accordingly, no matter whether we model the error theory in terms of (E1) or (E2), it is incompatible with mainstream deontic semantics: Whilst (E1) renders oughtsentences trivially true, (E2) leads to the truth of permissibility-sentences in all deontically relevant models. Given mainstream deontic semantics, it thus cannot be the case that all moral sentences are untrue. As a first interim result, then, we can conclude that in contrast to other metaethicists, error theorists cannot employ mainstream deontic semantics in order to explain the meaning of deontic moral sentences due to the incompatibility of the two positions. The diagnosis for this result is quickly found: Firstly, whilst we have understood (E1) and (E2) as simulations of the error-theoretic rejection of objective moral orderings, both merely describe well-known edge cases of mainstream deontic semantics which will standardly ascribe truth to deontic sentences as explained earlier. Secondly, the fact that mainstream deontic semantics treats permissibility as the dual of obligation implies that even if feeding error-theoretic assumptions into mainstream deontic semantics secures the falsity of obligation-sentences, this will automatically entail the truth of permissibility-sentences, and vice versa. There is no way round the result, then, that the error theory and mainstream deontic semantics are incompatible. 4 Ways out of incompatibility How could error theorists react to this result? The most radical way would, of course, be to abandon mainstream deontic semantics entirely and develop an altogether different analysis of deontic sentences. Given the overwhelming advantages offered by the mainstream account, though, this should certainly not be error theorists' first choice.13 Rather, it seems more reasonable not to abandon, but to modify mainstream deontic semantics such that compatibility with the error theory can be secured. One way to do so would be to examine whether or not well-rehearsed solutions to long-known trivialisation problems within modal semantics could also help in the error-theoretic case. After all, trivialisation also occurs in other cases where the set of accessible worlds is empty, or where the set of highest-ranking worlds is empty because there are 13 I thus agree with Evers' (2014: 290) "take-home message" that "there is little hope for a theory according to which moral modals are completely unrelated to other modal language." 9 inconsistent standards of evaluation.14 Accordingly, if such trivialisation problems have been solved elsewhere, their solutions might also be applicable to the problem at hand. However, I do not believe that this endeavour has much chance of success. For instance, error theorists cannot fix their semantics by emulating the standard approach to the trivialisation of necessity-claims, i.e. by restricting the semantics of moral deontic sentences by the condition that the set of best worlds be non-empty.15 For, endorsing this condition would commit error theorists to the existence of morally best worlds, which is something they would want to reject qua error theorists.16 Moreover, note that the problems generated by (E2) are not due to problematic accessibility relations. For, rather than taking no world to be morally accessible, (E2) grants that the set of morally accessible worlds contains all relevant worlds ∩f(w). Similarly, Kratzer's approach to solve trivialisation problems in cases of partially inconsistent evaluation standards will not help either. For, whilst Kratzer (1981: 67) seeks to avoid trivialisations due to competing ideals and inaccessible worlds by introducing ordering sources (cf. Chrisman 2016: 99), it is exactly moral error theorists' stance on such moral orderings that leads to their incompatibility with standard deontic semantics.17 Here, then, is a better way forward. Return to (P): (P) There are objective moral standards, which error theorists regard as non-negotiable but false. In §3, we simulated error theorists' rejection of (P) within our deontic model M in terms of empty sets of best worlds and empty ordering sources, which yielded the truth of ought-sentences and permissibility-sentences respectively. But there are also other ways of conceiving the relation between deontic sentences, M and (P). According to one, the mainstream analysis provided by (1) and (2) is crucially incomplete and must be augmented by adding (P) as a further semantic component of O and P. According to the other, (1) and (2) provide correct analyses of O and P, but must be supplemented by the observation that (P)'s relation to deontic sentences is one of conceptual entailment or presuppositional inference. The hope then is that once our understanding of the semantic relation between deontic sentences, M and (P) has been corrected along one of these lines, the modified semantics will return truth-values for deontic claims which are compatible with the error theory. I will look at these proposals in turn. 14 For more on inconsistent standards, see Chrisman (2016: 79) and Kratzer (1981: 67). 