Two Senses of 'Ought' in Forrester's Paradox

Two Senses of ‘Ought’ in Forrester’s Paradox Joseph Ulatowski∗ September 25, 2013 Abstract If Smith commits murder, he should do so gently. Suppose then that Smith commits murder. He should do so gently. From “Smith should do A” it logically follows that he should do anything logically implied by A. Smith’s murdering gently entails his committing murder. Thus, Smith should commit murder. Since a rule stipulates that Smith should not murder Jones, Smith both should and should not murder Jones. This paper will attempt to present a viable solution to Forrester’s paradox. I will argue that the different functions of two deontic operators show that the contradiction cannot possibly follow. [97 words] This is a DRAFT. Please do not cite without permission. Comments, criticisms, and suggestions are welcome. c 2013 Joseph Ulatowski. 1 Introduction The aim of this paper is to present a viable solution to the paradox of gentle murder, or Forrester’s paradox.1 First, I will summarize the paradox and explain its logical structure. Next, I will address a a few proposed solutions to the paradox. The first proposal has us reject one of the deontic principles to lead us out of the paradox. Such a solution overlooks an important aspect of deontic pragmatics. Then, I will consider Walter ∗ This paper has benefited from conversations or correspondence with Robert Barnard, David Beisecker, Donald Bruckner, Robert Colter, James Forrester, Franz-Peter Griesmaier, Marc Moffett, and Walter Sinnott-Armstrong. I am also indebted to members of the audience at the 2009 MidSouth Philosophy Conference for valuable feedback I received after a presentation of this paper. 1 James Forrester (1984) is the originator of the paradox. He called it the paradox of the adverbial samaritan because of its resemblance to the paradox of the good samaritan. (Åqvist 1967) 1 Sinnott-Armstrong’s (1985) recommendation that limiting the scope of the deontic operator to range over the manner in which the act is performed will solve the paradox. His solution has presumed that ‘gently’ may be treated as a predicate. Since not all adverbs of action may represent a predicate of action, Sinnott-Armstrong’s proposed solution fails. Finally, my solution consists in the distinction between two senses of ‘ought’. Under one formulation the obligation may concern how one ought to act and under the other formulation the obligation may concern how the world ought to be. The distinction suggests that there are actually two deontic operators at work in the paradox. Since the two deontic operators function in significantly different ways, I will argue that the paradoxical conclusion does not follow. 2 The paradox I will start with a summary of the paradox. Three assumptions and three rules of standard deontic logic (“SDL”) are at work in the paradox. Two of the assumptions are rules that govern a subject’s behavior and the third is an action sentence: 1. It is obligatory that Smith not murder Jones. 2. It is obligatory that if Smith murders Jones, Smith murders Jones gently. 3. Smith murders Jones. The three rules of SDL are2 : R1: (p ⊃ q) ⊢ (Op ⊃ Oq) R2: O(p ⊃ q) ⊢ (p ⊃ Oq) R3: O p ⊃ ∼O∼p The paradox arises when we apply the logical rules to the assumptions. First, 2 and R2 yields: 2 For the formal rules of SDL, let “O” stand for “it is obligatory that. . . ,” and let the variables “p” and “q” stand in for action sentences. 2 4. If Smith murders Jones, then it is obligatory that Smith murder Jones gently. From 3 and 4, we may derive: 5. It is obligatory that Smith murder Jones gently. It seems obvious that: 6. If Smith murders Jones gently, then Smith murders Jones. The application of R1 to 6 entails: 7. If it is obligatory that Smith murders Jones gently, then it is obligatory that Smith murders Jones. 5 and 7 entail: 8. It is obligatory that Smith murder Jones. Given R3, 8 yields 9: “it is not obligatory that Smith not murder Jones.” We cannot consistently hold 9 and 1. Forrester has rejected R1 to solve the paradox because other solutions are not going to work. Forrester writes: The most likely candidate for the scrap heap is [R1] - a basic inference principle in standard deontic logic. If this is indeed the rotten apple, the entire barrel of standard deontic logic must be in a bad way.”