Norms, epistemic norms, context, and counterfactuals

The paper defends an account of the context-sensitivity of norms that draws on the resources of counterfactual conditionals. The account combines two assumptions: the assumption that permission is rule-abiding performance in some contextually relevant situations; and the assumption that the contextually relevant situations are picked out by the mechanism that selects the possible worlds relevant for the evaluation of counterfactual conditionals. The account explains the non-monotonicity of permissions and solves a puzzle, raised by Timothy Williamson, about the seeming failure of permissions to distribute over conjunction. In the domain of epistemic norms, the account solves an analogous puzzle and deals successfully with so-called blindspot propositions.


Introduction
Norms of action and norms of belief are context-sensitive. In particular, the possible situations that are relevant for evaluating statements about permission and obligation depend on the context of those statements. In this paper I develop an account of this dimension of context-sensitivity that exploits the apparatus of counterfactual conditionals. The account solves a puzzle, raised by Timothy Williamson, that arises from the general context-sensitivity of norms, or at least reduces the puzzle to a well-known puzzle from the domain of counterfactual conditionals. The account also solves a more specific puzzle for norms of belief that arises from so-called blindspot propositions.
The structure of the paper is as follows: Sect. 2 introduces a general framework of norms in terms of standards of permissibility and a dimension of context-sensitivity of norms. Sect. 3 presents the account of this context-sensitivity in terms of counter-factual conditionals. Sect. 4 discusses and replies to objections to the account. Sect. 5 applies the account to the case of norms of belief and the issue of blindspot propositions. Sect. 6 concludes.

Permissions in context
How should we formulate permissions to act? Typically, types of actions are associated with standards of permissibility ('standards', for short). A standard for driving is that one owns a driver's licence; a standard for medical interventions and for catering is that one does not do harm; a standard for attire is that one follows the dress code for the event in question; a standard for believing is that the belief is true or perhaps that one has sufficient evidence for it, or perhaps that it constitutes knowledge. (Specific examples of standards of permissibility might be more controversial than the claim that they exist, so readers are welcome to substitute their own examples if they find the ones given here objectionable.) Let us assume, for simplicity, that only a single standard is in play in a given case. What does it mean to be permitted to perform an action in view of this standard? At first, it seems that we can simply say that I am permitted to perform the action if and only if I meet the standard. But it turns out that this suggestion works only if I actually perform the action. If I do not actually perform the action, I might or might not be permitted to perform the action depending on what is going on in certain merely possible situations, irrespective of whether I meet the standard in the actual world. We therefore need to introduce a modal element in the formulation of permissions.
Timothy Williamson (2020, pp. 102-103) raised the following puzzle, which brings out the relevance of merely possible situations for formulating permissions. (Here, I substitute my own example for Williamson's.) Suppose that I am going to the vice-chancellor's black-tie reception. Suppose further that the only standard of permissibility in play is that one follows the dress code. Am I permitted to wear swimming trunks for the reception? I do not actually do it, but am I nonetheless permitted to do it? The obvious answer seems to be 'No', because of certain possible situations where I violate the black-tie dress code for the reception by showing up in nothing but swimming trunks. So far, so good. But now let us consider a different question: am I permitted to wear swimming trunks and a dinner suit over them (and a shirt, shoes, etc.) to the reception? Now the answer seems to be 'Yes', because of certain possible situations where I comply with the dress code by wearing the swimming trunks with a dinner suit over them. What is puzzling here is that, generally, when I am permitted to do this and that, I am permitted to do this and I am permitted to do that. But now it seems that I am permitted to wear the swimming trunks and the dinner suit over them for the reception, from which it follows by the general principle that I am permitted to wear the swimming trunks for the reception, yet I am not permitted to wear the swimming trunks for the reception. What is going on?
Williamson's diagnosis is that permissibility statements are context-sensitive. The context of the conversation determines a set of relevant situations, he claims, and it is permissible for me to perform an action in the actual situation (roughly) if I perform it permissibly in some of these situations. 1 More precisely, in Williamson's account situations are represented by triples of a subject, a world, and a time, and instead of 'performing permissibly' he uses the notion of performing an action in compliance with a rule, such as the rule 'No dancing in the library'. For our purposes, we can assimilate rules to material conditionals featuring actions and standards of permissibility: for an action type ϕ and a standard σ, the corresponding rule is 'ϕ only if σ'. In Williamson's example, the action is dancing and the standard is that it does not take place in the library, so that, in the form in which I have presented it, the rule reads (roughly) 'Dancing only outside of the library'. More technically, we can state the rule in terms of the open sentence 'S dances at t only if S does not dance in the library at t'. One complies with the rule by satisfying the open sentence. Spelled out fully, Williamson's principle about the context-sensitivity of permissibility reads: PERMISSIBILITY R It is permissible with respect to rule R at t in w for S to ϕ if and only if for some triple 〈S, t*, w*〉 contextually relevant to 〈S, t, w〉 , S performs ϕ at t* at w* and S complies with R at t* at w*. 2 If we formulate Williamson's principle in terms of standards rather than in terms of rules and compliance, it reads: PERMISSIBILITY σ It is permissible with respect to standard σ at t in w for S to ϕ if and only if for some triple 〈S, t*, w*〉 contextually relevant to 〈S, t, w〉 , S performs ϕ at t* at w* and S meets σ at t* at w*.
For simplicity, I am going to write (as Williamson mostly does) as though permissibility itself is context-sensitive. If one wanted to be more cautious, one could formulate PERMISSIBILITY σ meta-linguistically: 'It is permissible with respect to standard σ at t in w for S to ϕ' is true in context C if and only if … The simplification is harmless, for, as we shall see, the only features of the context that matter are determined by σ, t, w, S, and ϕ, so we will not get situations where the left-hand side of the biconditional is true in the context of one speaker but false in the context of another speaker.
Once we have formulated permissibility norms by PERMISSIBILITY R and by PERMISSIBILITY σ , we can formulate obligation norms in the same spirit by using the duality of permission and obligation, that is, the fact that an action is obligatory if and only if it is not permissible not to perform that action (Williamson, 2020, p. 110). As long as we keep our restriction to a single standard of permissibility in place, however, the obligation norms we get are unlikely to give us any plausible positive obligations (that is, obligations to perform a given action as opposed to obligations to refrain from performing an action). It would seem odd to say, for instance, that I am obligated to drive because I drive in all contextually relevant situations in which I have a driver's licence. But this is merely an artefact of our simplification -not violating a single standard of permissibility does not generate any intuitive positive obligations. Since I would like to keep the simplification in place, I will continue to focus on permissions rather than obligations.