15 Compare the restriction of the semantics for modal system KD by the condition that the set of accessible worlds be non-empty, which corresponds to the axiom '£φ ® ◊φ' (Chellas 1980). 16 In §4.2, I discuss the more promising suggestion of understanding this condition as a presupposition of moral sentences. 17 Another unsuccessful putative 'easy fix' is the suggestion that error theorists should not proclaim that no moral assertion is ever true, but that no moral assertion is ever non-trivially true. For, note that the trivialisations exposed here do not concern negations or conditionals, but non-negated, substantive first-order assertions. Since error theorists themselves believe that accepting the truth of such atomic first-order moral sentences commits us to the existence of objective moral orderings, they should be unhappy about accepting the truth of 'Oφ' or 'Pφ', trivial or not. 10 4.1 The conjunctive account Let us start, then, with what we can call the 'conjunctive account'.18 This retains the semantic analyses of deontic operators provided in (1) and (2), but supplements them by adding (P) as a second conjunct: (3) ⟦Oφ⟧M &,(,) = {w : {v : v ∈ ∩f(w) and there is no v' ∈ ∩ f(w) such that v' <g(w) v } ⊆ ⟦φ⟧M &,(,)} and (P) (4) ⟦Pφ⟧M &,(,) = {w : {v : v ∈ ∩f(w) and there is no v' ∈ ∩ f(w) such that v'	<g(w) v } ∩ ⟦φ⟧M &,(,) ≠ ∅} and (P) Two reasons explain why this conjunctive analysis is attractive for error theorists. Firstly, by adding (P) as an explicit component of the definitions of O and P, (3) and (4) are fully in line with error theorists' contention that (P) is a non-negotiable part of the meaning of deontic moral sentences. Secondly, (3) and (4) assign falsity to all deontic sentences when combined with error-theoretic assumptions. For, since error theorists reject the second conjunct (P) as false, (3) and (4) will return the truth-value false for all formulae of the form 'Oφ' and 'Pφ'-just as error theorists maintain. Hence, in contrast to mainstream deontic semantics, the conjunctive account is indeed compatible with the error theory, both with regard to the truth-values it generates and the assumption (P) that it identifies as an integral part of the meaning of deontic moral assertions. Still, error theorists are well-advised not adopt it, as it is not only formally costly, but also semantically unconvincing. Starting with its formal costs, the conjunctive account affords compatibility with the error theory at the expense of unification. That is, since this analysis adds a conjunct about the existence of objective standards of evaluation that will not be shared by all deontic operators-for instance, the semantics of prudential 'oughts' will not include it-it implies that different deontic operators require different semantic analyses, and thus reduces the level of semantic unification that mainstream deontic semantics affords. More significantly, it also trades off compatibility with a deontic semantics against compatibility with standard deontic logic. For, it is obvious that (3) and (4) no longer treat the truth-conditions of 'Oφ' and 'Pφ' as duals: Since (3) and (4) make it possible simultaneously to assign falsity to 'Oφ' and 'P¬φ', the dual schema, Oφ « ¬P¬φ, no longer holds (Chellas 1980, Def. 7.2). Since this dual schema is one of the key pillars of standard deontic logic, adopting the conjunctive account thus precludes error theorists from accepting standard deontic logic. Most importantly for my purposes, though, the conjunctive account reaches compatibility with the error theory at the cost of semantic plausibility. Firstly, adding (P) as a second conjunct lacks semantic motivation. To elaborate, when asked why (P) must be included in the definitions of O and P, I suppose that error theorists will respond that (P) is a non-negotiable part of the meaning of deontic sentences, and must 18 This account has been suggested to me by prominent error theorists. Evers (2014: §5, 2016: §3) can also arguably be read as hinting at such an account. 