CONDITIONAL PERMISSION IN DEONTIC LOGIC

27

Ernest Nagel, The Structure of Science (New York: Harcourt, Brace, 1961 ). Ibid., pp. 49-50. Ibid., pp. 51-52. 5Ibid., pp. 56-67. Ibid., p. 72. 7 "Laws and Counterfactuals," p. 41. 8 Ibid., p. 42. Ibid.

1oIndeed, in most if not all cases that would come under consideration in the justification of counterfactuals,and certainly in all cases used for illustration by Nagel or Krimerman, the availabilityof a suitable law and of suitable true premises describingthe requisite initial conditions would constitute conclusive evidence for the existence of the required valid argument, for the validity of the argument is then decidable. 11 T h e Structure of Science, pp. 47-48. 12 Ibid., p. 66. 1~"Laws and Counteffactuals," p. 43. ~ Ibid., pp. 43-44.

Further Diffculties for Conditional Permission in Deontic Logic by J O H N ROBISON UNIVERSITY OF PITTSBURGH IN A series of papers between 1958 and 1962, Professors Reseher and Anderson discussed the status of the following proposition, one of the axioms in a set of seven proposed by Reseher for a system of deontie logic based on the notion of conditional permission: (i) {P(p/e) & P(q/e&p) } ~ P(p&q/c).1 Anderson pointed out that this axiom, together with certain other principles accepted by Rescher, yields the result that a contradiction, under suitable circumstances, might be permitted, in which case anything at' all would be permitted under those circumstances, a consequence acceptable to neither Rescher nor Anderson. Accordingly, Reseher proposed to remedy the situation by replacing (1) with (2) {P(p/c) & P(q/c&p) & ~) (p&q) } ~ P(p&q/e). My present purpose is to suggest that unwelcome results are still derivable, even with this modification. Let me begin by making what I take to be two noncontroversial, but important, observations. First, we cannot infer from a person's being permitted

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to do a certain act that he ever does the act; second, an act may be conditionally permitted on some other act in (at least) two quite different ways: the condition being, on the one hand, that this second act actually be done and, on the other hand, simply that this second act be permitted. For example, the normal condition for a citizen's being permitted to vote for the candidate of his choice is that the prospective voter has actually performed, and not merely been permitted to perform, some second act, viz., registering to vote in the election. In other words, on condition that one has, so to speak, actually exercised or taken advantage of the permission to register, one is permitted to vote. On the other hand, states normally have a policy of permitting visitors from other states to operate an automobile on condition that the visitor is a properly licensed operator for the current year in his own state, regardless of whether or not he has in fact taken advantage of this permission to drive during the current year. A licensed tourist from Maine, for example, is permitted to drive in Pennsylvania, it being sufficient that he is permitted by his resident state to drive, regardless of whether or not he has actually exercised this permission and driven there during the current year. With these points in mind, we may now turn to a second of Rescher's axioms,

(3)

(p-~ q)-+ {P(p/c) -+ P(q/c) },

from which is derivable as a theorem (4) P(p&q/c) ---> {P(p/c) & P(q/c)}. This, together with the axiom cited in (2) above, yields (5) {P(p/c) & V(q/e&v) & O (v&q) }-> (P(p/c) &P(q/c)}. Thus, if doing p is permitted to persons in circumstance c, and doing q is permitted to persons in circumstance c who have done or are doing p, it being possible to do both p and q, then doing p is permitted to persons in circumstance c and also doing q is permitted to persons in circumstance c. In view of the two points earlier noted, it would seem that (5) admits of a vitiating interpretation. For example, suppose that students in the honors program are permitted, but not required, to take a certain course, Philosophy 1; further, that a second course, Philosophy 2, is open only to those students in the honors program who have in fact taken, or are taking, Philosophy I. Now, according to (5), we would have the following: if a student is permitted to take Philosophy 1, on condition that he is in the honors program, and permitted to take Philosophy 2, on condition that he is both in the honors program and has taken, or is taking, Philosophy 1, it being possible, of course, to take both courses, then a student is permitted to take Philosophy