Within the general framework of PERMISSIBILITY R and PERMISSIBILITY σ , we can elaborate on the diagnosis of the attire puzzle. The contextually relevant situations for the question of whether I am permitted to wear swimming trunks for the reception simpliciter are situations where I do not wear a dinner suit over them. In these situations, I violate the dress code for the reception. Therefore, by PERMISSIBILITY R and by PERMISSIBILITY σ , I am not permitted to wear swimming trunks for the reception. By contrast, the contextually relevant situations for the question of whether I am permitted to wear swimming trunks and a dinner suit over them for the reception are situations where I only wear swimming trunks for the reception if I also wear a dinner suit over them; presumably, those contextually relevant situations also include situations where I wear swimming trunks (and a dinner suit over them) for the reception. In those situations, I do not violate the dress code for the reception. So there are contextually relevant situations where I wear swimming trunks and a dinner suit over them without violating the dress code for the reception. Therefore, by PERMISSIBILITY R and by PERMISSIBILITY σ , I am permitted to wear swimming trunks and a dinner suit over them for the reception. We can say all this and still hold on to the principle that permissibility distributes over conjunction -that is, the principle that a permission of a conjunction entails a conjunction of permissions -if we hold the contextually relevant situations fixed. For, given a certain set of contextually relevant situations, if this set contains situations where I perform both action ϕ and action ψ and meet the standard that is in play, these situations are ipso facto situations where I perform ϕ and meet the standard and situations where I perform ψ and meet the standard. 3 What exactly are the contextually relevant worlds in a given case? Williamson does not enquire any further, preferring not to play the "mug's game" of giving necessary and sufficient conditions for the "messy pragmatic relation[…]" of contextual relevance (Williamson, 2020, p. 109). 3 One might hold that a simpler solution to the puzzle is available. According to this purported solution, the expression "wear swimming trunks" is ambiguous: on one disambiguation, it means "wear swimming trunks and nothing else"; on the other disambiguation, it means "wear swimming trunks, but possibly in combination with other clothes". The first disambiguation is metaphysically incompossible with the black-tie dress code; the second disambiguation is not. We can solve the puzzle, the suggestion goes, by simply disambiguating the original question and checking whether it is metaphysically possible for the property referred to by each disambiguation to be instantiated while the dress code is satisfied. The ambiguity claim from the purported solution has implausible consequences, however. The constituent expression "swimming trunks" is certainly not ambiguous, so any ambiguity in "wear swimming trunks" must be due to an ambiguity in "wear". But then "wear" should be ambiguous (meaning "wear … and nothing else" vs. "wear …, but possibly in combination with other clothes") in other contexts too. Yet there seems to be no sense in which the prime minister, wearing a business suit (including a tie) in the normal way for a cabinet meeting, is not wearing a tie, as the first disambiguation would have it.
I believe that we should be more optimistic about the prospect of spelling out the context-sensitivity of norms. It is true that giving a neat analysis of contextual relevance in general seems to be a hopeless task. But in the case of permissions there is a feature that we can exploit: what matters for the context-sensitivity of permissions is what might have happened if the action in question had been performed. Now, at first blush 'what might have happened' might seem just as unclear as 'contextually relevant'. But we shall see that we can use some well-established results from the theory of counterfactual conditionals to make this idea precise. Overall, we will get an account of the context-sensitivity of permissibility that will prove useful not just in the cases discussed so far, but also for formulating epistemic norms.
Here is the apparatus about counterfactual conditionals that I am going to use. I am going to assume David Lewis's (1973) truth-conditions for counterfactual conditionals, according to which a claim of the form 'If p were the case, then q would be the case' (p □→ q) is true at a possible world w if and only if either (i) there is no possible world where p is true (the case of vacuous truth) or (ii) there is a possible world where p and q are true that is closer (that is, more similar overall) to w than any worlds where p is true while q is false (case (ii) is the case of non-vacuous truth). For simplicity, I will follow the common assumption that for every world w and every possible proposition there is a well-defined set of worlds that are closest to w where that proposition is true. 4 With this assumption in place, we can simplify condition (ii) and say that a counterfactual is non-vacuously true at a world w if and only if its consequent is true at all the worlds closest to w where its antecedent is true (simpler yet: at the antecedent-worlds closest to w). In addition to the 'would' counterfactual, Lewis defines the 'might' counterfactual 'If p were the case, then q might be the case' (p ◊→ q) as the dual of the 'would' counterfactual, such that 'If p were the case, then q might be the case' is true at a world w if and only if the 'would' counterfactual 'If p were the case, then not-q would be the case' is false at w. Given the truth-conditions for the 'would' counterfactual and our simplifying assumption that a set of closest antecedent-worlds always exists for possible antecedents, it follows that 'If p were the case, then q might be the case' is true at w if and only if q is true at some of the worlds where p is true that are closest to w. It is somewhat controversial whether Lewis's truth-conditions for the 'might' counterfactual correspond exactly to its use in natural language (Stalnaker, 1980), but this does not affect my project, which could equally well be stated without using the 'might' conditional. Notice that the non-vacuous truth of a 'would' counterfactual entails the truth of the corresponding 'might' counterfactual: if there are antecedent-worlds and all of the closest antecedent-worlds are consequent-worlds, then a fortiori some of the closest antecedent-worlds are consequent-worlds.