(Forrester 1984, 197) Forrester’s rejecting R1 will prevent the paradox from arising, but its removal will not come without a high cost. Recommending the rejection of R1 calls for a whole scale revision of SDL, since R1 is a rule derived from more primitive axioms of deontic logic. This is too large a task for him to undertake in his (1984) and by my own estimation it is something we should definitely want to avoid, if we can help it. 3 Rejecting R2 R1 may not be the only deontic principle we should reconsider in light of Forrester’s paradox. Someone may want to reject R2, given that deontic 3 logic is a branch of alethic modal logic.3 In alethic modal logic, the principle M2: (p ⊃ q) ⊢ (p ⊃ q) is false. So, by analogy, the deontic principle R2 must be false. Without R2, the paradox does not arise. Forrester has defended the truth of R2 because the principle holds in “certain special cases.” (Forrester 1984, 196) The paradox is one of the special cases. Suppose I converse with Smith before the killing takes place. I point to the moral rule that forbids Smith from killing Jones, and he responds that he is going to kill Jones regardless of what I or anyone else says. It seems natural for me to say to Smith, “well, then you had better kill Jones gently.” According to Forrester, I have used R2 to come to this conclusion; “and my reasoning, as well as my morals, would appear above reproach.” (ibid.) The principle may be formally inadequate; however, R2 ought to be upheld since it bears some importance for our moral deliberation. 4 Manners matter I will turn now to Sinnott-Armstrong’s radical way of disarming the paradox. Sinnott-Armstrong has used Donald Davidson’s (1967) formal analysis of action sentences to distinguish the occurrence of an act from the manner of its perpetration. The antecedent of 6, “Smith murders Jones gently,” in Davidsonian fashion becomes: 6.1. There is an act of murder by Smith of Jones and it is gentle, which in turn formalizes as: 6.2. (∃x )(Mxsj & Gx ) Since the act of murder and the gentleness of the act are disambiguated on Davidson’s account, the obligation operator, O, may then be placed 3I want to thank redacted for blind review for a discussion about this argument. See von Wright’s (1951) for discussion of the close connection between deontic and alethic modal logic. In that paper, von Wright argues that deontic logic is a branch of modal logic. 4 with distinct effect. This gives rise to a wide and a narrow interpretation of 5. The operator can express an obligation to murder when its scope includes the whole proposition (the “wide” view), or the operator can express an obligation to do so gently when it ranges over Gx (the “narrow” view). So, 5 may be interpreted as: 5.1. O(∃x )(Mxsj & Gx ) 5.2. (∃x )(Mxsj & OGx ) While the act of murder is obligatory in 5.1, the act of murder occurs and the gentle manner in which it is carried out is obligatory in 5.2.4 The distinction between 5.1 and 5.2 now allows for various interpretations of 4. 4 and 5.1 yields: 4.1. (∃x )Mxsj ⊃ O(∃x )(Mxsj & Gx ). 4 and 5.2 entails: 4.2. (∃x )Mxsj ⊃ (∃x )(Mxsj & OGx ). 4.1 generates the paradox, since Smith is not only obligated to murder Jones gently but is obligated to murder Jones. If, however, we employ 4.2, only the gentleness of Smith’s act is obligatory. 4.2 disables the inconsistency because it rules out an obligation of Smith to murder Jones. No contradiction can be derived from 1, 3, and 4.2 because only 5.2 follows from 3 and 4.2. If 6 is analyzed as: 6.3. (∃x )(Mxsj & Gx ) ⊃ (∃x )Mxsj then R1 only warrants the conclusion: 7.1. O(∃x )(Mxsj & Gx ) ⊃ O(∃x )Mxsj 4 One may claim that there is a third interpretation of 5. The third way is: 5.3. (∃x )(OMxsj & Gx ). This interpretation may be formally correct, but informally unsound. To say that “there is an act such that it is an obligatory murder by Smith of Jones and it is gentle,” is not an accurate interpretation of 5, that “it is obligatory that Smith murders Jones gently.” 5 and the antecedent of 7.1 is 5.1 rather than 5.2. Since 5.1 cannot be derived from 3 and 4.2, neither can 8. Since 8 generates the inconsistency, no paradox can possibly arise. Hence, 1, 3, and 4.2 are consistent. Sinnott-Armstrong’s revolutionary maneuver does not come without a serious disadvantage. It is not clear what it means for an agent to be obligated gently to do something without also being obligated to do something. The adverb ‘gently’ is not amenable to treatment as a predicate. Davidson (2001) claims that ‘slowly’ is such an adverb. If ‘slowly’ is not representative of a predicate of action, then adverbs like it are not either. We can now propose the Paradox of Slow Murder. Replace “gently” with “slowly” in the paradox, and we come to the same paradoxical conclusion as in the original. But, since Davidson’s account of adverbial modification does not apply to ‘slowly’, Sinnott-Armstrong’s solution does not apply to the paradox.5 5 ‘Ought to do’ v. ‘Ought to be’ The previous section showed that a theory of adverbial modification will not likely solve Forrester’s paradox.6 In this section, I will argue that there are at least two senses of ‘ought’. They have distinct meanings and their logical behavior differs too. I will show that the paradox employs both ‘ought to be’ and ‘ought to do’ statements without consideration for the differences between them. If my analysis is correct, then a solution of 5 Romane Clark (1986) has argued that by defining a special kind of adverbial modifier, M, where it governs the manner of doing but not the act done, renders the untoward obligation to murder inoperative. She then says something very curious, “From the general “truth” that one ought “gently” to do what one does, it does not follow, nor should it, that one ought to do that which one does do.” (Clark 1986, 55) So, for instance, from “one ought gently to pet my cat” it does not follow that “one ought to pet my cat.” I would agree if that was what was occurring in the paradox. But an obligation to do x gently is an obligation to do x because gently should not be interpreted here as a predicate. I think that Clark has generated an interesting problem about adverbial modification, but it is unclear to me how it applies to the paradox. I would like to thank Franz-Peter Greismaier for a discussion on this very point. 