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Anyone familiar with deontic logic knows that early work in this area was influenced by the view that permission and obligation are dual concepts standing in much the same relation to each other as do the concepts of possibility and necessity. This model presents a distorted view of the deliberations of moral agents making decisions under moral risk. While decisions about what one is or is not permitted to do are often informed by a set of abstract principles of duty or obligation, in practice the task of choosing a course which can lead to a situation which is most acceptable from a moral point of view is more complicated than this model would indicate. The moral agent does not make judgments from the vantage point of an omniscient observer. He is in the midst of the action. He is often under time pressure, and is plagued by ignorance of some or many morally relevant facts. Thus, even if he has a clear vision of the kind of world to which he is committed, and even if he has the strength of spirit to pursue this vision doggedly, he still faces the practical problem of determining which actions may make his vision real. A familiar notion of what is permitted is that anything is permitted which does not interfere with our pursuit of a morally ideal, or perhaps just a morally acceptable, life. Given any initial list of obligations, uncertainty about the ways in which future contingencies might interfere with our efforts to fulfill these obligations is likely to result in derivative moral restrictions. It is a practical concept of permission which recognizes these restraints that we will explore.

PERMISSION

AND

UNCERTAINTY

Whether it is because the future is not entirely determined by past and present events or it is only because of the limitations inherent in our epistemic situation, we cannot be certain of future events. This uncertainty complicates our moral decisions. We feel that we are not permitted to perform actions which would have certain outcomes, but whether Journal 0 1985

of Philosophical Logic by D. Reidel Publishing

14 (1985) Company.

169-190.

0022-3611/85.10.

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our actions will have such outcomes often depends on other factors over which we have no control and concerning which we have limited knowledge. Consider the following example which demonstrates the role that uncertainty about the future plays in our moral deliberations. The only parking place Tom can find is beside a fire hydrant. Tom knows that it is illegal to park next to a hydrant, but he has an important appointment for a job interview and the possible inconvenience of receiving a ticket or having his car towed is far outweighed by his need to keep his appointment. Is he permitted to park beside the hydrant? Even though he is willing to risk a ticket or worse, Tom decides not to park beside the hydrant because in the event of a fire his car might interfere with the efforts of the fire department to savelives and property. Tom probably thinks that a fire is even less likely than a ticket, but the possibility of a fire prevents his parking beside the hydrant when the possibility of a ticket does not. The prohibition which Tom recognizes is not a conditional prohibition, at least not one of the usual stripe. Tom does not say to himself, “If there will be a fire, then I may not park here.” Instead he says, “Because there may be a fire, I may not park here.” The prohibition is not conditional on there being a fire, but we might say that it is conditional on the possibility of there being a fire. Since the possibility is certain even if a fire is unlikely, the prohibition is normally expressed univocally and unconditionally. We may ask what kind of detachment principle is appropriate for a conditional obligation, but the ordinary way of expressing the prohibition on Tom is in the unconditional form for which the question of detachment does not arise. It is a subtle distinction, but 1 think an important one, that we see the possibility of a fire as a reason for the prohibition rather than a condition for it. Examples of this sort are common. We’refrain from certain actions or perform certain actions because to do otherwise could result in consequences which we feel we are not permitted to risk. It could be argued that agents may find themselves embroiled in irresolvable moral dilemmas. I will make the optimistic assumption that no conflict of obligations is in principle irresolvable, yet in actual practice uncertainty about the future and about the morally significant consequences of our actions can generate moral dilemmas which we cannot in fact resolve. The kind of case I have in mind is one in which an agent has

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a choice between bringing about or not bringing about some state of affairs, and in which either choice could have morally disastrous consequences should certain other things happen. Because the agent cannot determine which contingencies beyond his control will be realized, the agent cannot conclude either that he is permitted to act or that he is permitted to refrain. In the actual event, this is tantamount to concluding that neither acting or refraining is permitted. The result, at least for this particular action, is a kind of moral paralysis. Consider the plight of a very poor man whom we will call Dick. Dick has an opportunity to steal food for his family. If he does not steal the food and he is unable to procure other food by honest means, his family will starve. On the other hand, if he steals the food and is caught, he will be imprisoned and his family will starve. Of course Dick has a duty to preserve his family from starvation, and I will assume for the moment that this duty overrides any other obligation Dick might have. May he steal the food or not? He may not take the food since in doing so he runs the risk of allowing his family to starve. But he also may not refrain from stealing the food since in doing so he runs the risk of allowing his family to starve. Given the very real chance that he will be unable to procure other food, and the also very real chance that his theft will be discovered, Dick faces a dilemma which has no clear resolution. One important further observation must be made. Supposing that Dick is permitted neither to steal the food nor to refrain from stealing it, still he is surely permitted to accept a gift of clothing for his children. Just because there is some act which an agent is permitted neither to do nor to leave undone does not imply that the same agent is permitted to do nothing. AFORMALLANGUAGEFORPERMISSION

To simplify matters, I do not attempt to provide a semantics for moral pronouncements in English. Instead, I develop a formal language which includes devices playing roles similar to those played by such English words as ‘permitted’ and ‘may’ in the normative sensediscussed above. Since we are interested in the relationship between permission on the one hand and obligation, possibility and necessity on the other, this language also includes devices which correspond to the English words