Here is my suggestion about the context-sensitivity of permissions: the situations that are contextually relevant for the question of whether I am permitted to perform a certain action in view of a given standard are the closest possible situations where I perform the action. Let us combine this suggestion with the general modal frame-work for permissions that is spelled out in PERMISSIBILITY σ . Then we get that I am permitted to perform a certain action in view of a given standard if and only if the closest possible situations where I perform the action include situations where I meet the standard. Often, I actually perform the action. Given that every situation is more similar to itself than any other situation is, 5 it follows that actions that are actually performed are permissible for me if and only if I actually meet the standard. If I do not actually perform the action, whether I am permitted to perform it depends on the answer to the question 'What if I were to do it?'. This seems to be the most natural way of thinking about the permissibility of actions that I do not actually perform. If we make times explicit and use the 'might' counterfactual that was introduced above, we get the following overall suggestion: PERMISSIBILITY σ -CF It is permissible with respect to standard σ at t in w for S to ϕ if and only if it is true at w that were S to perform ϕ at t, then S might meet σ at t. 6 Here is how PERMISSIBILITY σ -CF handles the examples of context-sensitive permissions discussed above. If I had worn swimming trunks for the black-tie reception, I would have violated the dress code. Therefore, it is not the case that I might have met the standard of following the dress code if I had worn swimming trunks for the reception. Therefore, by PERMISSIBILITY σ -CF, I am not permitted to wear swimming trunks for the reception with respect to the standard of following the dress code. If I had worn swimming trunks and a dinner suit over them, however, I would have followed the dress code and a fortiori might have followed it. Therefore, by PERMISSIBILITY σ -CF, I am permitted to wear swimming trunks and a dinner suit over them for the reception. So PERMISSIBILITY σ -CF has the result that permissions are not monotonic: I can be permitted to do this without being permitted to do this-and-that. The reason for this result is that the closest situations where I do this and the closest situations where I do this-and-that may not coincide and may differ in what is going on in them. In our example, the closest situations where I wear swimming trunks for the reception are closer to actuality than the closest situations where I wear swimming trunks and a dinner suit over them for the reception, and I violate the dress code in the former, but not in the latter situations.
The result that permissions are not monotonic mirrors the result that counterfactuals are not monotonic, which is manifested by so-called Sobel sequences, such as the following: (i) If Otto had come, it would have been a lively party. (ii) If both Otto and Anna had come, it would not have been a lively party. 7 Suppose that Anna and Otto, an erstwhile couple, are individually genial and engaging, except in the presence of the other, when they become vibe killers. Suppose further that, whenever possible, Anna and Otto avoid one another. Then (i) and (ii) are both true, despite the fact that the consequent of (ii) contradicts the consequent of (i), because the closest worlds where both Otto and Anna come to the party are further away from (and involve drearier parties than) the closest worlds where Otto comes to the party (which involve lively parties, because Otto attends the party without Anna). Strictly speaking, the sequence (i)-(ii) is not perfectly analogous to the counterfactuals behind our example of non-monotonic permissions, but we can easily bring the sequence in line by replacing (i) with the corresponding 'might' counterfactual: (iii) If Otto had come, it might have been a lively party.
What about the distribution of permission over conjunction? Given PERMISSIBILITY σ -CF, this issue corresponds to pairs of counterfactuals like (i) and (ii) where we consider the counterfactual with the conjunctive antecedent first. Such reverse Sobel sequences sound odd. This holds irrespective of whether they are formulated in terms of 'would' or 'might' counterfactuals. Consider Bob and Ada, who are the opposite of Otto and Anna: together they are fun (though, for some reason, they avoid one another), but Bob by himself is a vibe killer. Then it sounds just as odd to utter (iv) after (v) as it does to utter (i) after (ii): (iv) If Bob had come, it would not have been a lively party.
(v) If both Bob and Ada had come, it might have been a lively party.
We can observe the same feature in permissions: 8 while it sounds fine to first say that I am not permitted to wear swimming trunks for the reception and then say that I am permitted to wear swimming trunks and a dinner suit over them, it sounds odd after having said the latter to reiterate that I am not permitted to wear swimming trunks for the reception. Given the approach of explaining permissibility norms in terms of counterfactuals that I have advocated, the oddity of saying that I am not permitted to wear swimming trunks for the reception after having said that I am permitted to wear swimming trunks and a dinner suit over them is simply a special case of the oddity of reverse Sobel sequences and their counterparts that involve 'might' counterfactuals.
In the case of reverse Sobel sequences, the source of the oddity is disputed. Some advocate possible-worlds truth-conditions of counterfactuals that differ from Lewis's 7 The example is from Lewis (1973, p. 10), with slight modifications. 8 Williamson (2020, pp. 104-105) also notices the similarity between reverse Sobel sequences and the puzzle about permissions but suggests that both are varieties of the same contextual effect and does not consider an explanation of norms in terms of counterfactuals. For further discussion of reverse Sobel sequences, see Nichols (2017) and Lewis (2018). truth-conditions such that when (i) is uttered after (ii), the range of relevant worlds still includes the closest worlds where both Otto and Anna come to the party, rendering (i) false (von Fintel, 2001;Gillies, 2007). Others advocate holding on to Lewis's truth-conditions while trying to explain away the oddity of reverse Sobel sequences as a pragmatic phenomenon, by claiming that after (ii) has been uttered, (i) remains true, but it becomes an epistemic possibility that if Otto had come to the party, then (Anna would have come too and so) the party might not have been lively (Moss, 2012). 9 In what follows, I will keep my earlier assumption of Lewis's truth-conditions in place, not least for methodological reasons. If we explain permissibility norms in terms of counterfactuals and assume Lewis's truth-conditions, we drastically reduce unexplained elements of context-dependence. The only remaining 'moving part' is the relation of closeness between worlds, but this relation is typically spelled out in a specific way, namely such that counterfactuals according to which the past depends on the future come out false. (I will say more about this issue below.) If we explain permissibility norms in terms of counterfactuals and assume von Fintel's or Gillies's truth-conditions, a range of contextually relevant worlds is in play that is partially determined by the antecedent, but also depends on what was said before and develops in ways that are not fully spelled out. For instance, eventually the range has to contract again after (ii) has been uttered, but no mechanism for this contraction is given. Overall, Lewis's truth-conditions are better suited for our proposal from the point of view of theory-building. But friends of the von Fintel-Sobel account could go along with this proposal too, at least mutatis mutandis.
