the prescriptional analysis of normatives

THE PRESCRIPTIONAL ANALYSIS OF NORMATIVES

D. S . Clarke, Jr. Southern Illinois University at Carbondale

Widespread agreement seem to have reached for the view that impera-

1) X,repayY tives such as

must be distinguished from their corresponding normative or deontic ‘ought’ sentences, e.g.

There are a number of distinguishing features of logical syntax, the most prominent being, as Geach has pointed out,l the fact that the negation of the normative does not correspond to the negated imperative. The negation of 2) is the external negation ‘It is not the case that X ought to repay Y’, rather than the internal negation ‘X ought not to repay Y’, the form that corresponds to the negation of 1).

Moreover, there seem to be a clear difference in the presuppositions of the use of the two sentences. One who uses 2) implies that there is some justification for the action of X repaying Y. The question ‘Why?’ in response to an utterance of it is legitimate and deserves an answer. In contrast, to command 1) is not necessarily to imply that any reason can be given for performing the action other than the fear of a sanction, and the response ‘Why?’ may be entirely inappropriate. It certainly would not occur to a recruit when told by his drill instructor ‘Stand at attention’. And even where the question is appropriate, as it may be in response to an utterance of l), it seems to mean ‘Why should I?. To ask for a justification of an imperative is thus to ask why it ought to (should) be obeyed; to give an answer is to state the grounds for an obligation to obey, e.g. the authority of the speaker or the benefit that would result.

For these and other reasons that have been given it seems clear, then, that 1) and 2) must be distinguished. But it is still far from clear how the two are related. I propose to defend in this paper a view similar to that proposed by Castanedaz which regards the relation as analogous to that holding between an alethic modal sentence of the meta-language and its mentioned indicative. This de dido interpretation requires us to analyze normatives as equivalent to sentences about a prescription expressed by a mentioned imperative. We shall refer to it as the prescriprionul analysis of

2) X ought to repay Y.

D. S. Clarke, Jr. is associate professor and acting chairman of the Department of Philosophy at Southern Illinois University at Carbondale. He is the author of Deduc- tive Logic (S. Il. U. Press, 1973) and of articles in Mind, Analysis, and Philosophical Studies. The paper printed here was wi t ten while a Recognized Student at Oxford University in I9 73.

21

normatives. In the first part of the paper alternatives to it will be consid- ered. In the second part the problem of substitution into deontic contexts will be discussed, and in the third, an attempt will be made to clarify the analysis by answering some possible objections. Finally, some consequences of it will be drawn for the construction of a deontic calculus and resolution of some paradoxes.

I

The principal problem in analyzing normatives is to decide to what the deontic predicate ‘is obligatory’ in a sentence such as ‘For X to repay Y is Obligatory’ is being ascribed. Alternatively, it is to decide for any sentences of the forms 0 (. . . ) and P (. . . ) what are represented by expressions within the scopes of the deontic operators 0 (it is obligatory to) and P (it is permissible to). Most writers have followed von Wright3 in holding that the subjects of predication are action-types. They are not particular actions, since we characteristically require actions that could be but have not yet been performed. Thus, we say that X ought to repay Y, but not that he ought to have repaid him at precisely the time and place and in the way he did. The particular action would be judged instead as an instance of what we require. Normatives are therefore regarded as sentences used to characterize action-types as being obligatory, permissible, or forbidden. To say that an agent X ought to repay his debt is to say that the action of X repaying is obligatory. In the deontic schemata 0 (A) and P (A) the operand A is regarded by Von Wright as representing a name of an action, e.g. ‘X repaying Y’. Others such as Stenius4 regard A as representing a complete sentence describing the action, e.g. ‘X repays Y’. But this difference is unimportant for our purposes. What is important is that normatives on this view are regarded as sentences used to characterize act ions.

This seems reasonable enough. But as formulated it runs into difficulties. For what, after all, are action-types? Unlike particular actions that can be located and dated they are not items of the world awaiting our description of them. And what are their criteria of individuation? Is the action of X repaying Y the same as Y being repaid by X? It apparently is, but if so, on what grounds do we judge them to be the same?

