A SOLUTION TO FORRESTER'S PARADOX OF GENTLE MURDER*

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2 A SOLUTION TO FORRESTER'S PARADOX OF GENTLE MURDER 163 where the subscript 'r' indicates that the obligation can derive from any source, including the law. (3) plus (2) yields (4) If Smith murders Jones, it is obligatory, that Smith murder Jones gently. (4) and (5) imply (6) It is obligatory, that Smith murder Jones gently. But it is necessary that (7) If Smith murders Jones gently, then Smith murders Jones. and standard deontic logics include a rule (8) F (p D q) and (6), (7), and (8) imply F (Orp D Orq) (9) It is obligatory, that Smith murder Jones. The final principle that Forrester assumes is (10) Orp D Or,p and (1), (9), and (10) yield the contradiction ( 11) Oip & _OI-P The contradiction can be avoided only by rejecting at least one step of the argument. Forrester says, "steps (1), (2), and (5) are the basic facts of the case: there seems no reason to consider them mutually inconsistent" (195). (4), (6), (9), and (11) are validly inferred from previous steps. (7) can be supported by any plausible theory of adverbs. Forrester argues for (3) in this case, and he says "giving up (10) will not be enough" (196). Forrester concludes that (8) should be rejected, i.e., that truth is not always preserved when a logical implication of a sentence is substituted for that sentence inside the scope of a deontic operator. This argument can be generalized. Forrester's example concerns legal obligations, but the crucial steps (3), (8), and (10) use the subscript 'r', which applies to any deontic operator; so similar arguments can be formulated for moral obligations and for what agents legally or morally ought to do. Thus, if Forrester's argument works, no deontic operator allows substitution salva veritate of logical implications. 1 This conclusion should be very disturbing. Forrester sees that, if 'Because the argument applies to every deontic operator, I will henceforth drop subscripts.

4 A SOLUTION TO FORRESTER'S PARADOX OF GENTLE MURDER 165 Forrester's paradox is seen as a legal dilemma [relative to laws (1) and (2)]. Nonetheless, the situation does not seem to be a dilemma, since Smith can follow both laws by not murdering Jones. Consequently, (9) is unwelcome in this case, so some paradox remains even without (10). The best solution to Forrester's paradox is not to deny (3), (8), or (10) but instead to claim that (1), (2), and (5) are jointly inconsistent. Forrester says only that "there seems no reason to consider them mutually inconsistent" (195). However, the reason to consider them inconsistent is that they imply a contradiction if otherwise acceptable principles are assumed. What better reason could you want? Forrester would probably respond that (1), (2), and (5) seem consistent, so any principles of deontic logic that allow us to derive a contradiction do not accord with our common ways of speaking and reasoning with deontic operators. However, it is easy to explain why (1), (2), and (5) seem consistent when they really are not. We should suspect that the problem lies in (2), because (1) and (5) are more common than (2). If some other principle is similar to (2) but consistent with (1) and (5), then anyone who confuses this other principle with (2) will think that (2) is consistent with (1) and (5). Which principle is confused with (2)? Forrester writes, "the legal system might have stated (4) as its principle in place of (2)" (194). However, the contradiction follows from (4), assuming (8) and (10), so (4) provides no escape. (4) and (2) are the only alternatives Forrester considers, and the reason is clear. Forrester uses propositional constants and avoids quantifiers "to simplify matters" (194); so the deontic operator can have only two scopes. Its scope can be wide if it includes the whole conditional, as in (2), or narrow if it includes only the consequent, as in (4). An even narrower scope becomes available if we analyze the logical form of the action sentences within the scope of the deontic operator. Following Donald Davidson's theory,5 we can analyze (5) as (5.1) There is an act of murder by Smith of Jones. or symbolically as (5.2) (3 x)mxsj6 "The Logical Form of Action Sentences," in Essays on Actions and Events (New York: Oxford, 1980), pp (5.2) could be broken down further into '(3x)(M*x & BY(x,Smith) & OF(x,Jones))', but a complete analysis is not necessary for my purposes.