On the account I have suggested, permissions do not generally distribute over conjunction, because I can be permitted to do this and that (e.g., wear swimming trunks and a dinner suit over them for the reception) without being permitted to do this (wear swimming trunks for the reception). The underlying reason for why permissions do not generally distribute over conjunction is that counterfactuals do not generally distribute over conjunction. We can, however, salvage the distribution principle for permissions by restricting it to cases where we artificially keep the contextually relevant situations fixed, as we did at the end of Sect. 2. Given this restriction, our original principle PERMISSIBILITY σ entails that a permission to perform a conjunction of actions entails a corresponding conjunction of permissions. In practice, it might often be impossible to hold the contextually relevant situations fixed, because different actions determine different relevant situations via PERMISSIBILITY σ -CF, by featuring in the antecedents of different 'might' counterfactuals. It is a common phenomenon of contextualist accounts that they can uphold certain principles only on the assumption that the context is held fixed, while in practice this assumption is seldom satisfied. For instance, contextualists about knowledge typically claim that knowledge is closed under some form of implication if the context is held fixed, while acknowledging that the context changes halfway through the sentence 'If I know that I have hands, then I know that I am not a handless brain in a vat deceived into thinking that it has hands.' 10 The Lewisian account of 'would' and 'might' counterfactuals that I am using to spell out permissions makes a number of substantial assumptions. For one thing, it assumes that possible worlds can be compared for their overall similarity or closeness to the actual world (more generally, to the world of evaluation of the counterfactual in question). But couldn't there be worlds that are incommensurable with respect to their comparative overall similarity? A Lewisian answer is that overall similarity is a function of various dimensions of similarity. Once the dimensions and their relative importance are fixed, the answer goes, there is no obstacle in principle to comparing worlds. 11 The answer to the incommensurability question gives rise to another question, namely how exactly should we spell out overall similarity? For our purposes, we should do this in a way that avoids so-called 'backtracking' readings of counterfactuals, that is, readings according to which the past would be different if the present or the future were different (Lewis, 1979). More precisely, we should identify the most similar antecedent-worlds of a counterfactual as those worlds that are exactly like the actual world until just before the time specified in the antecedent 12 and where the antecedent is then made true with minimal deviation from the actual course of events. A precedent for such an evaluation of counterfactuals can be found in counterfactual theories of causation (Lewis, 2004, p. 78). We do not want to say that the falling of the barometer reading caused the earlier drop in air pressure, so we had better not say that if the barometer reading had not fallen, then the air pressure would not have dropped earlier.
Applied to norms, the 'non-backtracking' reading of counterfactuals has the advantage of giving the correct verdict in cases such as the following. Suppose that you are my dinner guest. By coincidence, I have come into possession of a poison. I also know of, though I do not possess, an antidote that completely neutralizes the poison when administered with it. Let us assume that the single standard of not doing harm is in play. Am I permitted to add poison to your soup in view of this standard? One might think that the answer that we get from my account is 'Yes', for the following reason. Focus on my gentle character. I would go out of my way not to harm anyone. If I had put the poison in your soup, one might think, I would have made sure not to harm you by doing it and would have taken precautions to that effect. I would have acquired the antidote and would have put it in the soup together with the poison so that the poison would not have had any effect on you. Thus, one might think, if I had added poison to your soup, I would not (and hence might not) have harmed you. It would follow from my account that I am permitted to add poison to your soup. This is the wrong verdict. Fortunately, this verdict does not follow from my account 10 Lewis's (1996, p. 564) description of this phenomenon is perhaps the best-known. 11 Lewis (1973, pp. 91-94) gives an answer in this spirit. Morreau (2010, pp. 480-482) argues that incommensurability arises even when specific dimensions of similarity are fixed. Kroedel and Huber (2013, pp. 462-464) reply that this seeming incommensurability is due to ordinary vagueness. 12 Not all counterfactuals have an antecedent that talks about a specific time, but all the counterfactuals relevant for our purposes do, because the antecedents we get from PERMISSIBILITY σ -CF are about performing an action at a specific time.
if the relevant counterfactual is evaluated in a non-backtracking way. Without backtracking, if I had put poison in your soup, everything would have been just as it is in actuality until just before the time in question. There would have been no antidote in your soup if I had added poison and I would have harmed you. Thus, I would have violated the standard by adding poison and therefore I am not permitted to add poison in view of the standard.
In sum, the combination of principle PERMISSIBILITY σ -CF and a non-backtracking Lewisian reading of counterfactuals yields a tractable account of permissions that gives the correct verdict in individual cases. Admittedly, sometimes the counterfactuals from PERMISSIBILITY σ -CF might be difficult to assess, but such cases are fine as long as they involve claims about permissions that are likewise difficult to assess.
It can also happen that the counterfactuals from PERMISSIBILITY σ -CF reveal surprising consequences of possible actions, which correspond to surprising permissions (or the lack thereof). Let us change the previous example slightly. Suppose again that you are my dinner guest and that I cooked a perfectly healthy soup that does not contain any unusual ingredients. Suppose, however, that, unbeknownst to me, someone mixed a potent poison with the salt in my salt shaker. Suppose, lastly, that the sole standard of permissibility that is in play is again that of not doing harm. Am I permitted to add salt to your soup? If I were to do it, I would also (unwittingly) add poison to your soup and harm you. So, according to my account, I am not permitted to add salt to your soup. This result might seem objectionable at first sight, but we should bear in mind that my account talks about permissions in particular situations. What is at issue in the example is whether or not I am permitted to add salt to your soup in the particular -and unusual -situation where the salt has been intermixed with poison. In this situation, it seems, I am not permitted to add salt to your soup. Perhaps one needs to have consequentialist leanings to have this view. If so, I am happy to restrict my account to consequentialist norms. In any event, it does not follow from my account that one is normally or typically forbidden to add salt to other people's meals (in view of the standard of not doing harm), which would indeed seem problematic.