To answer these questions without prejudging another let us introduce some special terminology. By the linguistic specification of an action we shall mean any linguistic expression which either describes or prescribes the action. What this specification expresses we shall call its content. If descriptive, the expression is an indicative sentence expressing a true or false proposition; if prescriptive, it is an imperative expressing a prescription (or command) either obeyed (fulfilled) or disobeyed (unfulfilled). By the satisfaction of the content of a specification we shall mean its truth if a proposition and obedience if a prescription.

Now what seems intended as the referent of the term ‘action-type’ is

22

the content of some linguistic specification of an action. For our identi- fying one action as the same as another seems based solely on whether or not different specifications of an action have the same content. Thus, the action Al of X repaying Y is judged the same as A2, Y being repaid by X, but different from the action A3 of X repaying Z because (assuming our specifications are descriptive) ‘X repays Y’ expresses the same proposition as ‘Y is repaid by X’, but a different proposition than does ‘X repays Z’. Since this criterion can be extended to prescriptions, we can say that A1 is not identical with A3 because ‘X, repay Y’ expresses a different prescription than does ‘X, repay Z’. The criterion of identity of action-types is thus simply that of the content of their linguistic specifications.

If action-types are simply contents of linguistic specifications, then clearly to perform an action of a certain type is but to satisfy a given content, to make a proposition true or obey a prescription. And to say that a certain person X ought to perform an action is but to say that X ought to satisfy a certain content. Let us use forclauses of the form ‘for X to do A’ to stand for the content of linguistic specifications of an action A. Then we can say that the normative 2) is equivalent to ‘It is obligatory for X to repay Y to be satisfied’. Instead of characterizing actions per se, normatives like 2) are to be interpreted as stating that a certain content ought to be satisfied.

The neutral terms ‘specification’ and ‘content’ have so far been used for a linguistic expression standing for a given action and what it expresses for one who understands it. We come now to the problem of determining what form this specification must take, whether an indicative describing the action or an imperative prescribing it. If we opt for the former, then what is obligatory is the truth of a proposition expressed by some indicative. Sentence 2) would then become reformulated as ‘It is obligatory that X repays Y’, and this in turn becomes reformulated within the meta- language as

3) ‘X repays Y’ is obligatory. On this view there is an exact parallel between alethic modal sentences such as ‘It is necessary that X repays Y’ and normatives. Both are equivalent to sentences of the meta-language in which modal predicates are being ascribed to the truth of propositions. We shall label this interpretation of ‘specification’ and ‘content’ the propositional analysis of normatives. Under it the logical forms of normatives are represented by 0 (A) and P (A), with the schema A representing names of arbitrary indicative sentences expressing propositions. As we shall see below, this analysis is pre- supposed in the standard formalizations of deontic logic.

This analysis cannot itself account, however, for severe restrictions that must be imposed on the type of propositional that-clauses to which ‘it is obligatory’ is prefixed. Only those describing actions within the control of the agent on whom the obligation is imposed are suitable. To be sure, we do say ‘It ought to rain’ or ‘There ought to be no suffering in the world’, where the obligation is imposed on no particular agent or agents

23

and is clearly beyond anyone’s control. But when we do, we do not seem to be stating what is true or false. We are instead expressing a feeling or desire. What we are saying could be expressed by ‘Oh that it would rain’ or ‘I wish that there were no suffering in the world’. In contrast, when we say ‘He ought t o keep his promise’ we are stating what others can disagree with and judge true or false relative to supporting reasons. We can use the sentence to express our desire to have the person in question act in a certain way, but this use is clearly secondary.

Our other alternative is the prescriptional analysis we are advocating. Under it to say that X ought to repay Y is to say that the prescription for X to repay Y ought to be obeyed. As a reformulation of 2) we have ‘It is obligatory for X to repay Y’, where the for-clause stands for a prescription. Reformulated in the meta-language this becomes instead of 3)

in which the mentioned sentence is now in the imperative mood. The representation of a normative now takes the form 0 (A!) or P (A!), with the schema A! representing names of arbitrary imperative sentences. Since only imperatives are mentioned in normatives as formulated in the meta- language and imperatives like ‘X, repay Y’ can only be used to prescribe actions within the control of the addressee X, we gain the restriction on that-clauses we were seeking. The only propositions to which deontic predicates could be applied under the propositional analysis were those for which there was a corresponding prescription, as corresponding to ‘X repays Y’ we have the imperative ‘X, repay Y’. This restriction is most easily accomplished by simply ascribing these predicates to the obedience of prescriptions rather than to the truth of their corresponding propositions. Of course, if a prescription is obeyed, its corresponding proposition is true. To obey ‘X, repay Y‘ is to make ‘X repays Y’ true. But this does not alter the fact that ‘ought’ sentences describe the requirement of obedience and not truth, though it may help explain the plausibility of the propositional analysis.

