Access and Unknowable Obligations

The article is devoted to the question of whether unknowable obligations are possible. According to the popular view (known as Access), an act is obligatory only if its agent can know that this act is obligatory. Sorensen (1995) argues against Access


Introduction
Imagine the following situation. I participate in the presidential elections. I intend to vote for one of the candidates (say Tom) because I share his political views. Suppose now that Tom is a corrupted politician, but I do not know this fact. Of course, I agree that if Tom is a corrupted politician, then I have the obligation not to vote for Tom because I have the obligation not to vote for corrupted politicians. Then it turns out that I have the obligation not to vote for Tom, but at the same time, I do not know that I have the obligation not to vote for Tom (because I do not know that Tom is a corrupted politician). The question is: is a certain obligation an obligation (for me) if I do not know that I have this obligation? In other words, are there such things as unknowable obligations?
At first glance, it seems that the fact that a person X has the obligation O always presupposes X`s knowledge that he has O. If O (the obligation not to vote for Tom) is an obligation, even if X does not know that he has such an obligation (and, as a result, he votes for Tom), then based on the fact that violation of obligation is blameworthy 1 , X should be blamed for voting for Tom even if X didn`t know that he had O. But that seems to be extremely counterintuitive. In fact, it would be plausible to conclude that X should not be blamed for his violation of O. Therefore, those who deny that unknowable obligations are obligations, accept Access 2 (Access) An act is obligatory only if its agent can know that this act is obligatory. Sorensen (1995) argues against Access. By Access, if I cannot know that I have an obligation, then I do not have that obligation. This conclusion, as Sorensen expresses himself, "dumbs down ethics" (1995, p. 254). Moreover, we can imagine a certain "epistemological Robinson" -a person who cannot know that he has a moral obligation. Then, by Access, we can conclude that he has no moral obligations. This is highly implausible. Finally, it follows from Access that our obligations are epistemologically dependent -a certain obligation is an obligation only insofar we know about that obligation. So by eliminating the source of my knowledge that I have a certain obligation, I eliminate that obligation, since I no longer have a possibility to know if I have that obligation. Sorensen (1995) gives the following example: If all of one's obligations were knowable, one could mute the call of duty by diminishing one's cognitive capacity. After all, if I am not obliged to do something, then I am permitted to refrain from doing it. Thus if I can preclude the possibility of knowing that I am obliged to donate some of my inheritance to charity (by burning rather than reading the only copy of a will), then I can ensure that I am permitted to keep the entire inheritance. Simple incuriosity would considerably narrow one's obligations (Sorensen, 1995, p. 254).
By Access, I have the obligation to donate my inheritance to charity only if I can know that I am obliged to do that. If the will is the only source from which I can know that I am obliged to donate for charity, then if I burn the will (without reading it), I eliminate the only way to know if I have the obligation to donate for charity. Hence, I no longer have the obligation to donate for charity (after I burned the will), since I have no way to find out if I`m obliged to donate for charity. Thus, it follows from Access that I can make my obligation unknowable. This is a dubious consequence of Access. In the example above, if I have an obligation to donate for charity, then I must donate for charity 3 . It is not within my power to change the fact that I am obliged to respect my parents -and thus to donate for charity. However, Access seems to assert otherwise -it is possible for me to violate my moral obligation to donate for charity by keeping myself ignorant about the source of that moral obligation. Thus, if I can refrain from making the obligation knowable, I can refrain from fulfilling the obligation.

In Defence of Access
In response to Sorensen, Sider (1995) defends Access by introducing the following principle: (S) For any obligation O, individual X must refrain from making O unknowable. But (S) faces a problem. Suppose that X is a person who wants to avoid fulfilling his obligation 4 . Now, from X`s perspective we can argue that (S) generates an infinite regress of obligations, for if (S) is the obligation grounding the primary obligation, O, X can say that (S) is unknowable to him. Thus, to make (S) knowable (to prevent X`s making (or keeping) (S) unknowable), the defender of (S) must introduce another obligation: (SS) X must refrain from making (S) unknowable.