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‘obliged’ and ‘must’ in the normative sense, to ‘possibly’ and ‘necessarily’, and to ‘may’ and ‘must’ in the alethic senses.I offer suggestions about how English sentences may be translated into this formal language, but there will be well-formed formulae in the formal language which do not correspond in a comfortable way to any English sentence which is likely to occur in any real conversation, and the converse may also be true. The goal of the enterprise, nevertheless, is to provide a formal language and a semantics for that language which elucidates a common core of meaning underlying the use of normative language by ordinary English speakers and, presumably, by many other persons as well. I assume that particular persons are permitted or obliged to do particular things at particular times. Consequently, our formal language relativizes moral pronouncements to persons and times. Since only a sentential language is offered, it is impossible to represent universal moral principles within this language. It should be possible to represent such principles in a quantified version of this language, but that task is left for another time. To begin, our language includes a countably infinite set of sentential variablesp, 4, r, . . . and the truth-functional connectives -, A, v, 3, and z, i.e., the symbols of classical sentential logic. In addition, the language includes countably many names k, rn, n, . . . . for moral agents and countably many names t, t’, t”, . . . for times. Finally, we need a necessity operator 0, a permission operator P and an obligation operator 0. I use the letters A, B, C, . . . as variables which range over the well-formed fomulae of this language. Every one-place sequence whose only member is a sentential variable is a well-formed formula and where A and B are wffs, k is a name for an agent, and t is a name for a time, -A, (A A B), (A vB), (A 3 B), (A - B), WI, (Pkt)A and (Ok+4 are wffs. (I will routinely omit the outermost set of parentheses.) The intended interpretation of this formal language is that the sentential variables stand for simple English sentences. Then (Pkt)A corresponds roughly to the pseudo-English sentence ‘k is permitted at time r to cause or to allow it to come about that A is the case’. Suppose that A corresponds to the English sentence ‘John buys a new car on his twentieth birthday’, that k is a name for John, and that t is a,name for John’s twentieth birthday. Then we can render (Pkt)A more colloquially as ‘John is permitted on his twentieth birthday to buy a new car then’ or as ‘John may on his twentieth birthday buy a new car then’. (0kt)A corresponds to the

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pseudo-English ‘k has an obligation at t .to see to it that A’, or in the case of our previous example, ‘John is obligated on his twentieth birthday to buy a new car then’. Where A makes no reference to an agent named by k or to a time named by t, (Pkt)A and (Ok@4 may or may not have a comfortable English counterpart. Suppose Mary is John’s sister and A corresponds to ‘The registrar receivesMary’s tuition by noon Thursday’ and t is a name for Tuesday. If John promises Mary on Monday to deliver her tuition to the registrar by noon Thursday, then (Ok&4 is true, i.e., John has an obligation on Tuesday to see to it that the registrar receives Mary’s tuition by noon Thursday. Of course, obligations may change with time. Suppose B is the sentence ‘John leaves campus all day Friday’, and suppose John promises Mary on Tuesday that he will go with her to the freshman orientation on Friday. Then - (Pkt)B is true. But now suppose t’ is a name for Wednesday and that on Wednesday the freshman orientation is cancelled. Then (Pkt’)B is true. In other words, it is permitted on Wednesday that John leave campus on Friday, but this was not permitted to John on Tuesday. One reason careful translation of the formulae of our formal language into English produces at least mildly strange sounding results is that we do not usually explicitly indicate in ordinary discourse this temporal dimension of permission and obligation. WEAKPERMISSION

The familiar approach to a formal semantics for normative concepts elucidates these concepts in terms of a set of possible worlds which represent situations which are in some sense normatively acceptable. This same approach is used here although the way in which the deontically acceptable worlds are used in the truth conditions for the formulae of our formal language is different from the way they are used by other authors. Here I take the notion of a possible world to be primitive. I make no attempt to determine which worlds do and which do not represent normatively acceptable alternatives since this is the task of a normative theory. My goal is to explore those relations among normative concepts which are common to a wide range of ethical theories and the relation of these concepts to the set of normatively acceptable worlds a particular moral view determines. Let us examine the problems which arise for a more or less standard possible worlds treatment of normative concepts.