CONDITIONAL PERMISSION IN DEONTIC LOGIC

29

17 on condition that he is in the honors program, and also permitted to take Philosophy 2 on this same condition, viz., that he is in the honors program. But in our example, of course, it is false that a student is permitted to take Philosophy 2, on condition of being in the honors program, the condition rather being that he is in the honors program and has in fact taken, or is taking, Philosophy 1. Perhaps the reason for such unwelcome results as this may be seen by noting that the satisfaction of the antecedent of (5) only requires that (1) doing p is permitted, on eondition that e (from which it does not follow that p is done), (2) doing q is permitted, on the joint condition that c and p are in fact done, and (3) it is possible to do both p and q. From these three conditions being met, we cannot conclude (1) that on condition e, doing p is permitted and also (2) that on condition e, doing q is permitted, for the obtaining of c does not ensure the doing of p, part of the condition for the permissibility of doing q? Deciding exactly where the trouble lies and what revision should be made is another matter, for the troublesome (5) rests on two of the axioms, (2) and (3). Without making any specific proposals regarding revision, I will simply offer the comment that while (2), at least at first glance, is perhaps not as intuitively convincing as (3), there is something to be said for recasting (3) on other grounds anyway, namely its presumed susceptibility to the often discussed Good Samaritan Paradox. There is one final point which seems to me deserving of mention in the present discussion. This has to do with a puzzlement about the interpretation of the notion of conditional permission, a perplexity which I can perhaps best explain by means of raising a question, rather than making a judgment, about the acceptability of another of Rescher's axioms, namely {6) P(p&q/c) --~ P(p/c&q). It is clear that Rescher does not intend 'P(p/e)' to be construed as ' c ~ P ( p ) ' and that 'P(p/e)' is not incompatible with ',~P(p/c&d).' In other words, to say that the doing of an act p is permitted to someone circumstanced in conditions e is not to say that c constitutes a sufficient condition for asserting the permissibility of the doing of p. If, then, 'P(p/e)' is not to be understood as asserting that the obtaining of c constitutes a sufficient condition for the permissibility of doing p, suppose that c is some set of conditions under which the doing of q is extremely unlikely, but not imimssible, and that q is an act, the doing of which is of the very highest importance. Suppose, further, that p is an act, in itself undesirable and costly, but most effective in ensuring the doing of q, even given c. Our primary concern, then, is that q be done, and when the conditions e obtain, this

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becomes very improbable. Added to this is the fact that we can say but one good thing about the doing of p: given c, the doing of p will practically guarantee the doing of q. Now, with such a case in mind, the question is whether we can, in accordance with (6), make the inference from "the joint performance of p and q is permitted to persons circumstanced in conditions c, conditions which make the doing of q highly improbable" to "the doing of p is permitted to persons circumstanced in conditions c, conditions which make the doing of q highly improbable, even though q is being, or has been, done." Now, of course, if we had (7) P(p/c) ~ P(p/c&d), then, by (4), we would have (8) P(p&q/c) ~ P ( p / c ) . And from this, together with (7), we could then get to (6) and our question would be settled. However, since Rescher rejects (7) as a thesis, we are, I believe, left with a legitimate question about the precise interpretation of ' P ( p / c ) ' and, consequently, whether or not (6) is subject to a falsifying interpretation along the lines suggested above.

Received August 23, I965 NOTES 1 N. Rescher, "An Axiom System for Deontic Logic," PhitosophicaI Studies, 9:24-30 (1958) ; A. R. Anderson, "On the Logic of 'Commitment,' "Philosophical Studies, 10:2327 (1959); N. Rescher, "Conditional Permission in Deontic Logic," Philosophical Studies, 13 : 1-6 ( 1962 ) ; A. R. Anderson, "Reply to Mr. Rescher," Philosophical Studies, 13:6-8 (1962). In the first of these papers, Rescher explains that "The expression P(p/c) may accordingly be interpreted: 'To perform the act (i.e., to do) p is permitted to persons circumstanced in conditions c (or 'who are doing, or have done,' when appropriate because c is an act).'" It is interesting to speculate what effect the adoption of (5) might have had on an often heard claim of certain Christians, viz., that all men are permitted to examine and accept, if they will, the gospel, although only those who in fact do so will be permitted to enter the kingdom of heaven. Construing this claim in the fashion of (5), we would get the rather interesting "if one is permitted to examine and accept the gospel, simply ou condition of being a man, and one is permitted to enter the kingdom of heaven, on condition of being a man who has performed, or is performing, such an act of examination and acceptance, it being possible to examine and accept the gospel and to enter the kingdom of heaven, then one is permitted to examine and accept the gospel, on condition of being a man, and also one is permitted to enter the kingdom of heaven, on condition of 9eing a man." As might then be said, "Many are chosen, but few are called."