PERMISSIBILITY IS THE ONLY FEASIBLE DEONTIC PRIMITIVE

How many concepts do we need in ethics? Take the basic deontic concepts, that is, moral obligation and permissibility. Do we need both of these concepts in our ethical theorizing, or could we make do with just one of them? 1 A standard view is that these concepts are interdefinable —that is, either of them could be defined in terms of the other. On this view, either of obligation and permissibility could serve as a deontic primitive, allowing the other concept to be defined in terms of this primitive. More specifically, obligation and permissibility are usually thought to be interdefinable with the following duality definitions: 2


Johan E. Gustafsson
How many concepts do we need in ethics? Take the basic deontic concepts, that is, moral obligation and permissibility. Do we need both of these concepts in our ethical theorizing, or could we make do with just one of them? 1 A standard view is that these concepts are interdefinable-that is, either of them could be defined in terms of the other. On this view, either of obligation and permissibility could serve as a deontic primitive, allowing the other concept to be defined in terms of this primitive. More specifically, obligation and permissibility are usually thought to be interdefinable with the following duality definitions: 2 (1) It is obligatory to φ = df it is not permissible to not φ. 3 (2) It is permissible to φ = df it is not obligatory to not φ. 4 Part of the appeal of these definitions is the compelling idea that deontic modalities, such as obligation and permissibility, are related in the same way as alethic modalities, such as necessity and possibility. 5 Necessity and possibility are usually thought to be interdefinable with an analogous pair of duality definitions: 6 (3) It is necessary that p = df it is not possible that not p. 7 (4) It is possible that p = df it is not necessary that not p. 8 Together, these definitional schemes reflect the intuitive analogy between deontic and alethic modalities. 9 In this paper, I shall argue that neither (1) nor (2) works. Roughly, the problem is that a claim that some act is obligatory or permissible entails that there is a moral law, but the existence of a moral law is not entailed by a negative claim that some act is not obligatory or that some act is not permissible. Nevertheless, one direction of the interdefinability could (potentially) be salvaged. I shall argue that, if we are willing to leave out the conceptual possibility of moral dilemmas, then there is a plausible way to define obligation in terms of permissibility. So permissibility is the only feasible deontic primitive. 10

The varieties of obligation and permissibility
We shall be concerned with particular (rather than universal) obligation and permissibility. Bengt Hansson reminds us that Just as "it is obligatory to do p" often means "it is obligatory for everyone to do p" the phrase "it is permitted to do p" often contains a tacit "for everyone ". 11 It is universally obligatory to φ if and only if, for each person, it is obligatory for that person to φ. And it is universally permissible to φ i fa n do n l yi f ,f o re a c h person, it is permissible for that person to φ. These more universal notions are not interdefinable. 12 To see that universal obligation is undefinable in terms of universal permissibility, assume that there are just two people, Alice and Bob. And compare the following two cases, where Alice and Bob each face a choice whether to φ or to not φ: In the first case, it is permissible for each of Alice and Bob to φ, and it is only permissible for Alice to not φ. In the second case, it is permissible for each of Alice and Bob to φ, and it is permissible for no one to not φ. It seems then that, in the second case, it should be obligatory for everyone to φ whereas, in the first case, it is not obligatory for everyone to φ (it is only obligatory for Bob). So these cases differ in terms of universal obligation. Yet, in terms of universal permissibility, there is no difference, because it's permissible for everyone to φ in both cases and in neither case is it permissible for everyone to not φ. Hence we have a difference in terms of universal obligation which cannot be accounted for in any difference in terms of universal permissibility.
To see that universal permissibility is undefinable in terms of universal obligation, we consider a third and a fourth case, where again Alice and Bob each face a choice whether to φ or to not φ: In the third case, it is permissible for each of Alice and Bob to φ, and it is permissible for each of Alice and Bob to not φ. In the fourth case, it is only permissible for Alice to φ, and it is only permissible for Bob to not φ. Then it seems that, in each of the third and fourth cases, it is not obligatory for everyone to φ (in the fourth case, it is only obligatory for Alice) and it is not obligatory for everyone to not φ (in the fourth case, it is only obligatory for Bob). So these cases are equivalent in terms of universal obligation. But they differ in terms of universal permissibility, because, in the third case, it is permissible for everyone to φ but, in the fourth case, it is not permissible for everyone to φ (it is only permissible for Alice). Hence we have a difference in terms of universal permissibility which can't be accounted for in any difference in terms of universal obligation.