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The first items we need for an interpretation of our formal language are a set IV of possible worlds, a set A of agents, and a set T of times. Let us suppose we have a function [ ] which assignsto each wff A the set [A ] of those worlds in IV at which A is true. We know that we want [-A] to be IV- [A], that we want [A A B] to be the intersection of [A] and [B], and so on for the other truth functional connectives. (I am assuming that all our wffs represent Quinean eternal sentences and thus that we do not need to relativize truth conditions to times as well as to possible worlds.) To keep things simple, we let [nA] = W if [A] = W, and otherwise we let [OA] = 0. Thus, q A is true at a world w if and only ifA is true at every world. Let us also assume that [ ] assignsto each agent name k a member [k] ofA and to each time name t a member [t] of T. What we seek are restrictions on the function [ ] which will help us understand the logical properties of our permission operator P and our obligation operator 0. The assumption built into our formal language is that the deontically acceptable worlds may be different for different persons at different times and in different situations. We can represent this assumption in our developing model theory with a function d which assignsto each agent a, time s and possible world w a set d(u, s, w) of possible worlds. The intended interpretation, of course, is that d(a, s, w) is the set of exactly those worlds which are normatively acceptable for the agent a in the situation determined by s and w. The familiar approach to semantics for normative concepts tells us that [(Pkt)A] is the set of exactly those worlds w such that some member of d[(k], [t], w) is also a member of [A], i.e., those worlds where some world which is normatively acceptable to the agent named by k at the time named by t is a world where A is true. Furthermore, [(Okt)A] is the set of worlds w such that every member of d( [k], [t], w) is a member of [A], i.e., those worlds where A is true in all deontically acceptable worlds for the agent named by k at the time named by t. According to such a theory, (Pkt)A is equivalent to N (Okt) -A. This account may fairly represent a familiar notion of obligation, but there is a common senseof permission which is not reducible to obligation of this kind. There is nothing in this formal semantics which represents the role uncertainty about the future plays in moral deliberation. Consider again the case of Tom and the fire hydrant. There are many possible worlds which, for all Tom knows, might come about through Tom’s actions and

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other events beyond his control. Many of these are worlds in which this particular fire hydrant will not be needed during the time Tom’s car would be parked beside it. Suppose that a world is deonticahy acceptable for Tom at the time of his dilemma just in case it is a world in which Tom’s actions do not interfere with the efforts of the fire department to perform its customary function. Any world in which Tom parks his car beside the hydrant and the hydrant is not needed is such a world, so there is a world where Tom parks beside the hydrant that is deontically acceptable for Tom. We con&de, on the basis of the semantics under consideration and contrary to intuition, that Tom is permitted to park beside the hydrant. We might try to solve the problem by fmt and say that only worlds in which Tom does not park beside fire hydrants are deontically acceptable for him. But this is an ad hoc adjustment to accommodate the conclusion of our moral reasoning while obscuring the reasons leading us to this conclusion. A formal semantics which reflects this essential element of moral reasoning must be superior to one which does not, and the semantics we are considering clearly does not. Neither does this analysis leave room for moral dilemmas of even the most practical sort. Consider again the case of Dick. The only way that a world w could fail to be a member of either [(Pkt)A] or [(Pkt) -A], where k is a name for Dick, t is the time of his choice, and A is the sentence ‘Dick steals food for his family’, is if d([k], It], w) is empty, for if there is a member w’ of d( [k], [t], w) then w’ is a member of [A] or w’ is a member of [-A]. But if d( [k], [t], w) is empty, then neither is Dick permitted to acci;pt a gift of clothing for his family in w since, where B is the sentence ‘Dick accepts a gift of clothing for his family’, there is also no member of d( [k], [t], w) which belongs to [S]. This, however, contradicts the intuition that there may be casesin which, due to uncertainty about the future, a person is neither permitted to perform nor to withhold from performing some specific act, and yet not all his moral obligations or permissions are nullified. Another problem for this kind of semantics involves permissions expressed in sentences like ‘Alice may buy a new coat or a new hat’. Normally we would infer from a statement made with this sentence that either disjunct was permitted, i.e., that both ‘Alice may buy a new coat’ and ‘Alice may buy a new hat’ are true. Our example, like many others, implies the principle that from a wff like (Pkt) (A v B) we should be

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allowed to infer both (Z’Q4 and (Pkt)B. We might call this principles Simplification of Disjunctive Permissions, or SDP for short. On the semantics for normative concepts which we have been considering, SDP is an unmitigated catastrophe. By simple and familiar arguments, such a semantics makes (Pkt$4 3 (Pkt)B valid for any A and B whatsoever. Notice that SDP is not without its exceptions. Moving from the moral to the legal arena for a moment, suppose that every tax payer is entitled to stash some of his income into a Tax Sheltered Annuity (TSA) or into an Individual Retirement Account (IRA), that no tax payer is entitled to use both, and that the circumstances of the individual tax payer determine which shelter he is allowed to use. Then I might advise a friend, “You may put your royalties into a TSA or put them into an IRA and defer the taxes until later. You should talk to your accountant”. In this case I surely do not mean for my friend to infer either that he can put his money into a TSA or that he can put his money into an IRA. An analysis of the basic structure of normative concepts has the sticky problem of accounting in some way both for the strong tendency to simplify disjunctive permissions and the fact that such simplification is sometimes inappropriate. The present account can do neither. STRONG

PERMISSION

The formal semantics of the previous section offered a weak notion of permission, In contrast, a very strong notion of permission can be developed by defining deontic operators in terms of sentential constants representing sanctions of some sort.’ Authors who take this approach recognize that permission requires more than the mere possibility that one may be able to act in a certain way without incurring sanction. Their suggestion is that permission involves the much stronger requirement that in order for some act to be permitted, the performance of that act must be a sufficient condition for avoiding sanction. Von Wright [lo] provides a definition of a-permission operator in terms of a necessity operator o which has as its logic at least an extension of the modal system Kr. First, we define a possibility operator 0 by stipulating that OA is equivalent to - o - A. Next, we need a sentential constant representing the appropriate sanction. This sanction need not be actual punishment, but might be liability under the law, liability to public censure,

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or even something less concrete than these. For our language, which relativizes normative sentences to agents and times, we will need a sentential constant Skt for each agent name k and each time name t. Adapting von Wright’s definition to the circumstances of our formal language, the result is (1)

(Pk@i 5 [o(A 3 - S/u) A OA A OW].

