Ethical Autonomy Post-Prior? Jack Woods and Barry Maguire. Abstract

Transcription

1 Ethical Autonomy Post-Prior? Jack Woods and Barry Maguire Abstract In myth and legend, Hume denied that is -facts entail ought -facts. This is sometimes known as Hume s dictum and the resulting insulation of ought -facts from is - facts as ethical autonomy. Hume s dictum has exercised much influence over theorists in ethics and metaethics over the last century. Unfortunately, construed as a thesis about logical entailment, Hume s dictum is simply false. In light of Arthur Prior s famous counterexamples to the claim, it has been difficult to give a non-trivial substantive account of this supposed logical barrier. Many theorists have attempted to give model-theoretic or quasi-logical characterizations. We view this as a mistake since these types of account miss the substantive nature of Hume s dictum that we can t infer an ought from an is. We develop this point here, using a recent account by Daniel Singer (2015) as our stalking horse. Singer suggests that the problem with is-ought is that there is no legitimate argument from non-normative premises to a relevantly normative conclusion. We agree. Singer develops this point in terms of a model-theoretic property of norm-invariance. We disagree. The formal property used to explain Hume s dictum, the persistence of norm-invariance across entailment, holds even for metasemantic theories on which you can clearly derive an ought fact from is facts. We recast Singer s insight using the hyperintensional notion of grounding and argue the result is a useful amendment to existing hyperintensional accounts of ethical autonomy. Page 1 of 15

2 Ethical Autonomy Post-Prior? In myth and legend, Hume denied that is -facts entail ought -facts. This is sometimes known as Hume s dictum and the resulting insulation of ought -facts from is - facts as ethical autonomy. Hume s dictum has exercised much influence over theorists in ethics and metaethics over the last century. Unfortunately, construed as a logical thesis about ordinary entailment relations, Hume s dictum is simply false. A.N. Prior famously showed this with a pair of counterexamples to ethical autonomy (1960). Consider, for example, a normative claim N and a non-normative claim M. If N v M is non-normative, then the non-normative ~M & (N v M) entails the normative N. This shows that these non-normative premises can entail normative conclusions. If the disjunction is normative, then it is entailed by the non-normative M. This also shows that certain non-normative premises can entail normative conclusions. Since N v M is either normative or non-normative, we have an utterly compelling argument that the non-normative can entail the normative. These entailments are impeccable; in the ordinary sense of entailment, we really do have a case of the normative being entailed by the non-normative. 1 But there is a familiar shortcoming with these counterexamples: there is no way to argue from the premises of a Prior example to the conclusion without already being a position to assert the conclusion. Even though they are great entailments, Prior s arguments are lousy ways of acquiring information about the normative. Daniel Singer (2015) argues this point against Prior as follows. Anytime we can reason from intuitively non-normative premises to an intuitively normative conclusion, this is due to the fact that the possibilities consistent with the premises already validate the conclusion; he then argues that if the premises of an argument are insensitive to normative facts (in his terminology, if they are norm-invariant), then the conjunction of the premises and the conclusion is also insensitive to the normative facts. This means that we add no new normative information, information being construed in terms of sets of norm-world pairs, by so arguing. Singer s point here is absolutely apt you can see why the Prior arguments don t show that we can get an ought from an is by noticing that anytime you can make such an inference, we are already in a position to accept the conclusion and we gain no information about the normative, in the particular sense specified by Singer, by so doing. Put another way, getting an ought from an is is more than the latter being entailed by the former or, even, deductively deriving an intuitively normative proposition from non-normative propositions. It is rather about adding (permissibly!) into our stock of beliefs a proposition that makes a normative difference. 1 There are ways to modify the relevant sense of entailment to block these examples, but none of them have reached anything like acceptance. See Restall and Russell (2011) for the most sophisticated way of doing this. We address their account explicitly elsewhere and obliquely below. Page 2 of 15