There are cases that seem to take consequentialism too far, but they can be defused if we are careful with the standard that is in play and the time that we are considering. Suppose that James owns a single dinner suit. Is he permitted to wear it for the blacktie reception in view of the dress code? We might think that he is, but what if we learn that his dinner suit is old and shabby and has lots of holes in it? Then whether James is permitted to wear it depends on whether we read the standard of following the dress code as implicitly requiring an intact suit, and the original question turns out to be ambiguous. Or take Jones, who always gets so hot in his (flawless) dinner suit that he strips down to his underwear an hour after having put it on. Is Jones permitted to show up at the black-tie reception in his dinner suit in view of the dress code? It might seem that my account says 'No', implausibly so. But in fact, my account says 'Yes' if we add temporal qualifications and do so uniformly, as PERMISSIBILITY σ -CF requires. According to PERMISSIBILITY σ -CF, Jones is permitted to wear his dinner suit at any given time t just in case he might meet the standard of following the dress code at t if he were to wear the dinner suit at t. If t is a time that is less than an hour after Jones's dressing up, the 'might' counterfactual is clearly true. If t is a time an hour or more after Jones's dressing up, the 'might' counterfactual is still true, though perhaps less clearly so, because even if Jones were to strip down to his underwear immediately after t, he would still follow the dress code at t. Admittedly, at any time before his stripping down, Jones violates the standard following-the-dress-code-ata-later-time, but this standard is typically not the salient one because it is temporally extrinsic. 13 One advantage of our principle PERMISSIBILITY σ -CF is that it can handle cases where the performance of an action makes a difference to whether or not the relevant standard of permissibility is met. We will consider examples more thoroughly when turning to epistemic norms in Sect. 5, but it is worth noting that cases of this kind also arise outside epistemic contexts. Suppose that the standard of permissibility for assertion that we are dealing with in a given context is that what is said is true. 14 Suppose that no one is saying anything. Suppose, that is, that the sentence 'No one is saying anything' is true. Am I permitted to say it? According to PERMISSIBILITY σ -CF, I am not. If I were to say 'No one is saying anything', the sentence would be false, so it is not the case that I might satisfy the standard of permissibility (that is, truth) if I had performed the action (that is, asserted the sentence). This seems to be the right result. A simpler norm according to which I am permitted to say a given sentence if and only if the sentence is true would not have yielded the desired result. According to that norm, I am permitted to say 'No one is saying anything' if no one is saying anything. So the simpler norm grants me a permission that I lose once I make use of it, which makes it a strange kind of norm.

Objections and replies
In this section I discuss two objections to the account of permissions presented in the previous section. The first objection claims that the account is too simple to be true. The second one raises issues similar to Ross's paradox.
Here is the first objection. I have suggested that the situations that are contextually relevant for the question of whether I am permitted to perform a certain action are the closest worlds where I perform the action, where closeness is understood in the same way as in the standard Lewisian truth-conditions for counterfactuals. It might be objected that this suggestion is too simple to be true because there are more factors that determine which situations are contextually relevant for questions about permission.
I would like to make two points in response to this objection. First, there is a respectable precedent for this kind of account of contextual relevance. The central 13 This makes following-the-dress-code-at-a-later-time disanalogous to the standard of not doing harm from the earlier examples, which is naturally read as doing something at a given time that has harmful consequences at a later time. 14 Of course there are other standards of permissibility for assertion, some of them stronger than truth, such as knowledge (Williamson, 2000, pp. 238-269), some of them independent of truth, such as reasonable belief (Lackey, 2007). I am supposing the truth standard here purely for the sake of the argument, to bring out a structural feature of PERMISSIBILITY σ -CF. (1995, p. 36). DeRose holds that there are contextually relevant standards of knowledge, that is, standards for how good S's epistemic position has to be in order for her to count as knowing a proposition p. According to his rule, these standards tend to be raised (if they are not already sufficiently high) to a level that requires the counterfactual 'If p had been false, then S would not have believed p' to hold for 'S knows p' to be true. While obviously DeRose does not defend a thesis about the context-dependence of permissions, his apparatus for spelling out context-dependence is similar: it features constituents of the context-dependent claim (namely person S and proposition p) and a counterfactual conditional involving these constituents (the counterfactual 'If p had been false, then S would not have believed p'). Our set of constituents (person S and action ϕ) is different, and so is the counterfactual I have used to pick out the contextually relevant situations for permissions, but the overall approach is similar.

component of Keith DeRose's contextualism about 'knows' is what he calls the Rule of Sensitivity
The second response is to point out that an additional dimension of contextsensitivity emerges once we go beyond our simplifying assumption that only a single standard of permissibility is in play, which is, as it were, set by hand. The principle PERMISSIBILITY σ -CF is explicitly relativized to a single standard σ. Often, we do not talk about what we are permitted to do given a certain standard of permissibility, but leave the standard or standards implicit and talk about what we are permitted to do simpliciter. Context then determines what the relevant standard or standards are. 15 Once a set of standards is determined, we can generalize PERMISSIBILITY σ -CF by saying that I am permitted to perform a certain action in a given context if and only if, were I to perform it, I might meet all the standards from the set. My aim in this paper is not to suggest a mechanism for how context determines the relevant standard or standards, but merely to suggest how permissibility norms should be formulated once the standard or standards are in play.
The second objection I will discuss in this section has to do with a structural feature of any account of permissions that builds on the general principle of conceiving permissions along the lines of PERMISSIBILITY σ (or PERMISSIBILITY R , for that matter). We have seen that, if we hold the contextually relevant situations fixed (which is a big 'if'), the permission to do this-and-that entails the permission to do this. More generally, if we hold the contextually relevant situations fixed, permissions are closed under implication. Another facet of this closure is that the following principle holds for fixed contextually relevant situations: if I am permitted to do this, then I am permitted to do this-or-that. 16 But the latter implication might seem 15 The standards might come with an ordering of their own; see Kratzer (1981). For a recent discussion of the context-dependence of normative standards, see Worsnip (2019). 16 The principle that if I am permitted to this, then I am permitted to do this-or-that is the permissibility analogue of Ross's paradox (Ross, 1941), which arises from the implication of 'I am obligated to do thisor-that' by 'I am obligated to do this'. We can also derive this implication central to Ross's original paradox from the principle that if I am permitted to this-and-that, then I am permitted to do this together with the duality of obligation and permission and the claim that we can substitute logically equivalent propositions in the scope of deontic operators. Since my focus in this paper is on permissions and not on (positive) obligations, I confine myself to discussing the permissibility analogue of Ross's paradox, which seems just as problematic as the original paradox. For an overview of the debate about Ross's and related paradoxes, see Hilpinen and McNamara (2013). objectionable. Suppose that the standard that is in play is that of being a reliable correspondent. Then the following is true: (i) I am permitted to post the letter.
If the contextually relevant situations are held fixed, it follows from (i) that (ii) I am permitted to post the letter or burn the letter. Now it seems to follow from (ii) that (iii) I am permitted to post the letter, and I am permitted to burn the letter.
But (iii) is certainly false, because I am not permitted to burn the letter. What has gone wrong?