Two undesirable consequences of this analysis are (2)

and

(3)

(a%t

A A)

> -

(pkt)A

.

The first of these two theses is obviously unintuitive. The second says that once an agent incurs sanction, then nothing the agent ever did or will do is permitted at that time. This implies, for example, that for an agent who makes restitution to someone he or she has incurred sanction for wronging, such restitution is not permitted at the time the wrong is committed. While our first analysis of permission was entirely too weak, this analysis is much too strong. In effect, the requirement of this analysis is that for an agent to be permitted at any time to cause or allow A to come about, the truth of A must guarantee that the agent avoids moral (legal, etc.) sanction at that time no matter what else happens. In a way, this does force consideration of future contingencies, but it must surely be very rare that any agent is ever allowed to do anything in this sense. Hilpinen [3] proposes a strong concept of permission similar to von Wright’s, but Hilpinen interprets the notion of a sufficient condition for avoiding sanction in terms of a conditional with a weaker logic than that of strict implication. To consider Hilpinen’s proposal, we must add a dyadic conditional operator > to our formal language. The permission operator P is then a defined operator for Hilpinen. Adapting Hilpinen’s definition to our formal language, it looks like this:

(4)

(Pkf)bi= [(A >-skt)

A

OAAO%t].

A primary reason for replacing strict implication in (1) with some weaker conditional is that by doing so we avoid a result like (2). Equation (2) follows from the fact that even weak modal logics contain the following principle of weakening antecedents:

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O(A 3B)>o[(AAc)~B]. For HiIpinen to avoid this problem, he must provide a logic and a semantics for conditionals which does not contain a principle corresponding to (5). A number of such logics have been developed. (See Nute [9] for a discussion of some of the better known analyses of this sort.) Hilpinen completes his account of permission and avoids results like (2) by developing a conditional logic which resembles the system VC in Lewis [4].3 While this tactic is successful in avoiding (2) we cannot avoid (3) if we provide an interpretation for > which is adequate for an analysis of conditionals for which detachment is reliable. Consider a semantics for conditionals simpler than Hilpinen’s but which incorporates many of the important features of his semantics. The models for our new formal language with the conditional operator > are ordered quintuples ( W, A, T, f, [ ] >,where W is a set of worlds, A a set of agents, T a set of times, and [ ] an interpretation function for our language, just as in our earlier semantics. f is a selection function which assignsto each subset K of W and each member w of W a subset f(K, w) of K. The basic idea behind the interpretation of conditionals is that in evaluating a conditional A > B we consider all worlds enough like the actual world, at all of which,4 is true.4 If there are no such worlds, or if all such worlds are also worlds at which B is true, then the conditional is true; otherwise, it is false. Generalizing from the case of the actual world, A > B is true at world w (i.e., w is a member of [A >B]) just in casef([A], w) is contained in [B], for f( [A], w) is just the set of those worlds which we would consider in evaluating a conditional with A as antecedent if w were the actual world. We get rather different conditional logics depending on the restrictions we place on our selection functions. Of course we want f(K w) to be a subset of K since we want f([A], w) to be contained in [A]. When we consider what would happen if A were true, we obviously consider only worlds at which A is true. Another restriction which is widely accepted is (6)

If w is a,member of K, then w is a member ofj(K,

w).

Certainly ifA is true, than we must consider the actual world in determining what would happen if A were true. Condition (6) guarantees this. Practically all authors suggest additional restrictions for selection functions,

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but this is enough to see a fundamental flaw in this treatment of permission. Accepting (6) as Hilpinen does, commits us to the thesis (7)

(A A Skf) 3 - (A > - Sb).

But (7) together with (4) entails the objectionable thesis (3). We are once again plagued by (3) because we have adopted the restriction (6) for the selection function we use to interpret conditionals. Surely (6) is proper for an analysis of ordinary conditionals, but in analysing permission we must place an additional restriction upon our selection function, a restriction which the actual world may very well not satisfy. The worlds we should consider in deciding whether or not (PI@4 is true are not all those worlds at which A is true and which are very much like the actual world, but only those worlds which in addition to this are also worlds in which the agent named by k does everything he can do from the time named by t onward, compatible with A’s being true, to insure that some world which is normatively acceptable for that agent at that time is actualized. The problem we have encountered is not one which arises because of our choice of a selection function semantics for conditionals. We cannot reduce any interesting notion of permission to conditionals no matter how we interpret conditionals. What (6) guarantees, and what the unwanted thesis (3) really depends on, is a principle of detachment for conditionals which allows us to infer B from A and A > B. Since a principle or rule of detachment may be the one incontestable feature shared by all conditionals, rejection of (3) is tantamount to rejection of every analysis of permission developed along the lines suggested by von Wright or Hilpinen. MODERATEPERMISSION