3 All deductive argumentation is non-ampliative, so you never gain new information, in the sense of narrowing the set of (normative/factual) possibilities consistent with your beliefs, by arguing deductively. Singer's objection to Prior is that if you start with a set of premises that don't make a normative difference, then you will never shake loose a consequence that makes a normative difference. Of course, you might still gain new information in the sense of making explicit and accepting a proposition which is a consequence of what you already believe. In any such case, however, this proposition was already tacitly part of your informational state. While we agree with Singer that that Prior s counterexamples suffer from this sort of example, we think that his particular way of developing the point is inapt. It commits what we have come to think of as a pervasive error in dealing with the interaction of is facts and ought facts. The error is this: it is nearly impossible to simultaneously give a logical account of the implicational autonomy between is facts and ought facts while simultaneously giving a taxonomical account of the differences between these two types of facts. Taxonomical theses are substantive matters; giving a formal account of this difference tends to imply substantive claims about the nature of the normative and, more importantly, to rule out certain plausible conceptual and metaphysical claims about the normative. Singer s account is of a piece with this: in taxonomizing the normative and the non-normative, it implicitly makes the claim that there are no conceptual or metaphysical truths about the normative. This, however, is a claim not about the logical structure of normative and non-normative facts, but a substantive claim about the nature of the normative. We will turn to this shortly. First, a related point about what Prior was up to in giving his counterexamples. Prior gave a logical counterexample to is/ought transitions; since logic makes no assumptions about the normative, a logical counterexample to is-ought is the strongest possible. Consequently, showing that we can overturn Prior s examples or, rather, blunt them is to give the weakest possible defense of the barrier between is and ought. 2 We need to also consider whether there are other notions of inference or argument that might uphold an autonomy thesis for which this defense does not work. We will shortly introduce a variety of such notions, involving metaphysical or analytic background propositions, and show that Singer s defense does not help with these examples. To orient ourselves, it is illuminating to look again at what Hume had in mind by the thought that we can t get an ought from an is: 2 We say blunt here because Singer does not show that Prior s examples aren t instances of valid entailments. His point is rather that entailment doesn't capture Hume s dictum. Page 3 of 15

4 In every system of morality, which I have hitherto met with, I have always remark d, that the author proceeds for some time in the ordinary way of reasoning, and establishes the being of a God, or makes observations concerning human affairs; when of a sudden I am surpriz d to find, that instead of the usual copulations of propositions, is, and is not, I meet with no proposition that is not connected with anought, or an ought not. This change is imperceptible; but is, however, of the last consequence. For as this ought, or ought not, expresses some new relation or affirmation, tis necessary that it shou d be observ d and explain d; and at the same time that a reason should be given, for what seems altogether inconceivable, how this new relation can be a deduction from others, which are entirely different from it [I] am persuaded, that a small attention [to this point] wou d subvert all the vulgar systems of morality, and let us see, that the distinction of vice and virtue is not founded merely on the relations of objects, nor is perceiv d by reason. (Treatise, 3.1.1) For Hume, a logical deduction involves reasoning with relations of ideas. But even the most cursory inspection of Hume s account of relations of ideas shows that his notion of deduction involves relations which we would not ordinarily consider part of logic, including mathematical and geometrical claims like the interior angles of a triangle sum to 180 degrees. His account of deduction also plausibly includes facts based on knowledge of meaning (Noonan 2014). So there are some analytic statements built into what counts as a legitimate notion of deduction for Hume. Hume is therefore not objecting that we can t logically derive ought facts merely from is facts, but the stronger claim that we can t analytically derive ought facts merely from is facts. 3 Given his repeated request for explanation (italicized above), it is possible that Hume is also interested in the stronger claim that is-facts are not metaphysically sufficient for ought-facts. We will return to this point below. Singer s principle is designed to be preserve as much as possible of the logical autonomy thesis that Prior was opposing, without succumbing to the shortcomings Prior articulates. Singer argues we better capture the sense of Hume s dictum by means of: IS-OUGHT-GAP: There is no argument from non-normative premises to a relevantly normative conclusion. 4 3 Admittedly, given a notion of analytic entailment, all normative facts are analytically entailed by non-normative facts, but that is because they are analytic truths. This is irrelevant to our point, being analogous to the claim that any tautology follows from any set of sentences whatsoever. It s easy to set such examples aside. 4 Singer intends his analysis to explicate the notion of relevance in IS-OUGHT-GAP. It isn t entirely clear to us how this works. We will return to relevance below when we suggest our emendation to Singer s account. Page 4 of 15