The result will be the same: X can always answer that (SS) is unknowable to him, so to make (SS) knowable, the defender of (S) must introduce another obligation -(SSS) -such that by (SSS), X is obliged to refrain from making (SS) unknowable, and so on endlessly. Wieland (2014b, p.58) introduces this form of the argument against Access as follows 5 : ( We can now answer to the second crucial point -(8). By (8), we cannot have an infinity of obligations because we cannot know an infinity of obligations. But, as I pointed above, this statement is refutable. The defender of this position asserts that our cognitive abilities are limited, and so we cannot know an infinity of obligation. Thus, by Access, we do not have an infinity of obligations. This argument can be summarized as follows: (a) Suppose I have an infinity of obligations (b) I can have an infinity of obligations only if I can know infinity of obligations (c) My cognitive abilities are limited, so I cannot know an infinity of obligations (d) If I cannot know infinity of obligations, I do not have an infinity of obligations (e) I do not have an infinity of obligation (f) Thus, Access is false As we saw above, the correctness of this argument depends on what we mean by the word "know". If we say that, for the obligation O*, the word "know" means "to refrain from making the primary obligation O unknowable", the statement "We have an infinity of obligations" is compatible with Access, and also with the claim that our cognitive abilities are limited.
Nevertheless, the opponent of Access can always say that, by Access, I can have the obligation O only if can I know another obligation, O*, such that knowledge about this secondary obligation differs from knowledge about our primary obligation, and thus an infinite regress reappears. Consider:  (12)). But "to know something" is not the same as "to know that you know something". Thus, the argument will be as follows: ). Therefore, (11) has false instances -it is not necessary for me to have O2 in order to have O1. Does this fact entail the falsity of Access? No. Otherwise, I could say that X is obliged not to burn the will even if X does not know that he is obliged to refrain from making the fact that X is obliged not to burn the will unknowable. But in fact, X is not obliged not to burn the will, if he doesn`t have 7 Note that O*, taken separately from the context of our problem with (Access), does not assert that I can know O only if I can know O*. O* there is just an assertion that X must refrain from making O unknowable. However, we consider this problem in the context of shirker-style reasoning (i.e. from the standpoint of X  (11) is an instance of (Access), then (Access) is false since (11) generates an infinity of obligations. Contrary to X, I argue that (11) is indeed false, but this falsity does not entail that Access is false (see my argument under (26-28). Thus, I argue that both (10) and (11) are false - (10) and (11) both follow from Access only if we accept a shirker`s point of view. But this point of view is false. 8 The difference between (17) and (13) is that (13)  the obligation to refrain from making his primary obligation (not to burn the will) unknowable. Suppose I say to X: "You must refrain from voting for corrupted politicians (say Tom) even if you do not know that you have the obligation to refrain from voting for corrupted politicians because it is not necessary for you to know that you have the obligation to refrain from voting for corrupted politicians in order to know that you must refrain from voting for Tom". X would say that this claim is absurd, and we must agree with him. What the fact that it is not necessary for me to have O2 in order to have O1 really shows is that (13) does not differ essentially from (12). We can say that there is no epistemic improvement of our knowledge in the case of (13) comparing with (12). If I assert that I have (13), then I rather assert that: (29) If I have the obligation to refrain from burning the will, I am obliged not to downgrade my current epistemic level concerning my obligation to refrain from burning the will But I do not want to say that (13) entails (30),  (13), I have the obligation to distinguish between (12) and (13) But if (31) were true, then given the fact that I have (12) if I have (13), (32) would be true: (32) If I have the obligation (12), (12) obliges me to distinguish between (12) and (13), And this statement is clearly false -if I have the obligation to refrain from burning the will, the fact of my having this obligation does not oblige me to distinguish between different levels of obligations. I can have the obligation (12) without knowing a theory of obligations (that is, without having theoretical knowledge about the nature of obligation). Otherwise, I would have an infinity of distinctions within my primary obligation: (33) If I have the obligation (12), and (12) obliges me to distinguish between (12) and (13), (12) obliges me to distinguish between (12) and (14)… and so on, and (12) obliges me to distinguish between (distinction of (12) and (13)) and (14) One might reply that (as was shown above) it is not necessary for me to understand a theoretical meaning of the term obligation in order to understand the term obligation. However, this is not a trivial problem -even if the defender of Access can block X`s inference by claiming that this analysis does not essentially affect the problem with Access because it proves too much, we can formulate a similar argument against the possibility of Access. In the case of X`s analysis, X should always introduce new definitions of O has P to understand the meaning of has P". Within this regress, X must introduce (36) to understand (35), (37) to