4) ‘X, repay Y’ is obligatory

I1

Before considering some formal considerations in favor of the prescriptional analysis we must attempt to clear up some difficulties sur- rounding the interpretation of sentence 4). In claiming it as equivalent to 2) we can be taken as claiming only that a prescription expressed by any imperative whose subjects have the same reference as those of 1) and whose predicate is synonymous with its predicate ought to be obeyed. Any imperative from within the class of sentences expressing the same prescription, whether within a given language or from another, would qualify as this sentence. 4) can thus be interpreted as saying that the prescription expressed by ‘X, repay Y’ ought to be obeyed, with no requirement for any particular imperative to be mentioned within it. The imperative ‘X, repay Y’ is merely the representative of a class of sentences.

24

There are grounds for thinking, however, that normatives provide opaque or intensional contexts for substitution of singular terms, and hence that our choice of expression is restricted. Consider, for example, the inference,

P1. It is obligatory for X to repay the man from whom he

P2. The man from whom he borrowed is the man who plans borrowed (Y).

to use the money to traffic drugs (Z).

C. It is obligatory for X to repay the man who plans to use the money to traffic drugs.

All would agree that the first premiss P1 is true, that to pay one’s debts to the person named by the description Y is obligatory. But we would also agree that the conclusion C, which results from P1 by substitution of the definite description Z on the basis of the identity stated in P2, is false. Despite the fact that the action of repaying Y is the same action as repaying Z, the first action is obligatory, the second not. Normatives, like (alethic) modal sentences, thus seem to provide opaque contexts for referring expressions. And we thus seem lead to draw the analogue of Quine’s well-known conclusion for necessity. What are obligatory are not actions in themselves, since both P1 and C characterize the same action. This substantiates our previous rejection of the view that normatives characterize actions pet se. But neither can deontic predicates be ascribed to prescriptions. For by extending Lemon’s criterion of identity to prescriptions ‘X, repay Y’ and ‘X, repay Z’ would express the same prescription, since by P2 Y and Z have the same reference. Rather, these predicates are ascribed to prescriptions as expressed by a specific imperative. It does make a difference, therefore, which imperative is mentioned in the meta- linguistic formulation of a normative. As in P1 and C, a change in sentence,. even though both express the same prescription, can change a truth into a falsehood.

Attempts can be made, of course, to preserve the validity of the inference from P1 and p2 to C. An obvious one would be to argue that P1 describes only a prima facie obligation, is overridden by the obligation not to promote drug traffic, and is therefore false in the sense that we interpret ‘obligatory’ in the conclusion.

But it seems perfectly possible for P2 to be used to express an identity proposition. Suppose that you use the definite description Y to refer to a certain individual, and that I use the description Z to refer to an individual. If we were then to learn that were both referring to the same individual, then P2 would express a contingent identity proposition. From the fact that sentences such as P2 can be used predicatively it does not follow that they must on all occasions be used in this way. The sentence ‘The evening star is the morning star’ could be used to mean ‘The evening star is seen in the morning’, though in fact its actual use is (or at least was) quite different. If P2 is not used predicatively, we are not cancelling the

25

obligation of the first premiss by stating with it an extenuating circum- stance. We are instead stating that two different expressions refer to the same individual.

A second approach might be that of holding to the truth of the conclusion C, arguing that if P1 and P2 are both true then C must be true despite our intuitions to the contrary. But this argument simply begs the question, since it assumes the validity of a form of inference that we are claiming as invalid. We cannot simply assume that deontic contexts are in some way unlike modal and epistemic contexts in the absence of my reason other than an intuition that the above inference is valid. Our natural assumption would seem to be rather that the context r$ in ‘It is obligatory for qY, ‘It is necessary that QS, and ‘X believes that @ behaves in the same way under substitution.