5 In order to spell out the requisite notion of relevance, Singer appeals to a semantical criterion norm-invariance which he spells out in terms of Gibbard s expressivist semantics. 5 This semantics replaces the notion of a possible world with a hybrid notion of a world-norm pair consisting of a possible world and a set of norms. We can write such <w,n>. We proceed as usual for non-normative terms, treating propositions as sets of world-norm pairs, and the logical operations as set-theoretic operations (intersection, union, restricted complementation) on these. The normative component figures essentially in the semantics for normative expressions like ought, wrong, etc. in the obvious way details aren t important for the point we want to make here. Truth at a world-norm pair (<w,n> φ) is defined with reference both to the worldly component and the normative component since a sentence might contain both normative and non-normative materials. We can intuitively think of <w,n> φ as saying, when φ is a normative claim like we ought not murder as something like the norms in n forbid murdering, corresponding modeltheoretically to the claim that <w,n> is in the proposition (i.e. set of world-norm pairs) [φ]. When φ is a descriptive claim like grass is green, we can think of <w,n> φ as saying grass is green in w and, likewise, to the claim that <w,n> is in [φ]. We define the entailment of a sentence φ from a set of sentences Γ (Γ φ) in the obvious way ([Γ] is a subset of [φ] for [Γ] intersection of the propositions denoted by the sentences in Γ if there are any, the empty set otherwise). We let (as entailment or the world-verification relation above), as usual, be disambiguated by context. Given this set-up, we can define norm-invariance easily: NORM INVARIANCE: φ is norm-invariant iff w[ n<w, n> φ n<w,n> φ] 6 This says that a sentence in norm-invariant if and only if it is satisfiable at a worldnorm pair with the choice of some norm only if it is satisfiable by a world with the choice of any norm. This captures at least one sense in which the normative content of a sentence is irrelevant to whether or not it holds at a world-norm pair: if it can be true, then any old norms would do. With the notion of norm-invariance defined, Singer turns to arguing that WORLD- NORM GAP, a formal specification of IS-OUGHT-GAP, captures the essence of Hume s claim. WORLD-NORM GAP is a claim about the persistence of norm-invariance across valid argument: 5 Singer does not regard Gibbard s particular framework as essential to his overall point; we agree, but will follow him in developing it in these terms. 6 Alternatively, w( n<w,n> ϵ [φ] n<w,n> ϵ [φ]). That is, given a world w, if [φ] contains a pair <w,n> for a norm n, then it contains every pair <w,k>. Page 5 of 15

6 WORLD-NORM GAP: If Γ φ and all of X are norm-invariant and satisfiable, then Γ& φ (the conjunction of all the sentences in Γ and φ) is norm-invariant. 7 It should immediately be noted that there is nothing special about norms here. Let a world-octopus pair be a pair of a possible world and an favored octopus, letting the octopus slot interact with some select expressions, like Octo an expression dedicated to referring to the privileged octopus in the obvious way, allowing us to say things like If Bob is happy, then Octo is happy. We can then formulate the obvious notion of octopoidal-invariance and prove WORLD-OCTOPUS GAP: WORLD-OCTOPUS GAP: If Γ φ and all of Γ are octopus-invariant and satisfiable, then Γ & φ is octopus-invariant as well as proving similar things about time-invariance, location-invariance, speaker- invariance, and so on. There is simply a general fact here about the persistence of index-invariance across deductive argument; the generality of this fact is important since it means that Singer s claim that WORLD-NORM GAP captures Hume s is-ought gap is correct only if his definition of normative facts as those which are norm-invariant is correct. However, his definition only works cleanly when we deny that there analytic or metaphysically necessary claims about normativity we will develop this point shortly. If we reject views according to which certain propositions are norm-invariant because they are analytic or necessary, then norm-invariance does a reasonably good job at capturing the notion of a non-normative proposition. If the worldly facts do not interact with the non-worldly facts, then it shouldn t matter for a non-normative statement which norms we pick. If it matters, then this shows that it is a claim about the findings of certain norms and hence it will not be norm-invariant. If, then, this distinction between normative and non-normative facts is adequate, then WORLD- NORM GAP would seem a plausible analysis of Hume s dictum. But this is a big if. In support of our claim that the crux of the matter really is the taxonomic account of normative facts, note that WORLD-NORM GAP holds even when is-ought intuitively and paradigmatically fails. Suppose, as Searle thought, that we can impose normative demands on ourselves by making promises (Searle 1964) and this is analytic of the notion of promising. If Searle is right, we can analytically infer from the existence of a piece of non-normative behavior a sincere promise (perhaps with uptake, etc.) to the existence of a normative demand on ourselves. Even though this doesn t restrict the set of possibilities consistent with our beliefs presuming we restrict the set of worlds in such a way as to respect the analytic connection between promising behavior and promissory obligations the inference adds an explicit normative proposition that was antecedently only implicit in the combination of putatively analytic facts about normativity and non-normative facts. But it is still true, even on a 7 Strictly speaking, we need compactness to legitimate this definition, but it s easy to see how to modify the definition to accommodate cases where there is no (finite) conjunction equivalent to Γ& φ. Page 6 of 15