understand (36), and so on. But suppose that X has a clear understanding of his obligation not to burn the will (and, of course, X understands the meaning of obligation), but he wants to make himself unknowable about his obligation. In order to prove to X that he must refrain from making O (the obligation to refrain from burning the will) unknowable, I must introduce to X, by Access, that X has the obligation to refrain from making O unknowable. Doing that, we face a similar regress as with the case of X`s analysis in (35-37). Wieland (2014b, p. 63) introduces this regress as follows: (38) I have to demonstrate that X has O (39) I first have to demonstrate that X has the obligation to refrain from making O unknowable (40) I first have to demonstrate that X has the obligation to refrain from making (39) unknowable (41) I first have to demonstrate that X has the obligation to refrain from making (40) unknowable The argument (38-41) entails that I can never prove to X that he has the obligation O. Every time I try to prove to X that he has the obligation, I have to introduce more and more obligations. And every time I introduce a new obligation (that is, I provide proof that X has the obligation), X is within his right to ask me for a new proof. Hence, even if we can reject the argument (1-9), we are not in a position to reject 2. (S), Self-reference, and Unknowability Wieland (2014b, p. 64) suggests the following solution (call this solution (WA)). Suppose X has the obligation to refrain from burning the will. X wants to make (or keep) this obligation unknowable. X will not be able to refrain from this obligation, because he has O1 and O2: (O1) X should refrain from burning the will (O2) X should refrain from making (or keeping) O1 or O2 unknowable The argument runs as follows. The obligation O1 is either knowable to X, or unknowable to X. Suppose that O1 is unknowable to X. By O2, X is obliged to make O1 knowable. Thus, X cannot refrain from making O1 knowable. However, X can say that O2 is unknowable to him, and so O1 is unknowable to him. But O2 asserts that X has the obligation to refrain from making (or keeping) O2 unknowable. Thus, if X asserts that O1 is unknowable to him, it is true (by O2) that X should refrain from making O2 unknowable. Then, by (O2), it is true that X must make O2 knowable, so O2 entails that X should make O1 knowable even if X does not know that X has the obligation to refrain from making O1 unknowable.
Suppose otherwise -O1 is knowable to X. X wants to make O1 unknowable. Then, X knows that he should refrain from burning the will, but X wants to make this obligation unknowable. But if O1 is currently knowable for X, X knows that he must refrain from burning the will -that is, X must refrain from making the obligation to refrain from burning the will unknowable. Thus, if O2 is in power, X is obliged to refrain from making the obligation not to burn the will (O1) unknowable. X, as before, can argue that O2 is unknowable to him, and if O2 is unknowable to him, then O2 is not in power. But O2 is the obligation to refrain from making (or keeping) O1or O2 unknowable. Thus, if X argues that O2 is unknowable to him, he does not have O2. But then, X has O1, and thus cannot make (or keep) O1 unknowable. However, the obligation to refrain from making (or keeping) O1 unknowable is a part of O2, so X cannot make O1 unknowable. Could X say that he has not O1 because O2 is not knowable? No, because X cannot refrain from making (or keeping) O2 knowable -doing this, he violates his obligation O2. Thus, as Wieland argues, X cannot evade O1 by claiming that O1 (or O2) is unknowable to him.
But isn`t it true that O2 is a self-referential obligation -the obligation that asserts something about itself? Wieland seems to agree with this diagnosis: "…[X] should make O2 itself knowable, and refrain from making O2 unknowable. In this respect, O2 is self-referential…" 10 (Wieland, 2014b, p. 64). Why should we introduce such a suspicious "entity" as a self-referential obligation? The answer is this. O2 guarantees us that X will not be able to evade O1 or O2 by claiming that O1 and O2 are unknowable to him. Therefore, O2 plays a decisive explanatory role in the argument. But there is another question -is O2 true? As I understand it, there are two possible ways of defining (O2). If (O2) is just a conjunctive sum of obligation concerning O1 and O2 (the obligation to refrain from making and keeping O1 unknowable and the obligation to refrain from making and keeping O2 unknowable), I find the argument above implausible -if X asserts that he doesn`t have O1 because O2 is not knowable to him (O2 is the obligation to make O1 knowable), then the defender of (WA) simply asserts that X is not allowed to evade O2 (that is, to refrain from making O2 knowable) because O2 is the obligation asserting that X must make this 10 Wieland (2014b, pp. 64-65): "It is important to emphasize that Access is in force. This means that if O1 or O2 is not knowable to [X], then [X] does not have that obligation. Yet, given the special nature of O2, it can be shown that such a situation will not occur". I don`t think that this proposal can solve our problem. At least from Fine (2010) we know that the sentences of the form If , then grounds v are in general not true. If X asks why he is not allowed to evade O1, the defender of (WA) will reply that X a not allowed to evade O1 because X has O2. Thus, O2-or-O1 grounds O1, and X has O2-or-O1 because X has O2. But given Fine`s analysis, O2-or-O1 must be grounded in both O1 and O2. Does O1 ground O2-or-O1? No, because the proponent of (WA) presupposes that O2-or-O1 grounds O1. If O1 were a ground for O2-or-O1, then the whole argument would be circular.