The best response, in my opinion, is to accept that (ii) is a corollary of (i) if we hold the contextually relevant situations fixed, but to deny that (ii) entails (iii), while explaining away the seeming entailment of (iii) by (ii) as a pragmatic phenomenon. 17 More precisely, the pragmatic explanation claims that the occurrence of 'or' in the scope of a deontic operator can implicate, but does not imply, that each of the disjuncts is permissible. 18 Indeed, according to PERMISSIBILITY σ , the claim 'I am permitted to ϕ or ψ' does not generally entail the claim 'I am permitted to ϕ, and I am permitted to ψ' if we hold the contextually relevant situations fixed. For among these situations there might be some where I ϕ and meet the standard (which makes the first claim true), but none where I ϕ and ψ and meet the standard (which makes the second claim false). (Similarly, among the situations there might be some where I ψ and meet the standard, but none where I ϕ and ψ and meet the standard.) Now, according to my account as formulated in PERMISSIBILITY σ -CF, the contextually relevant situations can vary. In fact, we saw in the previous section when we discussed Williamson's puzzle about conjunctive permissions that it can be unrealistic to hold fixed artificially the contextually relevant worlds. What follows about the relation between (i), (ii), and (iii) if the contextually relevant situations are not held fixed, but are identified as the closest situations where I perform the action, as PERMISSIBILITY σ -CF has it? For the specific example of (i), (ii), and (iii), we get the same verdict as we do for fixed contextually relevant worlds. In at least some of the closest situations where I post the letter, I meet the standard, so I am permitted to post the letter, and (i) is true. The closest situations where I post or burn the letter coincide with the closest situations where I post the letter, so I am also permitted to post or burn the letter, and (ii) is likewise true. But the closest situations where I burn the letter are further from actuality than the closest situations where I post the letter, and I do not meet the standard in the closest situations where I burn the letter, so I am not permitted to burn the letter; a fortiori I am not permitted to post the letter and permitted to burn the letter, and (iii) is false.
If we take a step back and look at how my account of permissions deals with disjunctive permissions beyond the example of (i), (ii), and (iii), two points are worth mentioning. First, as the failure of (ii) to imply (iii) given PERMISSIBILITY σ -CF shows, my account denies that, in general, a permission to ϕ or ψ implies a permission to ϕ and a permission to ψ. My account can explain why it still seems that this implication holds, however. For counterfactuals, in a similar way to permissions, often appear to allow us to infer both 'If p were the case, then …' and 'If q were the case, then …' from 'If p or q were the case, then …'. According to our Lewisian truth-conditions for counterfactuals, the inference is invalid. 19 But one can give an explanation of the appeal of the inference as a pragmatic phenomenon (Franke, 2011). Thus, there is another important structural similarity between permissions and counterfactuals.
The second general point is that, while (i) and (ii) are both true, it is not generally the case according to PERMISSIBILITY σ -CF that a permission to ϕ entails a permission to ϕ or ψ. Suppose that if I made an effort, I might satisfy the relevant standard, such that, according to PERMISSIBILITY σ -CF, I am permitted to make an effort. Suppose further that if I were lazy, I would not meet the standard and that situations where I am lazy are closer to actuality than situations where I make an effort. Thus, the worlds where I am lazy are the closest worlds where I am lazy or make an effort. Since I do not meet the standard at those worlds, I am not permitted to be lazy or make an effort. It is difficult to say in general how often a permission to ϕ fails to entail a permission to ϕ or ψ, but the fact that it fails at least sometimes, given PERMISSIBILITY σ -CF, might explain why we feel a certain uneasiness even in cases where I have both permissions, such as the permissions expressed by (i) and (ii).

Epistemic permissibility norms
I have been advocating the general approach of spelling out permissions (with respect to a given standard) in terms of what might have been the case had I performed the action in question. The general approach can be followed for the special case of epistemic or doxastic norms, that is, norms about what one may, may not, or should believe. I admit that it is a bit odd to talk about beliefs as though they are actions, but classifying beliefs as actions is not essential to the project of formulating analogous norms for beliefs; what matters is that the norms for beliefs have the same structure as those for typical actions. As above, I will focus on permissibility norms that we get from a single standard of permissibility. 20 I will remain neutral on whether there 19 A classic instance of an invalid inference of this form is the inference from 'If Spain had fought on the Axis side or Spain had fought on the Allied side (in World War II), then Spain would have fought on the Axis side' (true) to 'If Spain had fought on the Allied side, then Spain would have fought on the Axis side' (false) (McKay & van Inwagen, 1977). 20 One structural advantage of permissibility norms for belief is that they allow for the non-agglomeration of doxastic permissions (that is, they allow for the permission to believe p and the permission to believe q might be multiple standards of permissibility for belief. I will also remain neutral on what the ultimate source of epistemic norms is. 21 There are several candidate standards of permissibility for belief. The most salient ones are that the belief is true, that the belief has evidential support, and that the belief constitutes knowledge. If we spell out the permissibility norms that PERMISSIBILITY σ -CF yields for these respective standards and simplify a little by omitting reference to worlds, we get: TRUTH S is permitted at t to believe p if and only if, were S to believe p at t, p might be true at t. 22 EVIDENCE S is permitted at t to believe p if and only if, were S to believe p at t, S might have evidence 23 at t for p. 24 KNOWLEDGE S is permitted at t to believe p if and only if, were S to believe p at t, S might know p at t. 25 If one wanted to, one could of course spell out further how one arrives at TRUTH, EVIDENCE, and KNOWLEDGE, by making explicit the intermediate steps of reading permissibility as meeting the standard in some contextually relevant situations and by then identifying the contextually relevant situations as the closest situations where S has the belief in question. Context-sensitivity seems to affect permissions to believe just as much as it affects permissions to act in general. There are cases similar to the attire example for permissions to believe, such as the following. 26 I am sitting at my desk at the moment. Am I permitted to believe that I am jumping? It seems not. But consider a situation where (i) I am jumping right now; (ii) I believe right now that I am jumping; (iii) I have evidence right now that I am jumping; (iv) I know right now that I am jumping; and to obtain without the permission to have both beliefs at once), which is exploited, in different contexts, by Whiting (2010), Kroedel (2012), and Raleigh (2017). 21 For recent contributions to the debate about whether the aim of belief is a source of norms, see Chan (2013). For an overview of the debate about the normativity of belief in general, see McHugh and Whiting (2014). 22 If propositions are true or false timelessly, there is of course no need to qualify 'true' with 'at t'. 23 EVIDENCE is most plausible if we understand S's having evidence for p as p's being sufficiently supported by S's total evidence; otherwise S counts as allowed to believe p and to believe not-p merely because S has some evidence for p and some evidence against p. 24 Raleigh (2013) discusses, but does not ultimately endorse, principles that are similar to TRUTH and EVIDENCE, but are formulated in terms of the 'would' counterfactual. Raleigh (2017) suggests the 'would' counterpart of TRUTH within the scope of a knowledge operator. Dahlback (forthcoming) suggests a principle similar to Raleigh's later principle, albeit one that is formulated as an indicative conditional. Olinder (2012) suggests an obligation norm for belief in terms of 'would' counterfactuals. None of these authors derive their principles from a more general principle about norms such as our PERMISSIBILITY σ -CF, however. 25 The three norms are not independent. Given that knowledge entails truth, a permission that is due to KNOWLEDGE entails a corresponding permission that is due to TRUTH. If knowing requires having evidence, a permission that is due to KNOWLEDGE also entails a corresponding permission that is due to EVIDENCE. 26 For a similar example, see Williamson (2020, pp. 116-117). (v) nothing abnormal is going on epistemically right now. 27 Let j be the conjunction of (i)-(v). According to Williamson, we can make a situation contextually relevant where j is true. Since I am epistemically flawless in such a situation, it would follow that I am permitted to be in a situation where j is true. But one conjunct of j is the claim that I believe right now that I am jumping, so if I am permitted to be in a situation where j is true, then I also seem to be permitted to believe right now that I am jumping, notwithstanding our earlier diagnosis that I am not permitted to believe this.