7 Searlean semantics, that if a set of sentences is normatively invariant and satisfiable, then the logical consequences of this set are likewise norm-invariant. The key fact here is that promissory behavior is not norm-invariant for Searle, so the premises here counts as normative, not non-normative, facts. Intuitively, this is incorrect. Or consider Russ Shafer-Landau and Terence Cuneo s (2014) thesis that many substantive moral propositions are also analytic truths. They include examples such as that it is wrong to torture others just because they have inconvenienced you, that it is wrong to rape a child solely to indulge one s lust, and that the interests of others are sometimes morally weightier than our own. 8 If any such proposition is analytic, then it will be included in any set of norms, and hence will be norm-invariant. But these are paradigmatically normative propositions. We get the same result if it is not analytically but metaphysically necessary that any system of norms will include some particular normative proposition. So choosing between conceptual and metaphysical construals of world-norm pairs doesn t alleviate our point. Can we rule out accounts, like Searle s, Cuneo and Schafer-Landau s, of the meaning or metaphysics of the normative? Or, more importantly, should we do so? Part of what motivates Singer to give his account is the prospect of an account of is and ought that also permits an illuminating deontic logic unlike the similarly motivated account given in (Pigden 1989). Deontic logic, like tense logic or modal logic, is a logic-of, not a logic in the broadest sense. As such, the semantic base over which the logic is defined needs to accommodate the analytic features of the notion being theorized. 9 When we do the logic of alethic modals, for example, we restrict the accessibility relation between worlds so that every world sees itself i.e. we requires that the accessibility relation on possible worlds, R, be reflexive. 10 We can then argue about whether R should be transitive, euclidean, etc. Some of these arguments take place at the level of claims about the meaning of alethic modals, corresponding to claims about the meaning of necessary itself; some take place at the level of fundamental metaphysics, corresponding to claims about the domain of application we want to apply necessary over. 11 Constraints motivated by the first type of argument, such as the reflexive property, correspond to features of the meaning of necessity itself. A semantics for a notion like necessity and, more importantly, a philosophical taxonomy, needs to take into account these 8 They also offer It is pro tanto wrong to impose severe burdens on others simply because of their physical appearance but we re confident it s ok for you to pay someone to move your piano. 9 Arguably, this is true even for logical expressions, but the case for this would distract here. It s clearly true for cases of like those we re discussing. 10 If the T axioms doesn t strike the reader as sufficiently general, consider instead the restriction to normal modal logics. The point is the same, even though the T-axiom is also plausibly part of the meaning of the alethic modal necessarily. 11 Compare, for example, the arguments against S4 in (Salmon 1989) to those in (Dummett 1993). Page 7 of 15