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obligation, O2, knowable! But this is wrong -such obligations do not exist. For suppose that O2 is such an obligation. O2 then asserts that X has O1. The defender of (WA) would then argue that X has O1 because X has O2. But if we asked why X has O2, the defender of (WA) would answer that X has O2 because O2 asserts that X has O2! But we can`t assert that O2 is true because O2 asserts that O2 is true. It is clear that (WA) should not be understood in this way. Thus, (O2), as I understand it, should be treated as a disjunctive self-referential obligation. Again -if (O2) is true?
Logic indeed allows us to formulate sentences like "If O2, then either O2 or not-O2", or "O2`s being the case grounds O2-or-O1`s being the case" 11 . In these cases, O2 entails something or grounds something. But in the case of (O2), O2 is the sentence about O1 and O2, -O2 is a part of itself. We have Then, replacing O2 with O2 V O1, we have Again, we face an infinite regress. However, the defender of (WA) could resist this argument by claiming that this regress is not vicious due to the nature of disjunction. However, even if this regress is not vicious and thus cannot serve as a counterexample to (O1-O2), we can formulate the following argument which is an instance of (O1-O2) In the case of (C1), (S) is knowable to me, because (A) is not knowable to me -it follows from the disjunctive nature of (S). But (A) is about (S) (about the obligation to refrain from making any obligation unknowable). Thus, if (A) is unknowable to me, then I know (from (S)) that I should refrain from making (or keeping) (S) unknowable, and I don`t know (from (A)) that I should refrain from making (or keeping) (S) unknowable. Contradiction! It is not surprising that we got such a result. (O1-O2) and (A-S) both contain self-reference -O2 says about itself, and (S) says something about (S), which in turn says about (A) such that (A) is about (S). We are within our rights to assert that (O2) -X should refrain from making (or keeping) O1 or O2 unknowable -is not consistent. If so, then (S) -I should refrain from making (or keeping) (S) (46), implies (48) X can know that X has (S) without knowing that X has (S) 14 (48) is false -it is possible that I could have O without knowing that I have O, but it is impossible that I could know that I have O without knowing that I have O. Does it mean that (S) is, in fact, self-defeating (because self-referential)? Suppose there is some full, consistent logical system of obligations Q containing the rule about all obligations (S). Is Q able to prove its own consistency? No, because this possibility would contradict Gödel`s second incompleteness theorem. From the perspective of (38-41) X can reply that if the obligation is not proven as an obligation, it cannot be considered as an obligation. But this answer is too strong -we do not need to be ethical instructors in Sorensen`s sense to recognize our obligations. Moreover, as we could see, there are unprovable obligations. But it is not the case that a certain obligation should necessarily be theoretically proven in order to be considered as an obligation. Therefore, the answer to the question "Are there unknowable obligations?" will be as follows -yes, (S) is an unknowable obligation. If unprovability implies unknowability then, by (38-41), (S) is unknowable. However, we can always defend Access and (S) by claiming that (S) is not unknowable for the case of (1-9). Obligations are not logical truths. If I am obliged to respect people, it would be wrong to assert that 14 An anonymous referee of the journal offers a suggestion that (48) must be formulated rather as follows: (48*) "It is possible for X to know that X has (S) without X`s actual knowing that X has (S)". I agree that (48*) is true for any ordinary obligation like to donate for charity if the will says that I must donate for charity (call this O). However, there is a crucial disanalogy between O and (S). O does not assert that I must make O knowable or refrain from making O unknowable. It is possible then that I can know O without having actual knowledge that I have O. But consider the case of (S). (S), unlike O, is a self-referential obligation (because (S) is about any obligation, including (S)) -an obligation saying of itself. Suppose now that (S) applies to (S). We have now an obligation of the following sort (S) Refrain from making me unknowable / make me knowable!