Our permissibility norms TRUTH, EVIDENCE, and KNOWLEDGE all say that I am not permitted to believe that I am jumping (given that I am actually sitting at my desk). For in the closest situations where, contrary to actual fact, I believe that I am jumping, my belief that I am jumping is brought about with minimal difference to the actual situation and without any change in what is going on before I form the belief. (Recall that the closest worlds in question do not standardly involve 'backtracking'.) Thus, if I were to believe that I am jumping, I would still be sitting at my desk; I would not have evidence that I am jumping; and it would be false that I know that I am jumping. So the right-hand sides of TRUTH, EVIDENCE, and KNOWLEDGE are all false.
What about the question of whether I am permitted to be in a situation where j is true? This question is not in the purview of our norms TRUTH, EVIDENCE, and KNOWLEDGE, because being in a situation where j is true is not just a matter of having a belief: situations where j is true also have plenty of non-doxastic constitutive elements (such as my jumping). Pointing this out may seem like a way of dodging the question, but it does not seem completely unjustified to doubt that permissibility standards for belief come into play for mixed actions that have doxastic and non-doxastic elements such as the 'action' of being in a situation where j is true. Still, one might stipulate (more or less plausibly) that truth/evidence/knowledge is the standard that is relevant for the question of whether I am permitted to perform the 'action' of being in a situation where j is true. 28 With this stipulation, it does follow from the general principle PERMISSIBILITY σ -CF that I am permitted to be in a situation where j is true. This seems puzzling, since we have established that I am not permitted to believe right now that I am jumping. The puzzlement can be explained analogously to that in the attire example, however. Specifically, one can again exploit the similarity to Sobel sequences for counterfactuals and their reverse such as the example presented in Sect. 3.
In many cases, TRUTH, EVIDENCE, and KNOWLEDGE deliver the same verdicts that norms formulated without counterfactuals would. For instance, in many cases, whether or not S believes a proposition does not affect the truth-value of that proposition; in these cases, a simple norm that says that S is permitted at t to believe 27 Perhaps (iv) entails (iii) and (v), but I include (iii) and (v) for good measure. 28 I am going along with this stipulation here for the sake of the argument. The stipulation should not be taken to indicate that TRUTH, EVIDENCE, and KNOWLEDGE are designed to apply to complex states, particularly complex belief states. On the contrary, these norms, when applied as intended, are about individual beliefs. To illustrate this for TRUTH, suppose that p is (timelessly) true; that I do not (yet) believe p; and that I falsely believe q. If I were to believe p, I would presumably continue to believe q. Thus, if I were to believe p, I would believe something false. Still, I am permitted to believe p according to TRUTH, because if I were to believe p, that very proposition would (and might) be true.
p if and only p is true at t would deliver the same verdicts as the TRUTH norm. There are, however, cases where belief affects the truth-value of the proposition believed. The most notorious cases are so-called blindspot propositions, that is, propositions that can be true but cannot be truly believed (Sorensen, 1988;Bykvist & Hattiangadi, 2007Williamson, 2020). It is an advantage of our epistemic permissibility norms that they can deal with such cases.
Take the proposition that no one believes anything or, more realistically, the proposition that it is raining and no one believes that it is raining (call the latter proposition r). In the following, I will focus on the TRUTH norm. 29 If I believe r, I ipso facto believe the first conjunct of r. But by believing the first conjunct of r, that is, by believing that it is raining, I make the second conjunct of r (the claim that no one believes that it is raining) false and thus make r false. It seems to be a necessary truth that believing a conjunction implies believing each of the conjuncts, and it is certainly a necessary truth that the falsity of a conjunct implies the falsity of the conjunction. This relation between believing r and r's truth-value constitutes the status of r as a blindspot proposition. It also entails how the TRUTH norm deals with blindspot propositions. If it is necessary that r is false if believed, then a fortiori the following counterfactual holds: if I were to believe r, then r would be false. This 'would' counterfactual directly contradicts the 'might' counterfactual that if I were to believe r, then r might be true. So the right-hand side of TRUTH is false; it follows that I am not permitted to believe r. (I have simplified the application of TRUTH a bit by suppressing references to times.) This seems to be the right verdict about whether or not we are permitted to believe blindspot propositions such as r.
Counterfactuals have been invoked to deal with blindspot propositions before (Olinder, 2012;Raleigh, 2013), but our account has the advantage of following a fully general rationale for using them: the idea that we should assess permissions to act by considering whether the standard of permissibility might have been met, had the action been performed. Thus, epistemic norms in terms of counterfactuals do not belong to the unpromising activity of adding "epicycles" (Williamson, 2020, p. 116) to simpler epistemic norms to solve specific problems for those simpler norms. Instead, using counterfactuals in epistemic norms is well motivated.