8 analytic and, perhaps, these metaphysical connections when distinguishing between types of statements. When we turn to giving a semantics for normative notions, then, we need also ask what features of normativity should be built into the semantics as corresponding to the meaning of the normative expressions themselves. 12 For a related example, suppose we, following Kaplan (1977), add into our index set a designated speaker slot (to interpret the first-person indexical I.) We can then develop a logic of the firstperson pronoun. But should we allow any object to serve as the speaker? This is by no means clear. If we do that, we have moved away from giving a logic of the firstperson pronoun, in a sense, since our notion of the reference of a first person pronoun is always an agent capable of representing themselves. Similar problems plague Singer s characterization of non-normative in terms of a wide-open version of Gibbards s semantics since there are alternative metasemantic views about the meaning of the normative expressions and more restrictive semantic constraints we might impose. Consider, for example, the widely-held claim that normativity supervenes on the natural. Representing this in a Gibbardian semantics as a metaphysical or conceptual claim about the normative would involve banning pairs of world-norm pairs which agree in their worldly component but disagree in their normative component. Suppose we do this. Now, let W be the conjunction of all the worldly facts about a possible world w. W is then norm-invariant over the supervenient worlds, but surely this is the wrong result W is paradigmatically non-normative. A similar point would hold on the assumption that the normative is metaphysically or conceptually necessary, which are not particularly uncommon metaethical stances. From the other direction, consider a metasemantic view on which there is no substantive gap between is and ought SIMPLE CONVENTIONALISM. Let the norms be related to the worlds in the following way: the norms figuring in n must cohere with the behaviors of the agents in w. 13 Call such world-norm pairs proper. Consider the claim that people tend to avoid murdering and say things like murdering is impermissible. This sentence is not norm-invariant over the proper worlds since certain choices of norms would clash with them. So the notion of a normative sentence here 12 Importantly, this is not to say that we cannot give a general semantic account of, say, necessity which doesn t build in these connections. However, such an account does not correspond to the intuitive meaning of the natural language expressions we re theorizing about when we do not build in these sorts of side-constraints. Rather, it corresponds to a more general account of the semantic function of alethic modals tout court. The important fact here is that moving from this type of abstract model theoretic account to one which actually represents the meaning of natural language expressions in some way requires side-constraints like those we are discussing. 13 For discussion of how to formulate such a view correctly, see (Einheuser 2006) and RE- DACTED. Note that when we interpret Gibbard s view literally in terms of plans, some such restriction like that to proper worlds is already called for not everything can be a complete plan. Page 8 of 15

9 overspills, marking clearly non-normative claims about behaviors as normative (intuitively, this is the analog to the Searle-ish example above.) One might worry that such claims are normative, presuming simple conventionalism, but this would be a mistake. These can (and should) be viewed as not normative claims, but rather claims that interact with normative claims. So, if the metasemantic view SIMPLE CON- VENTIONALISM is correct, then our semantics only ought consider proper worlds, and over proper worlds, norm-invariance cuts the distinction between normative and non-normative sentences in the wrong place. Of course, it might be thought that it is still progress enough to formulate a distinction between the normative and the non-normative on the assumption of an is-ought gap. This is also incorrect, which can be seen immediately by example. Let s add to the set of possible norms a null set of norms which holds when there there are no agents at all in the worldly component of a world-norm pair. We also hereby remove the restriction to proper world-norm pairs; all we require is that if there are non-null norms, then there are agents. But now notice that there is still a recognizable notion of an is-ought gap here. We cannot infer anything about the substantive nature of norms from a set of non-normative facts; the only conclusion we can make regarding the normative from the fact that there are no agents is that the null set of norms holds. 14 But this seems entirely consistent with what Hume has in mind we cannot infer anything about the character of normative facts or about what we ought to do from worldly facts. And, of course, there are intuitively non-normative facts here that are not norm-invariant like the fact that there are no agents. The upshot here is that glossing the non-normative in terms of normative invariance makes sense only if we allow, as a matter of meaning or metaphysics, norms to float free of the choice of worlds. To put it bluntly, Singer s claim that we can treat norminvariance as a non-controversial account of non-normativity is false. 15 The distinction between normative and non-normative propositions involves facts about the meaning of normative terms since model theory is a model of an underlying intuitive account of the meaning of things like normative expressions, we cannot simply set up a formal semantics where anything goes. See (Burgess 2008) and (Schroeder 2015) for sensible defenses of this point. Since the analysis of the non-normative in terms of normative invariance only makes sense on the maximally permissive set of 14 Note also that it doesn t follow from the existence of agents that there are non-null norms. Agents might, in this context, have no norms whatsoever. Note also that we could adapt the point about the possible necessity of norms to make the same point. 15 Singer could object here that his definition can be modified to accommodate this problem, but it is an easy problem to generalize. Hume s is-ought gap does not deny that there can be worldly consequences of facts about the existence or non-existence of norms in general or, even, worldly consequences of facts about the existence or non-existence of certain particular norms. Page 9 of 15