Despite the difficulties we have uncovered, the work of von Wright and Hilpinen points in the right direction. We can provide a selection function semantics for a moderately strong concept of permission which will avoid these difficulties and will capture a quite ordinary and useful notion of permission. We must simply recognize that the selection function used to interpret permission is not the same selection function we use to interpret ordinary conditionals. Since conditionals will not play any role in the rest of this discussion, let’s retreat to our original formal language whose only primitive symbols

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in addition to those of sentential logic are the names for agents and times, the necessity operator o and the deontic operators P and 0. Models for this language will be ordered hextuples (IV, A, T, d, g, [ ] >where W, A, T, d and [ ] are as before. We will take g to be a selection function which assignsto each subset K of W, member a of A, member s of T and member w of IV a subset g(K, a, s, w) of K, but we do not assume that g satisfies a condition like (6). Indeed, our only initial assumption about g is that g(K, a,. s, w) is a subset of K. Truth conditions for the truth-functional connectives, for modal sentences and for the deontic operator 0 are as before. Our intuitive understanding of permission now is that (Pkt)A is true just in case every world which is similar enough to the actual world in which A is true and in which the agent named by k does everything he can, compatible with A being true, from the time named by t onward to insure that some world normatively acceptable for that agent at that time is actualized, is in fact a world which is normatively acceptable for that agent at that time. This is insured in our model theory by requiring that w is a member of [(Pkt)A] if and only ifg([A], [k], [t], w) is both non-empty and contained in d( [k], [t], w). (Reasons for requiring nonemptiness are given below.) Unless we impose some additional restrictions on g, we are not forced by this analysis to accept either (2) or (3). Moderate permission better captures the way in which we talk about permission when we consider the dilemmas of real moral agents and uncertainty about the future. Recall the example of Tom and the fire hydrant. Since there will probably be no fire during the time Tom’s car would be parked beside the hydrant, it looks as if Tom might be weakly permitted to park beside the hydrant. But there is also a chance that there will be a fire, and until and unless it becomes implausible (for Tom) that there might be a fire, it is not permissible for Tom to park beside the hydrant. The operative notion is clearly one of moderate permission in the sensewe have just clarified. Consider also the case of Dick. In some plausible situations in which he steals food for his family, he is caught and imprisoned and his family starves. Since no world in which Dick allows his family to starve is normatively acceptable for Dick, he is not permitted to steal the food. On the other hand, some plausible situations in which he does not steal the food are situations in which he is unable to procure other food by honest means and thus his family starves. Therefore he is not permitted not to steal the

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food. Model theoretically at least, where A is the sentence ‘Dick steals the food at t’ and B is the sentence ‘Dick accepts a gift of clothing for his family at t’, it is possible that neither g( [A], [k], [t], w) nor g([- A], [k], [t], w) is contained in d([k], [t], w), whileg([B], [k], [t], w) is contained in d( [k], [t], w). Without further restrictions on g, then, our model theory allows for the possibility that - (Pkt)A, - (Pkt) --A, and (Pkt)B are all true at w. Unfortunately, this technical possibility does not fit as well as we might like with the intended interpretation for the deontic selection function g. Unless a better intuitive understanding of g can be achieved, this will be a weak point in the theory. Nevertheless, the technical possibilty that such a set of sentences can all be true is an improvement over the weak conception of permission. This semantics has some interesting consequences. Most obvious is that all theses of the modal system S5 are valid in our models, and validity is preserved by the rule of necessitation: from A to infer qA . Other theses are: (8)

qA 3 (Okt)A,

(9)

(Okt) (A 1 B) 1 [(Okt)A 1 (Okt)B],

(10)

[(Ok@4 A (Ok@]

(11)

(Pkt)A > OA,

1 (Okt) (A A B),

and (12)

(Pkt)A 3 - (Okt) -A.

We do not have the converse of (12). Remember that our operator 0 has the same semantics as that found in the most familiar systems of deontic logic. The thesis (8) may seem strange, but it is at worst a harmless anomaly. Additional theses we might include are: (13)

(0kt)A 3 OA,

(14)

(Ok&4 > (Pkt)A,

and (15)

[(Pkt)A A (Pkt)B] > (Pkt) (A vB).

We can guarantee (13) by imposing the condition:

182 (16)

DONALDNUTE d(a, s, w) is not empty.

One way to insure (14) is through the restriction:

(17)

If d(a, s, w) is contained in K, theng(K, a, s, .w) = @a, s, w).

Either of these two theses raise problems if we wish to maintain the possibility of real moral dilemmas. I am aware of no problem with Thesis (15) which will be valid in every model satisfying: (18)

g(K UK’, a, s, w) C g(K, a, s, w) U g(K’, a, s, w).