11 thus be explicated within our semantic analysis as envisaged by (3) and (4). However, (1) and (2) already allow us to model as much: All we have to do is to point to the ordering source g(w) and explain that in the case of deontic moral sentences, g(w) must not be empty and concern standards which are objective in a relevant sense. Consequently, since the second conjuncts of (3) and (4) merely replicate what is already contained within (1) and (2), we have been given no semantic reason to include them in our analysis of deontic moral sentences. Without such semantic reasons, though, the conjunctive analysis remains objectionably ad hoc: Whilst it generates truth-values that cohere with the error theory, it lacks any semantic motivation. Secondly, the conjunctive account is based on an unconvincing understanding of the relation between deontic sentences, M and (P). For, even if we grant that (P) is non-negotiable in error theorists' sense, it is not plausible to suggest that when asserting 'Oφ', say, we are asserting (amongst other things) that there are objective moral standards. Rather, it is far more convincing to hold that asserting 'Oφ' entails or presupposes as much. But if so, we should not model the relation between mainstream deontic sentences and (P) conjunctively, but in terms of entailment or presuppositional inference.19 Hence, whilst (3) and (4) are compatible with the error theory, they do not provide a convincing semantics of deontic modals. The conjunctive account, then, is no help to error theorists. 4.2 The Strawsonian account A more promising approach to the relation between deontic sentences, M and (P), then, is to propose that (P) stands to deontic sentences in some form of inferential relation. This can be spelt out in one of two ways. According to the 'entailment account', deontic sentences conceptually entail (P), such that anybody who is committed to the truth of 'Oφ' or 'Pφ' is also committed to the truth of (P). This, in turn, promises good news for error theorists. For, if we are to believe them that (P) is false, the entailment account implies that 'Oφ' and 'Pφ' are also false-just as error theorists maintain. According to the 'Strawsonian account', deontic assertions presuppose (P) in the sense that 'Oφ' and 'Pφ' can be ascribed determinate truth-values as spelt out by (1) and (2) only if (P) is true; otherwise, 'Oφ' and 'Pφ' are neither true nor false (Strawson 1950). Again, this holds much promise for error theorists. For, since they argue that this presupposition fails, the Strawsonian account will attribute the value neither true nor false to all deontic moral sentences. As long as error theorists are willing to interpret their characteristic thesis that all moral assertions are untrue not as proclaiming that all moral sentences are false, as the standard error theory does, but as stating that they lack determinate truth-values, this presuppositional semantics thus delivers exactly the right result for a Strawsonian, non-standard error theory.20 19 Error theorists might agree. For instance, Olson (2014: 65, my emphasis) speaks of "'the conceptual claim', namely the claim ... that moral claims entail claims about irreducibly normative reasons." Similarly, Kalf (2018) discusses in detail whether moral sentences' relation to (P) should be understood in terms of entailment or presupposition. 20 Despite, we may add, the reservations which standard error theorists have voiced about the Strawsonian account (Streumer 2017: 123-124; Olson 2014: 12-13). 12 For the remainder of this paper, I will focus exclusively on the Strawsonian account. Three reasons explain why. Firstly, without arguing this point here I believe that the presuppositional approach generally provides a more accurate depiction of the relation between deontic sentences and (P) than the entailment account.21 Secondly, note that the entailment account does not in fact modify the semantics of 'Oφ' and 'Pφ' as spelt out by (1) and (2). Remember, though, that as explained in §3, (P)'s falsity, modelled along the lines of (E1) and (E2), leads to the truth of 'Oφ' and 'Pφ' respectively when combined with (1) and (2). Accordingly, without adapting (1) and (2), it is by no means clear how (P)'s falsity is supposed to secure the falsity of 'Oφ' and 'Pφ', as the entailment account envisages. Thirdly, the arguments I will shortly develop against the Strawsonian account are also applicable to the entailment account. Accordingly, I will henceforth set the entailment account aside and turn to the assessment of the Strawsonian account instead. How does the Strawsonian account fare, then? To start with, it is clear that it once more proves formally costly. After all, following Strawson in introducing the truthvalue neither true nor false amounts to giving up the law of the excluded middle, and thus forces error theorists to replace classical logic with some trivalent logic. Furthermore, it is not obvious that presupposition failure precludes all ascriptions of determinate truth-values. For, if negation takes widest scope, as in 'It is not the case that the poor ought to be helped', this sentence is true whenever the statement 'The poor ought to be helped' is not true (Sinnott-Armstrong 2006: 34, Wright 1992: 40). Some suggest that this, in turn, requires introduction of different senses of negation together with their logical interactions, where so-called presupposition-preserving negation prevents the ascription