Here an obligation to refrain from making (S) unknowable is (S) itself. (S) is then at the same time both, an obligation and the source of knowledge that I have this obligation. Compare now O and (S). Suppose that (S) does not exist. Even if (S) does not exist, I can know that I have (S) without having actual knowledge that I have O. But in the case of (S), I cannot say that I can know that I have an obligation to refrain from making this very obligation unknowable, if there is no such obligation, or this obligation is not actually knowable to me, because only this obligation, (S), and nothing else, says me that I have this very obligation. Thus, I believe that a case of (S) is something different from any case of other obligations. I am obliged to respect people because I can logically prove this truth. I am obliged to respect people because this obligation is an ethical rule. It would be ridiculous to ask about the truth conditions for the obligation to respect people. But (S) is both an obligation and a truth condition 15 for an obligation. This is how (S) differs from other obligations. This complexity of (S) is the source of the contradiction. But if we consider (S) as an ethical attitude or rule (like the obligation to respect people), the contradiction will disappear 16 , and we can legitimately refer to (S) without violating Access. *** In agreement with Sider and Wieland, I argue that the argument from infinite regress of obligations poses no difficulty for (S) because none of its sub-arguments (an impossibility of having an infinity of obligations, an epistemic regress, an infinite regress in defining "obligations") is valid. But contrary to Wieland, I argue that we actually have an infinity of explanations, and thus we have an explanatory regress.
In the section 3, I argue that Wieland`s argument (O1-O2) does not provide us with a definitive solution to the problem with (S). The source of the problem is that (S) itself a self-referential universal obligation -the obligation about all obligations, and thus we have a good reason to think that (S) cannot be proven. However, if my argument is correct, (S) does not need to be proven. The whole issue rests on the assumption that there is a loophole between (S) and its knowability. But there is no such loophole. If I`m obliged to respect people, I know that, and so I know that I`m not allowed to evade this obligation. Surely, I can evade my obligation by making (S) unknowable, but it follows from the nature of ethical obligations that I`m not allowed to do that. In fact, (S) is an essential part of our ethical obligations, so (S) is rather an ethical than a logical statement.

Objections and Replies
It is now time to clarify some questionable points of my arguments and reply to criticism. I have argued that a shirker can introduce an argument, according to which Access entails that in order to be able to know O, it must be possible to know O*. A shirker formulates this argument by introducing (10) and (11). Then, a shirker argues that there is a substantial difference between O and O*. If so, as a shirker thinks, then it follows from Access that I must know infinity of substantially different obligations. It is impossible, and so a shirker concludes that Access is false. In this respect, I proposed an argument that this shirker`s conclusion is not sound. Following X, we can know O only if we can know O* (that is, only if we can know that we can know O). But I have provided an argument that, for any agent X, it is not the case that X can know O only if she can know O*. Thus, it is important to clarify that such sentences as (10) and (11)  Let`s move on to the argument (15-25). This argument may seem suspicious because it relies on the suspicious move from can know (in the case of (1-9)) to know. Note however that goal of (15-25) is different from the goal of (1-9). By formulating (1-9), a shirker tries to show that Access is false because my possibility of having O entails the existence of an infinity of obligations. Thus, contrary to our assumption that we can know O, as a shirker will be happy to assert, we cannot know O. Following (15-25), however, the argument is a little bit different. A shirker now argues as follows: suppose that I actually So, in this passage (which is a representation of (15-25) our shirker tries to say that even if she has actual knowledge (that is, not only a possibility to have this knowledge) that she has an obligation (she was told that she actually has this obligation), her having an actual knowledge that she has an obligation, as it follows from this argument, is not sufficient to state that she can get such knowledge. Thus, to be a strengthened version of (1-9). By (15-25), it is not the case that Access is false because there is an infinite number of obligations, but because every single obligation O*, O** is essentially different from other obligations, and our attempt to understand what is (S), as a shirker asserts, entails an infinite regress. In Sorensen`s original example, X can find out that she is obligated to donate for charity just by reading the will (of course, if the will asserts that X must donate for charity). By reading the will, X gets actual knowledge that she has an obligation to donate to charity. But in (15-25), a shirker tries to argue that a situation with instances of (S) (i.e. with O*, O**…) is essentially different from the situation with her reading the will. She asserts that even if someone told her that she has O* (for instance, an obligation to refrain from making her obligation to pay rent unknowable), the fact that she was told that she has O* (thus she now knows that she has O*) does not entail that she now actually knows that she has O* (since she argues that it is impossible for her to understand what is O* -in order to understand O*, she argues, she must understand all instances of (S) (she concludes from (15-25) that this is not possible. Hence, by formulating (15-25), a shirker argues that not only her possibility to know an obligation is not sufficient to make this obligation knowable; she now argues that even her having actual knowledge that she has an obligation is not sufficient to assert that she knows that she has this obligation because, as she argues, this knowledge is inconsistent.