10 possible norms, it is not neutral with respect to various metaethical positions, many of which accept an is-ought gap. 16 Of course, Singer might argue that, since his gloss on the is-ought gap is meant be semantic, in the sense of deriving from the meaning of various expressions, it should not make presumptions about the underlying distribution of norms. Perhaps we really ought to assume a maximally permissive way in order to make sense of the meaning of normative expressions. Unfortunately, this still fails to do justice to the sense in which meaning can be beholden to background metasemantic issues. Suppose, for example, the simple conventionalist is correct about the relationships of the normative component of a world-norm pair to the worldly component. It is then presumably analytic of the various normative notions that they co-vary with underlying conventional behaviors of the agents making judgments involving them. 17 The appropriate notion of argument for an is-ought gap plausibly encompasses analytic entailments and thus there is no principled objection to restricting ourselves to proper worlds if the conventionalist is right about normative language. Likewise with the single norm restriction and the null-norm example. If we are right here about the taxonomy, then there will be many entailments of intuitively normative facts from non-normative facts since Singer-invariance only corresponds with non-normativity in the absence of background conditions. So, Singer s claim that IS-OUGHT-GAP or WORLD-NORM GAP captures the sense in which Hume thought we can t get an is from an ought fails since (a) (b) WORLD-NORM GAP cannot be falsified even when we constrain the set of worldnorm pairs in such a way that we can seemingly analytically infer an ought from an is, as in the Searleian view of promises described above, and The formal notion of norm invariance which is persistent over deductive argument only captures non-normativity when we have no analytic or metaphysical constraints on possible sets of norms However, Singer s original insight, captured by IS-OUGHT GAP, is important and worth preserving. Singer s own account suffers from a dilemma: either we can view it as succeeding in its attempt to provide a purely formal characterization of an autonomy thesis, but being of little interest since the relevant notion of argument is 16 It might be objected here that Singer s aim is to just characterize the is-ought gap on a Gibbardian picture. That his account works here is doubtful (see fn. 13, for example), but this is also clearly not his intention, as his closing remarks about the applicability of his solution to any reasonable semantics suggests. In particular, he is willing to extend his definition of norm-invariance to any reasonable semantics for moral terms (see the end of Singer section V). 17 Note that this does not mean that it is analytic of such notions that they co-vary with the underlying conventional behaviors at a context where they are applied. To think this would be to confuse conventionalism with naive subjectivism. Page 10 of 15

11 broader or we can view it as failing in its attempt to provide an autonomy thesis of significance for the relevant notion of argumentation. An inductive argument from similar failures suggests that this dilemma will afflict any characterization of the autonomy of ethics that appeals just to extensional ideology. Importantly, the failure of Singer s account illustrates the implausibility of simultaneously attempting to run a logical account of the is-ought gap while using extensional ideology to taxonomize the difference between normative and non-normative claims. We ll now briefly sketch an alternative account to show how we might preserve Singer s insight without running afoul of these problems. The key is to present a different account of the taxonomy of the normative and the non-normative which appeals to the hyperintensional ideology of grounding. 18 We then accept IS-OUGHT- GAP, but we take relevant to be cashed out in a significantly different fashion. 19 First, some details. Consider a few paradigmatic examples of problematic is-ought transitions: 1. Jones uttered the words I hereby promise to pay you, Smith, five dollars, therefore Jones has an obligation to pay Smith five dollars. 2. Ronnie wants to dance, therefore Ronnie has a reason to dance These are ampliative inferences, of course. But many ampliative inferences are perfectly acceptable. The question is what exactly is wrong with these ones. To answer this, we need to reach beyond these purely formal characterizations of the distinction between natural propositions and ethical propositions. Then we need some background principles that explain why inferences specifically from natural propositions to ethical propositions are problematic at least when we assume that no ethical bridge principles are being assumed. A richer taxonomy starts with the following thought: METAPHYSICAL AUTONOMY: If some fact E is ethical, and E is fully grounded just by some fact or set of facts Γ, then Γ contains at least one ethical fact. 18 On this gambit, see Maguire For an important discussion of asymmetric metaphysical relations between is s and oughts, see Mark Schroeder 2007, chapter 4. For alternative ways of using hyperintensional ideology to finesse is/ought, see Raven (ms) and Fogal (ms). 19 An astute reader here might wonder about interpreting relevant in IS-OUGHT-GAP in terms of relevance logic. This won t work in any obvious fashion: disjunction introduction is relevantly (R-)valid and it s easy to manufacture examples like Prior s which avoid the problem that disjunctive syllogism is R-invalid. A more promising approach would make use of the notion of relevant predication (developed by Meyer and Dunn), but discussion of the advantages and disadvantages of this approach awaits another occasion. See Samuels (ms) for details. Page 11 of 15