of determinate truth-values, whereas so-called presupposition-denying negation does not (Horn 1985). Consequently, if error theorists chose to adopt the Strawsonian account, they would once more find themselves burdened with additional 'formal baggage' in the form of a non-classical, trivalent logic and possibly different senses of negation. More importantly for my purposes, though, the Strawsonian account once more remains semantically wanting. To see why, let us return to (P): (P) There are objective moral standards, and specify again how exactly (P) could be simulated within the framework of deontic semantics. In slightly modified form, we have met two possible interpretations in §3, namely the assumption that the set of best worlds be non-empty: (P1) {v : v ∈ ∩f(w) and there is no v' ∈ ∩f(w) such that v' <g(w) v }≠ ∅, and the assumption that the moral ordering source be non-empty: 21 For instance, it is very plausible that (P) passes the 'projection test', in that (P) arguably projects from embeddings such as negation, which speaks against the entailment account. However, see Lycan (2000) and Beaver/Geurts (2014) for the 'projection problem' and further controversial issues surrounding presupposition and its interpretation. 13 (P2) g(w) ≠ ∅. Next, note that the Strawsonian account will provide a successful deontic semantics for error theorists only if (P1) or (P2) are such that, firstly, deontic moral sentences plausibly presuppose either of them and, secondly, error theorists want to reject (P1) or (P2) as false. However, neither interpretation of (P) fulfils both conditions. Starting with (P1), we fortunately need not decide here whether or not this really is a presupposition of deontic moral sentences.22 For, even if it were one, it would not be a presupposition that error theorists should seek to reject. To elaborate, remember that according to mainstream deontic semantics, the set of best worlds will be nonempty, as demanded by (P1), only if the moral ordering source places demands on worlds which some world satisfies. For instance, if morality required that 'r' and 's' be the case, where 'r' and 's' can both be simultaneously true, (P1) will be met. If, in turn, 'r' and 's' were inconsistent, the set of best worlds would be empty because no world would satisfy both 'r' and 's'. Now, whether or not morality would ever place inconsistent demands on us is a matter of dispute-some will hold that there are genuine moral dilemmas, whereas others will deny as much. Most importantly for our purposes, though, this dispute should not be understood as a semantic debate about the meaning of moral words, but a substantively moral debate about the nature of moral principles. As Chrisman (2016: 101) explains, [e]ither way, the problem for a semantics for 'ought' based on any rule requiring us to interpret ought-claims in terms of prejacent propositions being true in all of some set of possible worlds is that the possibility of dilemmas seems to be a substantive question about the nature of moral ... demands-thus, not a question that should be answered by semantic fiat. Nor, we should add, is this a question that should be answered by error theorists. After all, error theorists should not be understood as denying that moral standards ever place consistent demands on us. That is, they should neither deny that moral standards can be understood as sets of consistent 'prejacent' non-moral propositions, {p, q, r, ...}, nor that once thus specified, these propositions might be satisfied by some worlds. More vividly, they need neither dispute that a moral ordering source might include the propositions 'The poor are helped' and 'Somebody works for charity', nor that in some of the worlds within the modal base, the poor are indeed helped and someone does work for charity. What they do contest is, rather, that this or any other moral ordering source induces correct moral orderings. Accordingly, since (P1) is not an assumption that error theorists should feel committed to rejecting, (P1) fails as a basis for the Strawsonian account. (P2) is more promising. For, since error theorists will want to deny that worlds can be put into some moral order, it is fair to assume that in contrast to (P1), they will indeed want to reject (P2) and thus defend the equivalence of all relevant worlds. However, I do not believe that error theorists can make a systematic case for (P2) being a presupposition of deontic moral sentences. 22 See also Chrisman's (2016: ch. 4) discussion of "the challenge of dilemmas". 