Moreover, we shall be concerned with unilateral, rather than bilateral, permissibility. A unilateral permission and a bilateral permission to φ each entail that it is permissible to φ. The difference is that a bilateral permission to φ also entails that it is permissible to not φ, whereas a unilateral permission to φ does not entail (nor rule out) that it is permissible to not φ. 13 If we take permissibility to be bilateral permissibility, we must give up the duality definitions. Neither obligation nor unilateral permissibility is definable in terms of bilateral permissibility. 14 To see this, compare a first case, where it's both obligatory and permissible to φ but neither obligatory nor permissible to not φ, with a second case, where it's neither obligatory nor permissible to φ but both obligatory and permissible to not φ. These cases differ in terms of obligation and permissibility but are equivalent in terms of bilateral permission, because in both cases neither to φ nor to not φ is bilaterally permissible. Hence we have a difference in obligation and permissibility that cannot be accounted for in any difference in bilateral permissibility.
Finally, we shall be concerned with moral obligation and moral permissibility rather than personal directives. It seems clear that the duality definitions do not hold for personal commands and permissions. A child who has neither been commanded to not smoke nor been forbidden to smoke cannot thereby plausibly claim to have been permitted to smoke. 15 In general, it seems that one could have been permitted to do some act φ without having been commanded anything. Yet that one hasn't been commanded anything does not entail that one has been permitted to φ. So there can be a difference in what one has been permitted to do without there being any difference in what one has been commanded to do. Hence having been permitted is undefinable in terms of having been commanded.T os e et h a thaving been commanded is undefinable in terms of having been permitted, consider a first case where you haven't been commanded anything and you have only been explicitly permitted to φ. So you have neither been permitted to not φ nor been prohibited to not φ. Compare this first case with a second case where you have been commanded to φ and explicitly permitted to φ. In terms of what you have been permitted to do, the first and the second case are equivalent, yet they differ in terms of what you have been commanded. Hence having been commanded is undefinable in terms of having been permitted.

Moral Error Theory
A first problem with (1) and (2) is that they rule out Moral Error Theory, that is, the view that all first-order moral claims are uniformly false. 16 While Moral Error Theory is controversial, it shouldn't be ruled out by conceptual fiat. Moral Error Theory seems reasonable at least to the extent that affirming it does not seem to involve a simple misunderstanding of the basic deontic concepts. 17 To see the conflict between Moral Error Theory and the duality definitions, note first that Moral Error Theory entails that, for any act φ, first-order moral claims such as its being obligatory to φ, its being obligatory to not φ, its being permissible to φ,a n dits being permissible to not φ are uniformly false. But, if its being obligatory to φ and its being permissible to not φ are both false, the definiendum of (1) is false while the definiens of (1) is true. Hence (1) rules out Moral Error Theory. Likewise, if its being permissible to φ and its being obligatory to not φ are both false, the definiendum of (2) is false while the definiens of (2) is true. Hence (2) also rules out Moral Error Theory. 18 This problem also applies to the standard interdefinability of prohibition and permissibility: 19 (5) It is forbidden to φ = df it is not permissible to φ. 20 (6) It is permissible to φ = df it is not forbidden to φ. 21 As we have seen, Moral Error Theory entails that it is false that it is permissible to φ and false that it is permissible to not φ. Moral Error Theory also entails that it is false that it is forbidden to φ and that it is false that it is forbidden to not φ. So Moral Error Theory entails that the definienda of (5) and (6) are false while their definientia are true. Hence (5) and (6) also rule out Moral Error Theory. 22 It may be objected that, given (1) or (2), only one of its being obligatory to φ and its being permissible to φ is a first-order moral claim; and likewise that, given (5) or (6), only one of its being permissible to φ and its being forbidden to φ is a first-order moral claim. If we, for example, adopt (2), then the claim that it is permissible to φ could arguably be understood as a second-order claim, since it is defined as the negation of the first-order claim that it is obligatory to not φ. But this objection highlights a further problem with (1), (2), (5), and (6), namely, that it seems that the claims its being obligatory to φ, its being permissible to φ, and its being forbidden to φ all seem to be first-order moral claims, rather than mere negations of first-order moral claims. It is especially implausible that its being obligatory to φ or its being forbidden to φ wouldn't be first-order moral claims. Hence this objection can't plausibly save the interdefinability of (1) and ( 2)o rt h a to f( 5)an d ( 6) .