The converse of (15) is our troublesome SDP. We might ask whether we really want (1 l), since there seems to be no moral problem in allowing people to do what they can’t do in any case. We could avoid (11) by dropping the condition for the truth of (pkt).4 atw thatHAl, PI, [tl, w ) is non-empty, but this would raise problems. Suppose that for agent a at time s bringing about A is entirely implausible though not logically impossible. This might be because bringing about A is a physical impossibility. For example, A might be ‘k pushes over a building full of people with her bare hands at t', where k is a name for a and t is a name for s. We could argue that g( [A], a, s, w) is empty since no one could bring A about, but we shouldn’t conclude from this that a is permitted to bring about A. We can arbitrarily make (Pkt)A either true or false atw where N-41, M [tl, w 1is empty, but caseslike this are a reason for making it false. We also do not want the permission-correlate of (10) since, for example, one may be permitted to pledge a piece of property to either of two charities, but surely one is not permitted to pledge the property to both charities. Nor do we want the permission-correlate for the converse of (lo), since it might be permitted to allow A A B to come about where B is really beyond our control, when it would not be permitted to allow A to come about in the absence of B. For example, it might be permitted for John to receive a large gift of money and to buy a new car, but it might not be permitted for John to buy a new car (without the gift). If we add as axiom schemata the theses (8)-( 15) to the modal logic S5, we produce a deontic logic which is easily shown to be sound with respect to the class of models satisfying (17) and (18). Since it is not difficult to construct such models, and since no contradiction is valid in such models, it is also easy to show that this deontic logic is consistent. This means that

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weaker and, to my way of thinking, more attractive deontic logics, such as a logic which contains neither (13) nor (14), are also consistent. Completeness is more difficult to prove, and my initial attempts to establish if have been unsuccessful.’ DISJUNCTIVE

PERMISSIONS

One reason mentioned earlier for developing a new analysis of permission is our perplexity over the thesis: (SW

(Pfq (A vi?) 3 ((Pi+4 A (my?).

How do we reflect the intuitive support for SDP without endorsing (PkQ4 > (pk?)B or some equally undesirable result? Hilpinen attempts to reduce the problem of disjunctive permissions to another problem, that of disjunctive antecedents. We get something like SDP if we accept Hilpinen’s analysis of permission and the following principle for Simplifying Disjunctive Antecedents: (SW

[(A VB)> cl ’ u > c) A(B> a*

But when we add SDA to most of the conditional logics which can be found in the literature, we wind up with a principle for weakening antecedents which is the conditional counterpart of (5). This will not work since it would once again commit us to the unwanted thesis (2). While there are many caseswhere we should want to apply both SDP and SDA in ordinary discourse, there are also caseswhere these two principles are not acceptable. Besides the example of the tax shelters mentined earlier, Hilpinen offers examples in which SDP is not appropriate, and examples in which SDA in inapplicable are discussed in my [8]. Hilpinen proposes to solve both difficulties by developing a complex conditional language within which two different ways are provided for symbolizing ordinary English conditionals with disjunctive antecedents. One of these symbolizations is subject to a rule for simplying disjunctive antecedents after the manner of SDA while the other is not. I call proposals like Hilpinen’s translation lore proposals since they all involve translating ordinary conditionals with apparently disjunctive antecedents into a formal language for conditionals in two different ways. Obviously, Hilpinen is also proposing a translation lore solution to the problem of disjunctive

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permissions. Translation lore solutions to the problem of disjunctive antecedents (or to the problem of disjunctive permissions) beg the question. They eliminate the problems which arise in our formal conditional (or deontic) logic, but we are left with the problem of deciding which ordinary language conditionals (or permissions) are to be symbolized in which way.6 I have suggested an answer to the problem of disjunctive antecedents in [8], and I will not repeat the details here. I reject the idea that we can define any interesting notion of permission in terms of ordinary conditionals, but we use selection functions in the interpretation of both conditionals and moderate permission and we can develop a solution for disjunctive permissions which resembles my solution to the problem of disjunctive antecedents. We begin by rejecting SDP. The intuitions which guided the development of our formal semantics support this decision. In order for (Pkt) (A vB) to be true, every world enough like the actual world at which A vB is true and in which our agent does everything he can, compatible with the truth of A v B, to accomplish one of those worlds which are deontically acceptable for him at that time, must be such a deontically acceptable world. One of the things an agent can do to achieve this goal is to pay attention to the way in which he brings it about that A vB is true. What the agent must do is bring it about that A is true and B is not when B is not permitted but A is. This case is very similar to many other caseswhich do not involve disjunction. Suppose, for example, that our agent is permitted to close a certain door. This may be true even though the agent is also absolutely prohibited from slamming the door. There is nothing counterintuitive about this. Similarly, in the previous case, the agent must bring it about that A v B without bringing it about that B. Yet we are inclined to use SDP in our moral reasoning. When we hear and evaluate a’disjunctive permission, we tend to consider for each disjunct the worlds enough like the actual world at which that disjunct is true and in which the agent does all he can, compatible with the truth of that disjunct, to produce a deontically acceptable world. Instead of considering whether every member of g(A v B, w) is deontically acceptable, where w is the actual world, we consider whether every member of either g(A, w) or g(B, w) is deontically acceptable. Because we tend to interpret disjunctive permissions in this way when we hear them, we also refrain from asserting a disjunctive permission unless both disjuncts are permitted. We

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are inclined to accept the following restriction on our selection function for interpreting moderate permission: (26)

g(A VB, w) =g(A, w) Ug(B, w).