5 166 THE JOURNAL OF PHILOSOPHY The antecedent of (7) (7a) Smith murders Jones gently. can then be analyzed as (7.1a) There is an act of murder by Smith of Jones and it is gentle. or symbolically as (7.2a) (3x)(Mxsj & Gx) This analysis shows why (7) is true. More relevantly, it allows several interpretations of (6), because the deontic operator can apply at several places or take several scopes, including (6.1) O(3x)(Mxsj & Gx) (6.2) (3x)(Mxsj & OGx) Roughly, (6.1) says the occurrence of an act is obligatory, whereas (6.2) says the act occurs and its character as gentle is obligatory. These distinctions allow various interpretations of (4). Taken strictly, (4) can be interpreted with (6.1) as its consequent: (4.1) (3x)Mxsj D 0(3x)(Mxsj & Gx) or with (6.2) as its consequent: (4.2) (3x)Mxsj D (3x)(Mxsj & OGx)7 Since (4.1) and (4.2) are so similar, they are easily confused. However, (4.2) avoids the paradox. No contradiction can be derived from (1), (4.2), and (5), because (6.1) does not follow from (4.2) and (5). All that follows from (4.2) and (5) is (6.2). However, if (7) is analyzed as (7.2) (3x)(Mxsj & Cx) D (3x)Mxsj then the rule (8) warrants only the conclusion (8.1c) 0(3x)(Mxsj & Gx) D 0(3x)Mxsj and the antecedent of (8.1c) is (6.1) rather than (6.2). Since (6.1) cannot be derived from (4.2) and (5), neither can (9). Therefore, (1), (4.2), and (5) are consistent. Their consistency plus an understandable scope confusion of (4.2) with (2) or (4.1) explains why (1), (2), and (5) seem consistent when they are not. (4.2) also serves all the legitimate purposes of (2) or (4). Forrester 7Someone who says (4) probably means to say (4.3): 'O(x)(Mxsj D Gx)' or (4.4): '(x)(mxsj D OGx)', because these avoid the absurd implication of (4.1) that, if Smith murders Jones roughly, it is obligatory for Smith to return and murder him gently. In any case, my solution is unaffected, because the contradiction follows from (4.3) but not from (4.4).

6 A SOLUTION TO FORRESTER'S PARADOX OF GENTLE MURDER 167 says that the purpose of a law such as (2) or (4) is to show that the legal system "considers murdering violently to be a worse crime than murdering gently" (194). (4.2) serves this purpose as well as (2) or (4), because murdering violently violates (4.2), but murdering gently does not violate (4.2). Furthermore, the justification for (4.2) is simple and intuitive. Forrester defines "'doing A to person m at time t gently' as 'doing A to m at t in such a way as to cause m the least amount of pain consistent with the agent's doing A to m"' (194). If a legal system wants to make it obligatory to cause the least pain consistent with doing an act of any kind, then the legal system can include a general rule that (12) (x)ogx which implies a general rule that, for any kind of act, A, (12.1) (x) (Ax D OGx) which implies that, for any kind of act, A, (12.2) (3x)Ax D (3x)(Ax & OGx) (4.2) is an instance of (12.2); so (12)-(12.2) can justify (4.2). No general rationale for (2) or (4.1) is this plausible. Thus, there are several reasons to interpret any actual law like (2) or (4) as (4.2) rather than as (4.1) and to prefer (4.2) to (2) or (4.1) as a moral rule. If anyone insists on (2) or (4.1) as a law or moral rule, and they also accept (1) and (5), then their views are inconsistent. Such inconsistency is not a paradox. Critics might respond that this solution assumes Davidson's theory of the logical form of action sentences, but that theory is questionable, and there are alternative theories of adverbs and action sentences on which no scope solution to Forrester's paradox is available. The most plausible alternatives8 analyze adverbs as operators on sentences, so (7a) Smith murders Jones gently. is analyzed as (7a*) Gently (Smith murders Jones) (6) must then be analyzed as (6*) O(Gently (Smith murders Jones)) 8 Cf. Romane Clark, "Concerning the Logic of Predicate Modifiers," Nouts, lv, 4 (November 1970): , and Terence Parsons, "Some Problems concerning the Logic of Grammatical Modifiers," Synthese, xxi, 3 (October 1970):

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