It may next be objected that it is less clear whether its being permissible to φ is a first-order moral claim. 23 Remember, however, that we are talking about moral permissibility-or, equivalently, moral rightness. 24 A claim that an act is morally permissible or morally right seems to entail that the act has the moral property of being morally permissible or of being morally right. 25 Since Moral Error Theory is typically motivated by the thought that there are no moral properties, it seems that claims that some act is morally permissible should be included on the list of first-order moral claims that Moral Error Theory rejects. 26 There seems to be a difference between a view where everything is permissible and a view where no acts have any moral properties or deontic statuses. Moreover, even if there is a reasonable version of Moral Error Theory which is neutral with respect to permissibility claims, my argument only requires one version of Moral Error Theory which rejects all claims that any acts are permissible and that that version is reasonable at least to the extent that it doesn't rely on a simple confusion about the concepts of obligation, permissibility, or prohibition.

The moral import of permissibility
The idea that permissibility is something stronger than a mere negation of a first-order moral claim is closely related to Georg Henrik von Wright's worry about the interdefinability of some deontic concepts: It seems much more plausible to regard [obligation] and [prohibition] as being interdefinable than to regard [permission] and [obligation], or [permission] and [prohibition], as being so. One can ask: is permission to do something simply the absence of prohibition to do this same thing? That permission should entail the absence of a "corresponding" prohibition seems clear. But does the reverse entailment hold? Is not permission something "over and above" mere absence of prohibition? 27 Von Wright supports this worry with a legal example: Suppose that some acts have recently been enabled by some new technology that the legislators have not considered. According to von Wright, these acts would be neither legally permitted nor forbidden; there would be a gap in the legal code. 28 But, if some new technology hasn't been considered by the legislators, it would normally be considered legal. 29 So the example isn't very convincing. 30 But, taking a cue from our discussion of Moral Error Theory, we can construct a better example: Consider an act φ in a state of nature, where there is no legal system in place. It seems that neither to φ nor to not φ would be legally required (obligatory), permitted, or forbidden, because there wouldn't be any legal system or law that could require, permit, or prohibit these acts. 31 Hence we must reject the legal analogues of (1), (2), (5), and (6). The upshot is that, in the same way as legal permissibility isn't the mere absence of legal prohibition, moral permissibility isn't the mere absence of moral prohibition. And, as with the corresponding legal analogues, we have that neither moral obligation nor moral prohibition is the mere absence of moral permissibility.
If, as von Wright maintains, permissibility entails something "over and above" non-prohibition, then this "over and above" might be false and then acts might fail to be permissible even if, as Moral Error Theory entails, no acts are prohibited.
Unlike (1), (2), (5), and (6), the standard interdefinability of obligation and prohibition (which von Wright is less worried about in the above quote) does not rule out Moral Error Theory. To see this, note that-unlike (1), (2), (5), and (6)-the following definitions do not define a first-order moral claim in terms of a negated first-order moral claim: (7) It is obligatory to φ = df it is forbidden to not φ. 32 (8) It is forbidden to φ = df it is obligatory to not φ. 33 Both of these definitions avoid ruling out Moral Error Theory, since both definienda and definientia are first-order moral claims; hence their definienda and definientia are jointly false on Moral Error Theory. 34 Von Wright wonders what, more precisely, distinguishes permissibility from mere non-prohibition: I think we are well advised to distinguish between things being permitted in the weak sense of simply not being forbidden and things being permitted in some stronger sense. Exactly in what this stronger sense "consists" may be difficult to tell. That which is in the strong sense permitted is, somehow, expressly permitted, subject to norm-and not just void of deontic status altogether. 35 Von Wright's first suggestion for what distinguishes permission in the strong sense from mere non-prohibition was in terms of immunity from punishment: I shall say that there is a strong permission to do an action, if and only if, commission of this action is a sufficient condition of immunity to punishment for it. The holder of a strong permission can do the action and be sure that he will not, on that account, have to suffer a punitive reaction on the part of the legal authorities or the community, as the case may be. 36 The problem with this proposal is that, on many ethical theories, the question of whether someone should be punished does not depend on whether they only performed permissible acts. Notoriously, utilitarianism entails that one ought to punish an innocent person if doing so would bring about the greatest sum total of happiness in the situation.