6 It should be noted that other people have tried to solve Forrester’s paradox by presenting alternative theories of adverbial modification. For example, see Hector-Neri Castañeda (1985) or Dale Jacquette (1986). 6 Forrester’s paradox is possible when the two deontic operators are properly differentiated.7 ‘Ought’ has many uses. Think of how the word comes up in ordinary conversation. First, a conjectural ‘ought’ may express an expectation. For example, “the train ought to arrive at 3pm.” According to a conjectural use, ‘ought’ merely indicates that the train will likely arrive at 3pm. Second, ‘ought’ may report a suggestion. For example, “the truck driver ought to use North McCarran Boulevard instead of Interstate-80.” An accident on Interstate-80 may have made the highway impassable, and the best alternative is for motorists to use North McCarran Blvd. Since nothing prescribes that the train arrives at 3pm or that the trucker takes North McCarran Blvd., neither the conjectural nor the suggestive ‘ought’ is a categorical use of the term. Two ‘oughts’ are often confused with one another in deontic speech. The first claims that a person should perform some action, so the ‘ought’ statement they contain is an ‘ought to do’. The second ‘ought to be’ statement tells us how the world would be improved if a given state-ofaffairs obtained or failed to obtain. What I will suggest now is not only that they have two different meanings but that the two senses of ‘ought’ behave in logically different ways. ‘Ought to do’ and ‘ought to be’ statements have different meanings. While ‘ought to do’ statements are generally directive, judgmental, and informative, ‘ought to be’ statements are optative. Imagine a case where Donna Elkin has competed in the new hit reality television contest American Rocker. Suppose that Donna’s performance is clearly superior in comparison with the other contestants, but that the judges are biased, and it is likely that the next American Rocker goes to someone else. If one then said, “Donna Elkin ought to win American Rocker,” this kind of statement is about the situation, not about Donna. A legitimate para7 Jim Forrester (1996) distinguishes between these two forms of obligation, but he does not attempt to apply the distinction to his own paradox in that book. 7 phrase of the statement is “It ought to be that Donna wins American Rocker.” Saying that Donna should win Rocker is not to judge her or blame her if she loses. The sentence tells us how the world ought to be, but it does not prescribe actions Donna should do to bring about her winning the competition. In Forrester’s paradox, 1. governs Smith’s behavior by indicating how the world ought not to be. The rule states that, “It is obligatory that Smith not murder Jones.” The rule is logically equivalent to “It ought not to be that Smith murder Jones.” Under this reading, the rule refers to a hypothetical state of the world that should not be brought about. Since the rule refers to a hypothetical situation, rule 1 is an ‘ought to be’ statement. ‘Ought to do’ statements prescribe how one ought to act. Suppose that Donna has not kept up with her voice training. So, one says, “Donna ought to practice harder.” It tells Donna what she ought to do. The statement implies that Donna is able to practice harder, and places blame on her for not doing so. 7, which is logically derived from the assumption 6, says “if it is obligatory that Smith murders Jones gently, then it is obligatory that Smith murder Jones.” Since in this case the antecedent and consequent prescribe how Smith ought to act, “it is obligatory that Smith murders Jones gently” is logically equivalent to “Smith ought to murder Jones gently.” A paraphrase of the modified antecedent is “Smith ought to do x.” Therefore, “Smith ought to murder Jones gently” is an ‘ought to do’ statement and he should do so if he can. Whereas ‘ought to do’ statements imply can, ‘ought to be’ statements do not. It is a commonly accepted principle that ‘ought implies can.’ Statements of the form ‘x ought to y’ imply, entail or presuppose statements of the form ‘x can y’.8 “It ought not to be that Smith murder Jones” does not imply that Smith cannot murder Jones. In fact, Smith 8 Similarly, ‘x ought not to y’ implies, entails, or presupposes that x can refrain from, avoid, or stop y-ing. 8 can murder Jones under the appropriate circumstances. But, when we say, “Smith ought not to murder Jones,” it implies that he can refrain from doing so. If Smith murders Jones, then he may be held morally responsible for his action. The predicate of an ‘ought to do’ statement allocates responsibility to the agent. The two meanings of ‘ought’ seem to imply a difference between two deontic operators. ‘Ought to do’ and ‘ought to be’ have different logical behaviors. So, we must employ distinct logical operators for each. The de re/de dicto distinction is familiar from modal semantics, and I believe that deontic operators can also be either de dicto or de re. The sentence “Sam can move the car” presents an apparent de re possibility. A certain possibility holds of Sam, and Sam must exist for the sentence to be true. Similarly, “Smith ought to murder Jones” can only be a de re deontic modality. The proposition can be true only if there is such a person as Smith. The sentence predicates a certain ‘ought’ of Smith. The ‘ought to do’ operator does not operate on the entire proposition because the subject term is outside the scope of the operator. It ranges over predicates only. An ‘ought to be’ statement is a de dicto modality. Consider “It is possible that Sam moves the car.” This represents a de dicto possibility, and Sam’s existence is not required for its truth. Correspondingly, ‘ought to be’ statements are not committed to the existence of any of its components in stipulating how the world should be. The rule, “It ought to be that Smith not murder Jones,” would be true and would apply to the world, even if there is not and never will be such a person Smith. Unlike the ‘ought to do’ deontic operator, the ‘ought to be’ operator ranges over the entire proposition, not merely predicates. The deontic operators for ‘ought to do’ and ‘ought to be’ statements J may now be applied in Forrester’s paradox with great effect. Let “ ” stand in for ‘ought to be’ statements, let “O” stand in for ‘ought to do’ 9 statements, M is “Smith murders Jones,” and G is “Smith murders Jones gently.” Modified versions of the three rules, R1, R2, and R3 may be J used with the ‘ought to be’ operator, but O should be replaced with in J each of them. The deontic operators in 1 and 2 should be replaced by because they refer to states of a hypothetical world. The argument now reads: 1*. 2*. 3*. 4*. 5*. 6*. 7*. J J ∼M (premise) (M ⊃ G) (premise) M (premise) J M J ⊃ G (2, modified R2) G (3, 4) G ⊃ M (assumption) OM ⊃ OG (6, original R1) Something like 8 does not follow because 5* and 7* cannot possibly yield anything like “It is obligatory that Smith murder Jones” without conflating the two senses of ‘ought’ that were clearly distinguished above. A contradiction does not follow, thus circumventing the paradox. 6 Why two deontic operators? One may object by arguing that the introduction of two different deontic operators is too cumbersome for deontic logic. The introduction of the new deontic operators would result in the development of whole new systems of deontic logic. That would merely muddy matters already quite obscure in SDL. As I have mentioned, SDL is not well off now by not distinguishing between two deontic operators. If we use an operator that stands in for ‘ought’ in a generic way, we run the risk of making matters far worse by continuing to employ just one operator. Two operators permit us to circumvent paradoxes, such as Forrester’s paradox, and they may shed some light on other pressing matters such as conditional obligation. Finally, it seems possible to argue that the employment of two operators generates two paradoxes rather than just one. If 7 were derived 10 from the modified R1, then it seems like we could derive a contradiction because the operators would be consistent all the way down. Either the paradox goes through using the ‘ought to be’ operator or it goes through using the ‘ought to do’ operator. But, if it goes through with the ‘ought to be’ operator, then it has nothing whatsoever to do with how we ought to act. The paradox is impotent at best. If the paradox goes through with the ‘ought to do’ operator, the function of moral rules in deontic logic is unclear. Rules would apply to certain activities without governing our behavior generally. Thus, it is highly unlikely that the paradox obtains when we apply just one of the deontic operators to Forrester’s paradox. 7 Conclusion Forrester’s and Sinnott-Armstrong’s proposed solutions to the paradox of gentle murder have failed. In Forrester’s case, we have no reason to reject a principle of SDL if in rejecting that principle we must revise all of SDL. In Sinnott-Armstrong’s case, since ‘gently’ is not an adverb of action, it does not act like a predicate. So, his Davidsonian analysis of propositions in Forrester’s paradox does not lead us out of the paradox. I have argued that two distinct deontic operators are at work in the paradox. Since ‘ought to be’ and ‘ought to do’ have two distinct meanings and behave in logically different ways, some of the propositions refer to how the world ought to be and other propositions prescribe how Smith ought to act. 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