12 This principle would be enough to diagnose the flaw in arguments 1 and 2. In many contexts when we infer B from A we mean that A together with any pragmatically implied background facts is metaphysically sufficient for B, or, more strongly, that A provides the grounds for B. But, in 1 and 2, the premises are all plausibly natural, and the conclusions all plausibly ethical. If METAPHYSICAL AUTONOMY is true, the premises in these arguments fail to constitute full grounds for their conclusions. We should look around instead to see whether some ethical principles have been presupposed in the background. Perhaps it is so obvious that some version of humeanism is true, that you can simply assume the principle taking you from premise to conclusion in 2. Or perhaps the semantic/metasemantic thesis relating certain utterances in contexts with obligations is implicit, and can play the role of underwriting the transition from premise to conclusion in 1. To this taxonomic principle, for completeness, we can another principle such as the following: CONVERSE METAPHYSICAL AUTONOMY: If some fact or set of facts Γ contains at least one ethical fact, and Γ grounds or partially grounds some fact E, then E is ethical. 20 These two principles need some further taxonomic principles to play the role of the base clause. It is enough for current purposes to assume some intuitive account of which propositions are uncontentiously ethical to flesh out the definition. With this pair of theses, we can vindicate a version is-ought gap. Let us interpret it as follows: there is no argument from non-normative premises to a normative conclusion where the normative conclusion is fully grounded just by these premises. 21 If we interpret relevance in terms of being the full set of grounds, then we get a neat interpretation of Hume s claim about is and ought which we can falsify, but which expresses a full-throated claim about the interaction of facts of these two domains. This interpretation has other advantages as well. Singer has to rule out unsatisfiable premises by fiat. But it is easy to explain why arguments from inconsistent natural premises to ethical conclusions don t trouble anything in the vicinity of Hume s thesis; such premises never ground anything since grounding is factive. Inconsistent natural premises could thus not constitute the grounds of the ethical fact picked out by the conclusion. We can deal with Prior s other arguments easily as well. Take the first argument Singer discusses: Tea-drinking is common in England. 20 This principle overgeneralizes a bit. This can be fixed, but the relevant refinements are not crucial for our purposes here. 21 The use of just in the above accounts is crucial. We presume that a true disjunction is fully grounded in each true disjunct, but we could ground a mixed normative disjunction in a nonnormative disjunct. It would not, however, be fully grounded just by this disjunct. Page 12 of 15

13 Therefore either tea-drinking is common in England or all New Zealanders ought to be shot. Take our world, in which it is not the case (presumably) that all New Zealanders ought to be shot. The conclusion here obtains just in virtue of the natural disjunct. Since this is not ethical and it s the total grounds of the disjunction, the conclusion had better not be ethical. According to our taxonomy, it s not since it s grounded only by a natural fact. Change the world to one in which all New Zealanders ought to be shot. This might be because they were all so badly behaved, or because the true ethical principles in this world are very different from ours, or because some diabolical genius will destroy humanity otherwise. In any such scenario, the conclusion is true partly in virtue of an ethical fact. Assume that tea-drinking is still common in England in this world. Here we also have no counterexample since the fact that teadrinking is common in England does not constitute the full set of grounds for the disjunctive conclusion. Analogous things can be done for the other examples. *** Page 13 of 15

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15 Schroeder, M Slaves of the Passions. Oxford: Oxford University Press. Schroeder, M Is Semantics Formal? in Expressing Our Attitudes (Oxford University Press) Singer, Daniel J. (2015). Mind the Is-Ought Gap. Journal of Philosophy 112 (4): Woods, J. (forthcoming). The Normative Force of Promising in Oxford Studies in Normative Ethics, volume 6. Page 15 of 15