Nevertheless, the account von Wright ends up finding most attractive (even though he doesn't fully defend it) is an account of permissibility as declarations of toleration, which, he writes, can be regarded either as declarations of intention not to interfere with the permission-holder's conduct in a certain respect, or as a sort of promise of noninterference. A promise of this kind [...] might be viewed as a self-prohibition on the part of the permission-giver. 37 This approach, as von Wright points out, offers a way to define permissibility in terms of prohibition-and then, via (8), permissibility in terms of obligation. 38 Yet a problem with this account is that it doesn't seem to fit with moral permissibility on many ethical theories. On many ethical theories, when some act φ is permissible this isn't due to some authority permitting this act; rather, it is due to the act's conforming to an impersonal moral law or principle. 39 This last observation, however, suggests the following way to distinguish permissibility from mere non-prohibition: Moral permissibility has moral import-that is, its being permissible to do some act entails that there is a moral law. Its being morally permissible to φ means, roughly, that φ conforms with the moral law. Similarly, its being morally forbidden to φ means that φ violates the moral law. And its being morally obligatory to φ means that φ is required by the moral law. So its being permissible (forbidden, obligatory) to φ entails that there is a moral law. But merely its being not obligatory (not forbidden, not permissible) to φ does not entail that there is a moral law.

Obligation in terms of permissibility
There is, however, a way to define obligation in terms of permissibility which avoids this problem, namely: (9) It is obligatory to φ = df it is permissible to φ and it is not permissible to not φ.
In this definition, definiendum and definiens each makes at least one positive claim about obligations or permissibility. So (given that permissibility has moral import) definiendum and definiens each entails that there is a moral law. 40 Moreover, (9) is consistent with Moral Error Theory, since the falsity of its being obligatory to φ only entails the falsity of its being permissible to φ and not permissible to not φ. The latter claim is false according to Moral Error Theory, since its first conjunct is a first-order moral claim. Hence (9) avoids the conflict with Moral Error Theory, since Moral Error Theory entails that both definiendum and definiens are false.
But (9) has another problem: It rules out the possibility of obligation dilemmas, that is, a form of moral dilemmas where, for some act φ, it is both obligatory to φ and obligatory to not φ. 41 To see this, assume that it is obligatory to φ and obligatory to not φ. Given that it's obligatory to φ, (9) entails that it is not permissible to not φ. And, given that it's obligatory to not φ, (9) entails that it is permissible to not φ. Hence we have a contradiction.
It may be objected that we could avoid ruling out obligation dilemmas if we, instead of (9), adopted the following variant: (10) It is obligatory to φ = df it is not permissible to not φ and there is some possible act χ such that it would be permissible to χ. 42 While (10) allows for obligation dilemmas, it is open to a variation of the same problem. Consider a maximally prescriptive view, where, for all acts φ, it is both obligatory to φ and obligatory to not φ and no act is permissible. It may be objected that some acts cannot not be done; so, if these acts are obligatory, it cannot be obligatory to not do them, since ought implies can. But, if we have no choice about such acts, it seems that they needn't be in the domain of acts which moral theories cover, because moral theories are often restricted to free, volitional acts. 43 Hence the maximally prescriptive view need not assign a deontic status to these non-voluntary acts. 44 While the maximally prescriptive view is normatively strange, it doesn't seem to be based on a confusion of the concept of obligation, at least, it doesn't seem to do so if obligation dilemmas are conceptually possible. Yet (10) rules out the maximally prescriptive view, because (10) entails that no acts would be obligatory if there were no possible permissible acts. Hence (10) doesn't seem to have any advantage over (9), which is simpler and less ad hoc.