When our selection function satisfies (26) for any two propositions A and B, we say that our selection function is standard for A and B. Although we tend to standardize our selection functions, we do not always do so, as is shown by the kinds of counterexamples mentioned earlier. in the course of a conversation, we adopt more and more restrictions on the selection functions we use to interpret both conditionals and permission statements. For the most part, these restrictions are added as we tacitly come to agree more completely with our interlocutors about what worlds will count as being sufficiently like the actual world to warrant consideration in our evaluations of conditionals and permission statements. These restrictions on selection functions affect the acceptability of statements and other utterances made at later stages of the same conversation, although they may have no affect on statements made later in a different conversation. These restrictions on selection functions are components of what David Lewis has called conversational score, a set of tacitly accepted parameters of acceptability which evolve in an at least partly rule-governed manner during the course of a conversation or other linguistic exchange.’ Certain of the rules which govern the evolution of conversational score are rules of accommodation. Lewis gives us the general form which such rules take: (27)

If at time t something is said that requires component s of conversational score to have a value in the range r if what is said is to be true, or otherwise acceptable; and ifs does not have a value in the range r just before t; and if such-andsuch further conditions hold; then at t the score-component s takes some value in the range r. ([ 51, p. 347).

In other words, we give a speaker a sympathetic reading by adjusting the tacit parameters which make up the conversational score, in such a way as to accommodate the speaker’s utterance whenever we can plausibly do so. In the case of permission statements, this means that we restrict our selection function in such a way as to make the speaker’s claim acceptable.

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Counterbalancing this tendency to accommodate the speaker, however, is our inclination to standardize selection functions. Somehow both of these features of the manner in which we understand permission statements must be incorporated into an account of the pragmatics of permission. I suggest that our rule of accommodation for permission should take the following form: (28)

If at time I a sentence of the form (Pkt)A is uttered that requires that we restrict the selection function g in a certain way if the sentence is to be true; and if a restriction on g of the required sort has not been adopted prior to t; and if a restriction of the required sort is available and plausible which does not conflict with any of the restrictions adopted for g prior to t; then at time t, g is to be restricted in the required manner.

In most and perhaps in all possible situations there will be certain restrictions on our selection functions which I am completely unwilling to make. These at least are implausible for me, but there is also a range of possibilities which I tend to discount but about which I may be somewhat flexible. To accommodate ‘You may both stay and not stay’, I would have to admit that there is a world in which I both stay and do not stay. But I will not admit this since it violates my basic conception of what a possible world is. To accommodate ‘You may slay your friend’, I would have to agree that there is a world which is deontically acceptable for me in which I slay my friend. In its own way, this requirement is at least as absurd, and is even more repugnant, than the requirement that I just rejected. Presumably, my deontic acceptability function d is determined by my basic principles of morality and I do not change it merely in order to accommodate the utterances of others. My selection function g for permission, on the other hand, is determined in part by what courses I believe events might really take as opposed to scenarios which I can imagine but which I discount as too unlikely for serious consideration. I might make concessions here to accommodate the utterances of another, agreeing to consider such situations even though I think they have no real chance of coming about. While (28) provides an accommodation rule for permission, it does not address the problem of disjunctive permissions. To do this, we need to

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impose a further restriction upon our accommodation rule. The following restriction serves our purposes: (2%

Any restriction on g adopted through an application of (28) to a sentence of the form (pkt) (A v@ must insure that g be standard for A and B unless there is no restriction on g satisfying the conditions for (28) which does insure that g be standard for A and B.

It is the pragmatic restriction (29) which guarantees that we will be able to simplify disjunctive permissions in all but two sorts of case. The first exception is where the prior, present or immediately subsequent course of the conversation precludes such simplification. (Remember from examples mentioned above that we often qualify a disjunctive permission in the utterance immediately following it.)s The other exception is where one or the other of A and B is not possible. In this case,g is still standard for A and B, but another condition for the truth of (P&&4 or (P/c+? is not satisfied. The notion of conversational score provides a formal device mirroring our practice of keeping track of what has gone on in previous stages of a conversation so that we may determine at a given stage whether we can simplify a particular disjunctive permission. We could use the information provided by the conversational score to answer the question left unanswered by translation lore approaches to the problem of disjunctive permissions, i.e., to decide in which of two possible ways an apparently disjunctive permission couched in ordinary language is to be symbolized in our formal language. But once we have taken note of the role that conversational score plays in our moral discourse, we no longer need to find a solution to the problem of disjunctive permissions within our formal calculus. The problem has been solved at the pragmatic level before we even translate our permission statements into the formal language of our deontic logic. Both SDP and SDA can be treated as what we might call rules of pragmatic entailment rather than as theorems of our formal calculus. NOTES ’ Portions of this material were presented to the Georgia Philosophical Society in November of 1980, to the American Philosophical Association in April of 1981,