A contrast should be noted between our deontic inference and the corresponding imperative inference,

X, repay the man from whom you borrowed. The man from whom you borrowed is the man who

plans to use the money to traffic drugs. ~ ~

X, repay the man who plans to use the money to traffic drugs.

which does appear to be valid. It is impossible to obey the first premiss and for the second to be true without obeying the conclusion, and one who CommaiiA the first premiss and asserts the second would be committed to also commanding the conclusion. Imperatives are sentences of the object language used to prescribe actions, and as such provide extensional contexts. What we command does seem to depend on this choice, as we have seen, Availability to substitution thus serves to distinguish imperatives from normatives.

It should be emphasized that the correctness of the prescriptional analysis does not hinge on the correctness of the opaqueness thesis for normatives just advanced. What is at issue is not whether 4) is equivalent to 2). It is rather the status of the imperative mentioned in 4), whether it is a representative of the class of imperatives expressing the same prescription, or whether restrictions must be imposed on the expression that occurs. Our general claim will be unaffected if, as seems to me unlikely, reasons can be advanced that show that deontic contexts differ from (alethic) modal and epistemic contexts with regard to substitution.

We now consider several objections to our account. 1. It: can be first argued that a sentence such as ‘X, you ought to do A’

is used to influence the conduct of X, to persuade him to perform the action A. Unlike 4) it is not used to make a statement about a prescription. Since its standard intended use or illocutionary force is different

26

from that of our meta-linguistic formulation, it CaMOt be regarded as equivalent to 4).5

It should be first pointed out that only normatives whose subject is ‘you’ seem to be standardly used to influence the conduct of another. To say of some third person X that he ought to do A seems simply to make a statement. But even if all normatives were used to influence conduct, it would still not follow that 4) is not equivalent to 2). For we are claiming only an analysis of the logical or locutionary meaning of 2). The fact that a normative can be used with what is primarily prescriptive illocutionary force rather than the force of a statement should in no way influence our judgment of its logical analysis. The propositional content of 2) can be used in a variety of ways: we can ask ‘Ought X to repay y?’, use 2) to make a statement, or use it to bring about a change in X’s or some other person’s conduct. But it is only this common content that is being reformulated by 4).

One concession must be granted to this objection, however. We un- doubtedly use a sentence of the form ‘You may do A’ (e.g. ‘You may wash your hands now’ said to a child) to grant permission, rather than to describe the fact that the action of doing A is permissible. In this permission- granting use there is no implied justification for a normative proposition; there may be no sense to a ‘why’ question. In such a use ‘You may do A’ seems synonymous with the performative ‘I permit you to do A’, and truth and falsity seem inapplicable to it. In its permission-describing use, on the other hand, the sentence is synonymous with ‘It is permissible to do A’, which is in turn synonymous under our analysis with ‘It is permissible to obey “DO A” ’. It is thus only to this latter use of ‘may’ that the prescriptional analysis can be applied. As used to grant a permission the sentence is indeed within the object language and is invulnerable to trans- lation into the meta-language. There appears to be no parallel duality of function for the modal word ‘must’ when used normatively. Within sentences of the form ‘You must do A’ it invariably means the same as

2. A second objection may be that the meta-linguistic sentence 4) ascribes obligatoriness to the prescription expressed by the mentioned imperative, whereas 2) ascribes it to an action. Hence the former cannot be regarded as a paraphrase of the latter. They differ in their subjects of predication.

But this is simply a misunderstanding of the analysis. 4) must be understood as an ellipsis for ‘The prescription expressed by “X, repay Y” ought to be obeyed’ or ‘It is obligatory for the prescription expressed by “X, repay Y” to be obeyed‘. Now to obey the prescription for X to repay Y is just to perform the action characterized in 2). Hence, the meta- linguistic sentence 4) is used to characterize this action.

3. It can also be argued that the prescriptional analysis cannot account for the possibility of past tense normatives. We can say

5 ) X ought to have paid Y

‘ought’.

27

where the verb is in the past tense. But verbs in the imperative mood can never be in the past tense; we can only command someone to perform an action now or sometime in the future. Hence, the normative cannot be interpreted as a sentence about an imperative.