Could there be some other definition of obligation in terms of permissibility which avoids these problems? If we wish to allow for the conceptual possibility of obligation dilemmas, there couldn't. Consider again the maximally prescriptive view where all acts are obligatory and no acts are permissible. In terms of permissibility, the maximally prescriptive view is extensionally equivalent to Moral Error Theory, since both entail that no acts are permissible. But, in terms of obligation, the maximally prescriptive view differs from Moral Error Theory: on the maximally prescriptive view, all acts are obligatory; on Moral Error Theory, no acts are obligatory. No definition of obligation in terms of permissibility could account for this difference.

Permissibility in terms of obligation or prohibition?
Could we avoid these problems if we instead define permissibility in terms of obligation or prohibition? We cannot. The trouble is that an adequate definition of permissibility shouldn't rule out a maximally permissive view where all acts are permissible and nothing is obligatory or forbidden. And, if we wish to neither rule out this maximally permissive view nor rule out Moral Error Theory, no definition of permissibility in terms of obligation or prohibition could possibly work. To see this, note that, on both the maximally permissive view and Moral Error Theory, nothing is obligatory and nothing is prohibited. So, in terms of obligation and prohibition, these two cases are equivalent. But they are different in terms of permissibility: on the maximally permissible view, all acts are permissible; on Moral Error Theory, no acts are. Since these cases differ in terms of permissibility but not in terms of obligation or prohibition, permissibility cannot plausibly be defined in terms of obligation or prohibition. 45

Prohibition in terms of permissibility
If obligation dilemmas are conceptually impossible, then (9) is a plausible definition of obligation in terms of permissibility. Combining (9) with (8), we get a definition of prohibition directly in terms of permissibility: (11) It is forbidden to φ = df it is not permissible to φ and it is permissible to not φ. 46 This proposal avoids the conflict with Moral Error Theory, since both the definienda and last conjunct of the definientia of (11) are first-order moral claims.
A possible drawback of (11) is that it rules out another form of moral dilemmas. It rules out the possibility of prohibition dilemmas, that is, a form of moral dilemmas where, for some act φ, it is jointly forbidden to φ and forbidden to not φ. 47 To see this, assume that it is forbidden to φ and forbidden to not φ. Given that it's forbidden to φ, (11) entails that it is permissible to not φ. And, given that it's forbidden to not φ, (11) entails that it is not permissible to not φ. Hence we have a contradiction.

The only feasible deontic primitive
We have seen that both (9) and (11) rule out moral dilemmas. Nevertheless, the conceptual possibility of moral dilemmas (such as obligation and prohibition dilemmas) is controversial. 48 If moral dilemmas were conceptually impossible, it seems credible that they would be ruled out by the definitions of the deontic concepts. And, if we aren't worried about ruling out moral dilemmas, there seems to be no reason to reject (9) or (11). 49 Thus, with (9) and (11), we have plausible definitions of both obligation and prohibition in terms of permissibility-that is, plausible if we can pass over the conceptual possibility of moral dilemmas. Since we have seen that permissibility cannot be defined in terms of obligation or prohibition, we have that permissibility is the only feasible deontic primitive. 50 p. 63. For the traditional deontic square of opposition and equipollence, see Prior 1955, p. 220. Prior (1957 drops the alethic duality definitions for his modal system. But see Williamson 2013, pp. 69-71 for a critique of that system. 7. Lewis and Langford 1932, pp. 160, 224. 8. Carnap 1946, p. 33. 