14 To elaborate, let us start by pointing out the obvious, namely that the Strawsonian account depends on reading (P2) as a presupposition of deontic sentences, and its falsity as a case of presupposition failure. However, there is also a second interpretation of (P2)'s falsity available. This takes (P2)'s falsity at face value, in that it understands its implication of all possible worlds being morally indistinguishable to mean exactly that: namely, that all possible worlds are of equal moral value. Put differently, this second understanding does not read (P2)'s falsity as a case of presupposition failure, but as expressing the content of a first-order moral theory. To illustrate, assume that we are dealing with a radical moral theory according to which all possible worlds are just as morally good as one another, no matter what these worlds comprise. Assume further that according to this toy theory, no action is ever obligatory, whilst all courses of action-whatever they might involve-are permissible. Of course, we might not find this theory morally plausible. But that does not matter here. What does matter is that modelling this toy theory within deontic semantics implies that we are dealing with an empty ordering source, in that all relevant worlds are equivalent with respect to the moral ideal. Yet this time, we would not want this case to be a marked instance of presupposition failure that prohibits the ascription of determinate truth-values. Rather, mainstream deontic semantics along the lines of (1) and (2) generate exactly the truth-values that this toy moral theory envisages: All moral ought-claims with prejacent propositions that are contingent in the model come out as false, whereas all permissibility-claims with contingent prejacent propositions come out as true. The emerging problems should by now be evident. Firstly, given that in the case of the moral toy theory, we would want to ascribe determinate truth-values to deontic sentences despite modelling this theory in terms of an empty ordering source, it cannot be the case that deontic moral claims generally presuppose non-empty ordering sources. Secondly, given that the deontic formalisation of this moral toy theory is formally identical to our analysis of the error-theoretic detection of presupposition failure, in that both are modelled in terms of empty ordering sources that hold all worlds to be morally equivalent, we cannot formally distinguish between them. Accordingly, we have no systematic way to differentiate between cases in which deontic sentences are true or false, and cases in which determinate truth-values must be withheld because of presupposition failure. Thirdly, it is clear that moral error theorists will want to regard this moral toy theory to be just as erroneous as any other moral standard. But if so, it must rest on the same false presupposition as all other moral theories, so that error theorists will also want to withhold ascription of determinate truth-values to all of its moral verdicts. However, if this presupposition cannot plausibly be simulated in terms of non-empty ordering sources, nor non-empty modal bases, how is this presupposition to be modelled within the Strawsonian account? Now, I fully agree that the error-theoretic case of presupposition failure and that of the toy moral theory are intuitively different despite being formally indistinguishable. After all, both give competing explanations as to why all relevant possible worlds are morally equivalent, in that the latter endorses a specific moral theory, whereas the former rejects any such theory. However, it is not sufficient to point to intuition at this point. Rather, for the Strawsonian account to work, it must present a semantics that 15 makes possible systematic identification of cases of presupposition failure, together with the systematic, and not intuitive, attribution of the values true, false and neither true nor false to deontic claims. Given their formal identity, no such systematic differentiation between the error-theoretic simulation of presupposition failure and the moral toy theory has been offered as yet. Unless moral error theorists can provide convincing answers to all three problems, then, the Strawsonian account's promise to provide a systematic reconciliation of deontic semantics and the error theory remains exactly that: a mere promise which is yet to be kept. 5 What to take away When discussing the error theory, metaethicists have almost exclusively focused on its ontological thesis that there are no categorical reasons or objective moral properties. As this paper has shown, it is time that we start to put the error theory's semantic and formal commitments to the test. In this paper, I have made a start on that project by arguing that although error theorists aver that moral utterances are meaningful assertions, it is by no means clear that they can provide a persuasive account of deontic sentences' meaning. I conclude, therefore, that at least as far as things stand presently, moral error theorists still owe us a convincing semantics of deontic moral sentences. 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