Under the prescriptional analysis 5 ) becomes paraphrased as ‘ “X, repay Y” ought to have been obeyed‘ or ‘ “X, repay Y” was obligatory’. The obligation to be obeyed is thus ascribed in the past tense to an imperative as it would have been uttered in the past with its verb in the imperative mood. What we are saying with 5 ) is that the prescription expressed by such an imperative when uttered on some specific past occasion ought to have been then obeyed. There is here only a partial parallel with necessity past tense sentences. ‘X was necessarily Y’ can be paraphrased by either ‘ “X was Y” is necessary’ or ‘ “X is Y” was necessary’. What the latter states is that the proposition that X is Y as expressed by the mentioned sentence as it would have been uttered on some past occasion was then necessarily true. Only this form has an analogue in deontic logic.

IV

These considerations should lend at least some initial plausibility to the prescriptional analysis. Further confirmation of it rests with some of its consequences.

The analysis requires a restriction on the form of schemata within a deontic calculus. Since deontic schemata are interpreted as representing sentences mentioning imperatives, only schemata of the forms 0 (@!) and P (#!) can be admitted as well-formed, with @! for some arbitrary imperative schema. No expression can be admitted in which a deontic operator has within its scope an indicative schema. Thus, O(A!AB!) and P(A!VB!) are well-formed, but not O(AAB) and P(AVB) if A and B represent indicatives. Further, the deontic calculus must be constructed on the basis of an imperative calculus and not on the standard (indicative) sentential calculus. In Prior’s calculus we have the rule permitting the inference from @ to O(@) if 4 is a theorem in the sentential calculus.6 This must be replaced by the rule permitting the inference from an imperative theorem @! to O(#!), e.g. permitting the inference from (A!V-A!) (‘Close the door or don’t close it,) to O(A!V-A!) (‘You ought to either close the door or not close it’).7

Several consequences follow from this restriction on the form of deontic schemata.

1. ‘Conditional Obligations. It is an oft-noted feature of conditional imperatives, e.g.

6) X, if you have money, pay Y that their antecedents are in the indicative mood. Their form is thus A>B!, with indicative A and imperative B!. The form A!> B! can never occur, since the antecedent is invariably used to state the circumstances in which

28

the prescription expressed by B! is to be obeyed. This restriction on the form of conditional imperatives carries over to the representation of conditional obligations. The normative corresponding to 6), ‘X ought to repay Y if he has the money’, must be represented to O(A>B!). The form O(A!>B!) cannot be used, since the operand is of an improper form. Similarly, for conditional permissions such as ‘X may enter if he is alone’. Their form is P(A>B!), not P(A!>B!).

Now since the prescriptional analysis permits only imperative schemata as operands within deontic schemata, it follows that there can be no inference in deontic logic corresponding to the modal inference from o(A3B) to o(A)>O(B). We cannot infer from O(A>B!) to O(A)3O(B!), since the latter has an antecedent ruled out by our analysis. But A>O(B!) is a perfectly proper conclusion to draw. Indeed, under the prescriptional analysis there is no logical difference between O(A>B!) and A>O(B!), and the two must be regarded as logically equivalent. Hence, any deontic calculus constructed on the basis of this analysis should permit the inference from O(A3B!) to A>O(B!) and from the latter to the former. This carries over to conditional permissions, with P(A>B!) equivalent to A>P(B!).a This result would seem to accord with our intuitions: to say ‘It is obligatory (permissible) for X to pay Y if he has the money’ is but to say ‘If X has the money, he ought (is permitted) to pay Y’.

To adopt the propositional analysis of normatives would require our representing conditional obligations by O(A>B), with A and B representing names of indicative sentences. In the standard deontic calculi based on this analysis, e.g. Prior’s, we find permitted the inference to O(A)3O(B), there being no problem with the form of the antecedent. Attempts have been made to interpret O(A3B) in such a way as to justify this inference and to distinguish it from A 3 q B ) . For Stenius O(A3B) is true when the satisfaction of A commits one also to the satisfaction of B; for Hintikka it describes a relation of “deontic consequence” holding if “it is impossible to realize A in a ‘deontically perfect world’ without realizing B, too.” 9 What perhaps both have in mind (I confess to being unclear about the status of a “deontically perfect world”) is the relation between the premisses and conclusion of a valid imperative inference. From the conjunction ‘Pay Y and Z. we can validly infer ‘Pay Y’, since it is impossible to obey the former without obeying the latter. But the validity of this inference cannot be represented by the ill-formed O(A!>B!). Of course, if the imperative inference from A! to B! is valid, then if O(A!) it follows that O(B!). Thus, if X ought to pay Y and Z, it follows that he ought to pay Z. But this cannot be represented by the distribution of the obligation operator over the implication connective.