9. Leibniz 1930, pp. 465-466, 480-481, von Wright 1951a1951b, pp. 1-4 andFøllesdal andHilpinen 1971, p. 8. One might question the strength of the analogy between deontic and alethic modalities, because there are many differences, for example, in their relation to truth; see von Wright 1951b, pp. 2-3, 41. Crucially, we have that its being necessary that p entails p and that p entails its being possible that p,y e tits being obligatory to φ does not entail φ's being performed and φ's being performed does not entail its being permissible to φ. 10. My arguments regarding the relationship between obligation, permissibility, and prohibition also applies to the relationship between oughtness, rightness, and wrongness. Each of the classificatory deontic concepts-that is, rightness and wrongness-seems to be equivalent to a corresponding deontic prescription: An act is right if and only if it is morally permissible to do it. And an act is wrong if and only if it is morally forbidden to do it. Moreover, as long as we are concerned with particular acts (each of which could only be performed by a single person), it seems that the following equivalence holds: An act ought to be done if and only if it is morally obligatory to do it. In the case of an act that ought to be done but which could be done by anyone of several people, it could be that it is morally obligatory for no one to do it; see Williams 1981, p. 116. One reason for focussing on the first trio of deontic concepts is, as Zimmerman (1996, pp. 33-34) points out, that 'right' is sometimes used in a sense that is ambiguous between obligation and permissibility. 11. Hansson 1970, p. 246. 12. Hansson 1970, pp. 246-247. 13. Raz 1975, p. 161 and Castañeda 1981, p. 76. 14. Hansson (2001, crediting Wlodek Rabinowicz, also points out that unilateral permission can be defined as follows: (I) It is unilaterally permissible to φ = df either it is bilaterally permissible to φ or it is obligatory to φ.
So unilateral permissibility is definable in terms of both obligation and bilateral permissibility. Of course, as Hansson (2001, p. 133n14) points out, bilateral permissibility is definable in terms of unilateral permissibility: (II) It is bilaterally permissible to φ = df it is unilaterally permissible to φ and it is unilaterally permissible to not φ.
But bilateral permissibility is undefinable in terms of obligation; see §5, note 45. 15. Ross 1968, p. 122. Compare Lewis 1979, p. 164. 16. Russell 1986, p. 148. See Mackie 1977 15-17 for a classic statement of Moral Error Theory. 17. It may be objected that, if Moral Error Theory were true, then no deontic logic would be needed to begin with. From this perspective, the falsity of Moral Error Theory could be seen as a prerequisite of the very project of deontic logic. But, according to the semantic part of Moral Error Theory, first-order moral judgements are meaningful and have truth values. So there would be logical relations between such judgements, even if there might not be much practical use for deontic logic if we take all first-order moral judgements to be false. Note that the topic of this paper is the alleged interdefinability of the central deontic concepts. It only connects with deontic logic in so far deontic logic aims to provide a general logic of these central deontic concepts. Systems of deontic logic that merely aims to model an ethical standpoint given that we have adopted that standpoint do not aim to provide a general logic for the central deontic concepts. So those systems are not relevant for the topic of this paper. 18. See Boghossian 2006, pp. 27-28, Pigden 2007, pp. 452-454, Tännsjö 2010, p. 43, Olson 20112014, pp. 11-15, andStreumer 2017, pp. 124-128 for a discussion of a closely related problem for Moral Error Theory, namely, that the falsity of the first-order moral claim 'torture is wrong' seems to entail the firstorder moral claim that 'torture is permissible'. 19. Just like with (1) and (2), Knuuttila (1981, p. 236) traces the corresponding equivalences back to the fourteenth century. 20. Von Wright 1951a, p. 3;1951b, p. 37. 21. Chisholm 1963. Moreover, Moral Error Theory also conflicts with the following axiom of standard deontic logic: The Principle of Tautological Obligation It is obligatory to either φ or not φ.