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to the Department of Philosophy, University of North Carolina at Chapel Hi& in April 1981, and to the Institute for Philosophy, Psychology, and Methodology, University of Turku, Finland, in October of 1982. I am grateful for the helpful comments of Anthony Anderson, Risto Hilpinen, Larry Thomas, Ray Jennings, and the editor and a referee for this journal. * Perhaps the earliest example of a reduction of this kind is in Anderson [ 11. Anderson’s system is equivalent to one of the sort discussed in the previous section, and hence it involves a weak concept of permission. Proponents of strong concepts of permission actually use a propositional constant which indicates immunity to sanction. (See Hilpinen [ 31 and von Wright [lo].) I have modified their accounts to comply with Anderson%. ’ Hilpinen’s logic has a more complex language, axiomatization, and interpretation than Lewis’s VC. This increased complexity is needed for Hilpinen’s solution for the problem of disjunctive permission which is discussed briefly in the last section of this paper. Nevertheless, Hilpinen’s logic is, in a familiar sense, a modest extension of Lewis’s VC. 4 The notion of what is required for one world to be “enough like” or “similar enough to” another for the purposes of such an analysis as this is highly problematic. For a discussion of some of the issues, see my [8] and [ 91. A nice discussion of some of these problems in deontic contexts can be found in DeCew [ 21. ’ We can introduce the weak notion of permission into our logic even though we prefer the moderate notion for representing all or most English permission statements. We can also introduce a weak notion of obligation. These would be defined by (1%

(P’kt) = - (Okt) -A

(20)

(O’kr)

and = .-. (Pkt)

- A.

Two immediate consequences in the deontic logic including (8)~(15) are

c-m

(Pkr)A 3 (Pk&i

(22)

(Okt)A 3 (O’koA.

and

We also get

(23)

(P’kt)A

v (P’kt)

(24)

q

-A

3 (0’kt)A.

- A.

Thesis (23) is objectionable to those moral theorists who insist that moral conflicts which are in principle irresolvable are possible. Thesis (24) is so peculiar that it suggests we use something other than (20) to define weak obligation. More suitable might be

(25)

(0’kr)A

= (oA h - (Pkt)

-A).

This is still strong enough to get (22). 6 Others who have proposed translation lore solutions to the problem of disjunctive

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antecedents include Loewer [6] and McKay and van Inwagen [ 7 1. Warmbrod [ 111 presents a translation lore solution to the problem of disjunctive antecedents which may be immune to these criticisms. ’ In [ 81 I maintained that it was the selection function itself which was a component of conversational score and that we replaced the selection function in use with a new one from time to time in the course of a conversation. Instead, we probably never have in mind a completely specified selection function, but we reach increasingly greater agreement about specific restrictions which any selection function employed in interpreting statements made during the conversation must satisfy. It is this set of restrictions which is a component of conversational score. ’ We may also change our minds in the course of a conversation about the way in which we wish to restrict g and d, but to signal such a change requires special measures. Having said, “You ought to bring about A”, it is not sufficient to indicate a change of heart by later saying, “You may refrain from bringing about A .” If we made two such statements in the same conversation, we could rightly be accused of contradiction (or at least of equivocation). We might, however, say, “I made a mistake. You may after all refrain from bringing about A.” We might also say that not bringing about A is permitted once we have rescinded some other condition upon which the claim that bringing about A is obligatory was founded. But we can’t expect even the most sympathetic of listeners to accommodate us when we casually utter the contradictory of some sentence uttered previously. We need to make such revisions explicit and we cannot expect to accomplish them through application of accommodation rules of the usual sort.

REFERENCES [l] [ 21 [3]

[4] [S] [6] [ 71 [ 81 [9 ] [lo]

A. R. Anderson., ‘The formal analysis of normative systems’, in N. Rescher (ed.), The Logic of Decision and Action, university of Pittsburgh (1966). J. W. DeCew, ‘Conditional obligation and counterfactuals’, J. Philosophical Logic 10 (1981), 55-72. R. Hilpinen, ‘Disjunctive permissions and conditionals with disjunctive antecedents’, in Ilkka Niiniluoto and Esa Saarinen (eds.), Intentional Logic Theory and Applications, Acta Philosophica Fennica, Vol. 35, Societas Philosophica Fenmca, Helsinki (1982), pp. 175-194. D. Lewis, Cbunterfactuals, Harvard University Press (1973). D. Lewis, ‘Scorekeeping in a language game’, J. Philosophical Logic 8 (1979), 339-359. B. Loewer, ‘Counterfactuals with disjunctive antecedents’, The Journal of Philosophy 73 (1976), 531-536. T. McKay and P. van Inwagen, ‘Counterfactuals with disjunctive antecedents’, Philosophical Studies 31 (1977), 353-356. D. Nute, ‘Conversational scorekeeplng and conditionals’, J. Philosophical Logic 9 (1980), 153-166. D. Nute, Topics in Conditional Logic, D. Reidel, Dordrecht (1980). G. H. von Wright, ‘Deontic logic and the theory of conditions’, in R. Hilpinen (ed.), Deontic Logic: Introductory and Systematic Readings, D. Reidel, Dordrecht (1970), 159-177.

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K. Warmbrod, ‘Counterfactuals and substitution of equivalent antecedents’, J. Philosophical Logic 10 (1981), 267-289.

Department of Philosophy, University of Ceolgia, Athens, GA 30602, U.S.A.