In the above discussion of blindspot propositions, I have simplified matters by suppressing reference to times. Sometimes we must make the times explicit, however, to avoid counterexamples similar to the example of Jones (who would strip down after an hour in his dinner suit) from Sect. 3. In the following example, suppose that everyone, including Jordan, is happy. Suppose further that Jordan has a psychological quirk that immediately makes her sad when she believes that everyone is happy. Is Jordan permitted to believe that everyone is happy? It seems that she is, but it might seem that according to TRUTH she is not, because if she believed that everyone was happy, her belief would be false. We must be careful with the temporal qualifications, however. Jordan's psychological quirk cannot be instantaneous, but must take some amount of time (however short) to operate. If Jordan were to believe at a given 29 The results from the TRUTH norm will easily generalize to the KNOWLEDGE norm, because violations of the right-hand side of TRUTH entail violations of the right-hand side of KNOWLEDGE. The issue of whether there are evidential blindspots is tricky; see Raleigh (2013) for discussion. time t that everyone was happy, she would still be happy at t and thus would (and might) truly believe, at t, that everyone was happy. (Once again, the evaluation of the counterfactual relies on a 'non-backtracking' reading.) Thus, according to TRUTH, Jordan is permitted at t to believe (at t) that everyone is happy. 30 Before concluding, I would briefly like to discuss another potential counterexample to the TRUTH norm. Consider the following proposition (call it q): it is raining, and S believes that it is not raining (Olinder, 2012, p. 299;Bykvist & Hattiangadi 2013, p. 110 note 10). Suppose that q is true. Is S permitted to believe q? According to TRUTH, that depends on what would or might have been the case if S had believed q (again, I am suppressing reference to times for simplicity). If S had believed q, then S would have believed both conjuncts of q. Given that S does not have any magical powers that could instantaneously change the weather, if S had believed q, then this would not have made any difference to whether it rains. So it would still have rained if S had believed q. Thus, S would have believed the first conjunct of q truly had S believed that it rained. What about the second conjunct of q? S's believing the second conjunct means that S believes that S believes that it is not raining. Assume that, for any proposition, if someone believes that they believe that proposition, then they believe that proposition. We might call this principle 'BB→B'; it is the converse of the principle of positive introspection for belief from epistemic logic. Given BB→B, S's believing the second conjunct of q implies that S believes that it is not raining. The latter belief would have been false if S had believed q, but this by itself does not forbid S from believing q according to the TRUTH norm. According to TRUTH, what matters for S's permission to believe q is whether q as a whole might have been true if S had believed q. And it seems that it might (indeed, would) have been the case that S's belief in q would have been true. S's believing q would have resulted in a weird situation in which S believes that it is raining and believes that it is not raining, however. Doesn't this result undermine S's permission to believe q and thereby refute TRUTH?
A situation where I end up believing both that it is raining and that it is not raining is indeed weird. But it is far from clear whether such a situation could arise, were I to believe q. Let NON-CONTRADICTION be the principle that one does not believe both a proposition and its negation at the same time. 31 NON-CONTRADICTION idealizes our thinking somewhat, but so does BB→B (or, for that matter, the principle that by believing a conjunction one ipso facto believes its conjuncts). If one idealizes by assuming BB→B, one should likewise idealize by assuming NON-CONTRA- 30 The requirement that counterfactuals be read in a 'non-backtracking' way also gives the correct verdict about the following variant of the example. Assume that Jordan's quirk operates differently than in the original example: her sadness is triggered not by her belief that everyone is happy, but instead by the earlier processes that form her belief that everyone is happy, such that, if these processes take place, she believes that everyone is happy and feels sad at the same time, t. Given that, actually, everyone is happy at t, Jordan seems to be permitted at t to believe that everyone is happy, as in the original example. TRUTH delivers this verdict too if 'backtracking' is not allowed: if Jordan had, at t, believed that everyone was happy, then history prior to t would have been just as in the actual world and the processes that normally form Jordan's belief that everyone is happy (and that normally form her co-occurring sadness) would not have been operational; instead, her belief that everyone is happy would have emerged without the processes that normally precede it, and she would (and might) still have been happy at t. 31 By itself, NON-CONTRADICTION does not rule out that one believes a larger set of propositions that are jointly inconsistent.
DICTION. But if one assumes both BB→B and NON-CONTRADICTION (and the principle that by believing a conjunction one ipso facto believes the conjuncts), then proposition q is no longer believable, for by BB→B subject S would end up in a situation that NON-CONTRADICTION rules out, namely a situation where S believes both that it is raining and that it is not raining at the same time. If q is not believable, it is false that q might have been true, had S believed q. 32 So the right-hand side of TRUTH is false for q, and it follows from TRUTH that S is not permitted to believe q after all.
While I believe that the TRUTH norm can be defended successfully by the argument just given, it is not my aim here to defend TRUTH to the death. Perhaps in the end it turns out that there are standards of permissibility for beliefs in addition to truth or different from truth. Nevertheless, it seems very likely that ultimately the epistemic permissibility norms will have a shape similar to TRUTH, EVIDENCE, or KNOWLEDGE, both in view of their descendance from the more general norm PERMISSIBILITY σ -CF and in view of their potential to deal with blindspot propositions.

Conclusion
I have argued that the context-sensitivity of norms, or at least one important dimension thereof, can be explained if we take the contextually relevant situations for the question of whether I am permitted to perform a certain action to be the closest situations where I perform the action. By quantifying over contextually relevant situations and using the apparatus of counterfactual conditionals, we get the result that I am permitted to perform a given action if and only if I might meet the relevant standard of permissibility were I to perform the action. This account explains how it can happen that I am not permitted to do this, while I am permitted to do this-and-that. The account also explains why it seems odd to re-assert that I am not permitted to do this after having said that I am permitted to do this-and-that, or at least reduces this oddity to a familiar feature of counterfactual conditionals. In the realm of epistemic permissions, the account provides a rationale for formulating norms both in terms of counterfactuals and in terms of truth, evidence, or knowledge, and the structure of the account makes it well suited to deal with problems arising from blindspot propositions. which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/ licenses/by/4.0/.