See Føllesdal and Hilpinen 1971, p. 13. Since Moral Error Theory seems logically consistent, the Principle of Tautological Obligation cannot plausibly be a principle of logic. 23. While Mackie (1946, p. 90;1977, p. 9), Pigden (2007, p. 453), Olson (2014, p. 14), and Streumer (2017, p. 106) include claims about what acts are permissible or right among the first-order claims that are false on their moral error theories, Sinnott-Armstrong (2006, p. 36) doesn't explicitly include permissibility on his open ended list of first-order claims. 24. See note 10. 25. Pigden 2007, p. 453 and Streumer 2017, p. 107. 26. Olson (2014 argues that an advantage of including permissibility claims among the claims that Moral Error Theory rejects is that Moral Error Theory then avoids the vulgar implication that everything is permitted. Yet it is unclear whether this potential vulgarity would be relevant for the plausibility of Moral Error Theory. Just like we shouldn't let inconvenience stop us from believing inconvenient truths, we shouldn't let vulgarity stop us from believing vulgar truths, other things being equal. Olson (2014, p. 14) also makes the following point: But Mackie's contention that his error theory is purely a second-order view and as such logically independent of any first order view must be taken to include the first-order moral view that anything is morally permissible. In other words, Mackie's moral error theory holds that all first order moral claims are false and claims about moral permissibility are no exception. This is puzzling: If Moral Error Theory entails that first order views are false, Moral Error Theory and these first order views are logically dependent rather than independent. Unlike Olson, I don't think that Mackie denies that Moral Error Theory (even though it is a second-order view) has a logical dependency with first-order moral views. Olson's interpretation might seem plausible given Mackie's (1977, p. 16) claim that These first and second order views are not merely distinct but completely independent: one could be a second order moral sceptic without being a first order one, or again the other way around.
But Mackie does not claim here that all first and second order views are independent. By '[t]hese first and second order views', Mackie refers to the two particular first and second order views he mentions earlier on the same page as the above quote. He only claims that whether someone is a moral sceptic of the first order in the sense that they express a positive moral condemnation of all that conventionally passes for morality is independent of whether they accept Moral Error Theory. Mackie is not saying that all second-order moral judgements are logically independent of all first-order moral judgements. My reading is also suggested by the 'not necessarily' weakening in Mackie's (1977, p. 22) claim that 'first order judgements are not necessarily affected by the truth or falsity of a second order view.' 27. Von Wright 1981, p. 6. See also von Wright 1963, pp. 85-87. 28. Von Wright 1963, p. 166. 29. Kelsen 1949, pp. 146-149 and Ross 1968. See Alchourrón 2015, pp. 327-329 for similar examples. 31. Williams 1985, p. 62

similarly claims
If there is a system of rules, then no doubt if the rules are silent on a certain matter (at least if the rules are otherwise wide enough in their scope), that fact can naturally be taken to mean permission. The law, like other sovereign agencies, can say something by remaining silent. But if there is no law, then silence is not meaningful, permissive, silence: it is simply silence. 32. Von Wright 1951a, p. 3;1951b, p. 37. 33. Hintikka 1957, pp. 4-5. Kanger (1957) defines wrongness in this manner. 34. Hintikka (1957, pp. 5-6) objects to (7) and (8). He argues that its being obligatory to φ is a shorthand for its being obligatory that there is some act which is an instance of φ,andtha tits being forbidden to φ is a shorthand for its being, for all acts x, obligatory that x is not an instance of φ. If this is correct, then (7) and (8) are inadequate. This objection, however, only applies if the objects of obligation and prohibition are kinds of acts rather than individual acts, which is what we are concerned with. See also Cox 1978 for an objection to Hintikka's argument. 35. Von Wright 1981, p. 25. 36. Von Wright 1969, p. 95. 37. Von Wright 1989. See also von Wright 1963, p. 92;1999, p. 37. 38. Von Wright 1989. This objection also applies to Alchourrón's (1969, p. 251) analysis of strong permissibility as the existence of an act issuing a permission norm.
40. If we wish to preserve the analogy with alethic modalities, we would have to define necessity as follows: Given (III), we can still derive the standard duality biconditionals, p ⇔¬♦¬p and ♦p ⇔¬ ¬p, if we adopt the axiom that at least one of p and its negation is possible, that is, ♦p ∨ ♦¬p. In terms of Kripke's (1963, p. 84) semantics (giving up the reflexivity of the accessibility relation), it seems weird that, in a deadend world with no access to any possible worlds, we have p even though ¬♦p.