My own answer is as follows. We must agree that (15-25) poses a real problem for Access. In the discussion of (15-25), I argue that this argument is not sound, but my diagnosis relies on the idea that obligations are ethical, but not logical entities, -that is, we must not assert that we know O only if O is appropriately logically explained (see my argument for explanatory regress).
Regarding (WA), I raised several objections to this disjunctive proof. My first worry concerns the consistency of (WA) -given (C1), (that is, an assumption that our primary obligation A (for example, not to burn the will) is unknowable), (WA) entails that (S) -an obligation to refrain from making A unknowable -is both knowable and unknowable. My second worry is that (WA) entails a new infinite regress.
(WA) asserts that if O1 is not knowable, then O2 must be knowable. O2 is defined by (WA) as (O2 v O1).
But if O2 is (O2 v O1) then, by replacing O2 with (O2 v O1), we have that O2 is (O2 v O1) v O1...)). Our shirker might then ask: even if, as you say, O2 -that is, O2 v O1 is knowable, what is a reason to think that (O2 v O1) v O1)) is knowable? And what is a reason to think that (O2 v O1) v O1)) v O1))) is knowable? A shirker can thus object that since O2 entails a new regress, O2 is not properly defined by (WA).
My third worry is this. By (WA), if O1 is not knowable, O2 is knowable. Suppose that O2 is now knowable (thus I have O2), and O2 says that I have a disjunctive obligation (O2 v O1). That is, (WA) accepts that (D) The fact of my having O2 grounds that (O2 v O1) (D) is an instance of the principle, known in the literature about grounding as Disjunctive Grounding. According to this principle, if there is a fact P, then P fully 17 grounds that either P or Q. Or, technically: (DG) P → P < (P v Q) But (DG) is an invalid principle (see Fine ,2010, p.117 andLitland, 2015). In order to show that (DG) (and thus (D)) is not valid, consider the sentence (O2) such that (O2) is (O2) Either the fact of my having O2 grounds that (O2 v O1), or the sentence with label (O2) is true 18 O2 < (O2 v O1) v T⌜O2⌝ Note that (O2) is an instance of (DG) because, by (WA), O2 says of itself that it grounds a disjunction (O2 v O1). The argument will be as follows. Suppose that it is the case that O2 (i.e., O2 < (O2 v O1)). Assume (DG). Assume the following plausible principles (more about these principles in Fine, 2010) (Factivity) P < / ≺ Q → P, Q (If P grounds Q (fully or partially), then both P and Q are the case (Truth-grounding) P → P ≺ T⌜P⌝ (If P, then the fact that P partially grounds the fact that P is true) (Irreflexivity) (P ≺ Q) → ~ (Q ≺ P ) (If P grounds Q, then it is not the case that Q grounds P) We have then the following argument (I) O2 < (O2 v O1) (Assumption) (II) (O2 < (O2 v O1)) < (O2 < (O2 v O1)) v T⌜O2⌝ )) (I), (O2) (III) (O2 < (O2 v O1) v T⌜O2⌝ ) ≺ T⌜O2⌝ (II), (O2), (Truth-grounding) 19 (IV) T⌜O2⌝ (III), (Factivity) (V) T⌜O2⌝ < (O2 < (O2 v O1)) v T⌜O2⌝ ) (IV), (DG) 17 P fully grounds Q if nothing needs to be added to P in order to get a full ground for Q. We say that P partially grounds Q there is a plurality of facts Г such that Г, together with P, fully grounds Q. 18 Note that the sentence (O2) is just the same assertion as the assertion of the obligation O2-that O2 grounds that O2 v O1. 19 Given that, by assumption, our obligation O2 is equivalent to (O2 grounds that O2 v O1), if we have that (O2 grounds (O2 v O1) v T⌜O2⌝ ) is true (from (II) ), then it is the case that either (O2 grounds (O2 v O1)) or (T⌜O2⌝ ) is true. So, if O2 is (O2 grounds that O2 v O1), in any case we have that T⌜O2⌝