We avoid this consequence of the duality definitions if we instead adopt (III). Likewise, if we would like to keep the analogy with existential modalities-see von Wright 1951b, p. 2-we need to replace the standard duality definitions of the quantifiers with the following: The difference is that universal affirmative claims have existential import given (IV) but not given the standard duality definitions, championed by Venn (1881, pp. 141-143). Carroll (1896, p. 33;1977, pp. 74-75, 88) opts for (IV) and argues that universal claims do have existential import. Carroll's (1896, pp. 165-170;1977, pp. 232-237) argument, however, seems to rely on (IV), so it isn't very convincing; see Carroll 1977, p. 233n2 and Quine 1977, p. 1018. Bartley (1977 and Abeles (2010, pp. 14-15) suggest that, later on, Carroll may have changed his mind about existential import. 41. Vallentyne 1989, p. 302. 42. Alchourrón andBulygin (1971, p. 42) state the corresponding equivalence, but they (1971, p. 38) define obligation with (1). 43. Moore's (1912, pp. 16-17) version of utilitarianism, for example, only applies 'right' and 'wrong' to voluntary acts. 44. It may next be objected that the maximally prescriptive view violates The Principle of Entailment If doing φ entails doing χ , then it is obligatory to χ if it is obligatory to φ.
See Kanger 1957, p. 32 andStenius 1963, p. 252;1982, p. 56. If you perform an act φ, then it seems that you must also perform the tautological act to either φ or not φ. So, by the Principle of Entailment, this tautological act is obligatory if φ is obligatory. The trouble is that the maximally prescriptive view is then committed to not only that these tautological acts are obligatory but also that it is obligatory to not do these tautological acts. So the maximally prescriptive view would be committed to impossible acts being obligatory. Yet the Principle of Entailment is implausible. It is open to Ross's (1941, p. 62) counter-example that, if it is obligatory to post a letter, the Principle of Entailment entails that it is obligatory to post or burn the letter. So, if you burn the letter, you do something you ought to do. The Principle of Entailment can also conflict with Act Consequentialism; see Wedberg 1969, p. 223. Suppose that the consequences of posting the letter are better than those of any alternative act, such as, burning the letter. Then, if one burns the letter, to post or burn the letter has worse consequences than to post the letter; so only the latter is obligatory on Act Consequentialism.
45. This argument also shows that bilateral permissibility cannot be defined in terms of obligation, changing what needs to be changed. 46. Alchourrón and Bulygin (1971, p. 42) state the corresponding equivalence, but they (1971, p. 38) define prohibition with (5). 47. Vallentyne 1992, p. 118. 48. See Mason 1996 for a short summary of some of the debate on the alleged possibility of moral dilemmas. One of the main arguments for the possibility of moral dilemmas is blocked by (9). Lemmon (1962, pp. 149-150) argues that 'must φ' and 'must not φ' are contrary since 'must φ' entails 'will φ' and 'must not φ' entails 'will not φ', which contradicts 'will φ'. And Lemmon claims that we cannot derive a similar contradiction from 'obligatory to φ' and 'obligatory to not φ'. Given (9), however, 'obligatory to φ' entails 'permissible to φ'a n d 'obligatory to not φ' entails 'not permissible to φ'. Hence we get a contradiction similar to the one we got from the combination of 'must φ' and 'must not φ'. Marcus (1980, p. 129) suggests that moral laws or rules are consistent if 'there are possible circumstances in which no conflict will emerge': moral rules can be consistent even if they yield conflicting moral dilemmas in some circumstances. But this suggestion assumes that moral dilemmas don't yield contradictions. Hence the suggestion is point-assuming as a challenge to (9), which entails that this assumption is false. 49. It may be objected that this conflicts with our allowing for the conceptual possibility of Moral Error Theory, because the latter implies that we allow for the conceptual possibility of situations where no acts are permitted. Hence we allow for situations where all acts are impermissible (in the sense of not being permitted). Personally, I do not think these situations should count as moral dilemmas. But, if they should, we can allow for such dilemmas even though we rule out other kinds of dilemmas such as obligation and prohibition dilemmas. 50. This goes against the tradition in deontic logic, which has mainly taken obligation as the primitive; see Hansson 2013, p. 205. Stenius (1982 argues that obligation is a better primitive because it is easier to get an intuitive grasp on than permissibility. Yet this seems to be an unavoidable cost if we are to adequately define one of obligation and permissibility in terms of the other.