2. Chisholm’s Paradox. The distribution of the obligation operator required by the prescriptional analysis allows a natural resolution of the paradox posed by Chisholm’s much discussed “contrary-to-duty imperatives,” conditionals such as ‘X ought to tell his neighbors he is coming if he goes to their assistance’, where there is an obligation to fulfill an

29

antecedent which is in fact unfulfilled, i.e. sentences of the form O(AZ)B!)AO(A!)A-A. As Chisholm shows, it is possible to deduce from a set of plausible premisses in which such a sentence occurs incompatible conclusions stating that an agent ought to both perform and not perform a certain action.10 Thus, from the consistent premisses O(A), O(A>B), -AX(-B), and -A we can infer O(B) and 0(-B). (Take A to represent ‘X goes to the assistance of his neighbors’ and B ‘X tells them he is coming’.) The deduction is only made possible, however, by assuming that the obligation operator distributes over implication, that is, by assuming, as do the standard calculi based on the propositional analysis, that conditional obligations are represented by O(A3B) from which O(A)>O(B) follows. By denying this assumption the prescriptional analysis thus enables the resolution of the paradox.

3. The Paradox of the Good Samaritan. Allowing the obligation operator to operate only on imperative schemata allows us also to resolve, as Castaneda has pointed out, Aqvist’s version of the “Good Samaritan” paradox.11 If we accept the propositional analysis, then we must say that if O(A) and the proposition A entails B, then it follows that O(B) (we ought to do what is entailed by what we ought to do). But suppose that the Good Samaritan ought to help the man Y whom X robbed and left helpless. Then that the Good Samaritan helps Y whom X robbed entails that X robbed Y. Yet it is plainly false that X ought to have robbed Y.

If obligation sentences must be of the form O(c$), this result is avoided. The reformulated rule of inference now permits us to infer from q A ! ) and the entailment of B! by A! to O(B!). The inference is now

The Good Samaritan ought to help Y. ‘Good Samaritan, help Y whom X robbed entails ‘X

robbed Y’. ~ ~~ ~~~~

X ought to have robbed Y. since it is the proposition that X robbed Y that is entailed in the second premiss and not the prescription for him to rob Y, the conclusion is not of the form O(B!). Hence it is not an instance of the valid inference form.

This does not establish, of course, that this paradox can only be resolved under the prescriptional analysis. As for Chisholm’s paradox, it is, no doubt, possible to patch up the framework embodying the alternative analyses. But this resolution should not be, as it has been, an ad hoc one aimed at the paradox alone. It will not do, for example, to distinguish, as does Aqvist, two kinds of obligation (“primary” and “reparational”), when the only justification for the distinction is that it enables the resolution.

4. Reiterated Modalities. Another consequence following from our restriction is the exclusion within any deontic calculus of reiterated deontic modalities, expressions such as OO(A!) or PO(A!).12 Since what is expressed by ‘X ought to do A’ is a proposition and not a prescription, it cannot in turn be given a deontic characterization. This seems to be a

30

welcome result that accords again with out intuitions. Little sense can be made of sentences such as ‘It is obligatory that X ought to do A’ and ‘It is permissible that X ought to do A’. What are obligatory and permissible are actions, not the truth of propositions characterizing these actions. Quite harmless is the expression O(O(A!) 3 A!) (the analogue of one of Prior’sls). This should be interpreted as saying that it is obligatory for A! to be obeyed if to do A is obligatory, and this is no more than the tautology O(A!) 3 O(A!).

5 . Inferences between Normatives and Imperatives. A further simplifi- cation of the deontic calculus has been claimed by Fisher to follow from the prescriptional analysis. Within alethic modal logic the inferences from “(A) to A and from A to O(A) are valid. Where deontic operators are regarded as having within their scopes indicative schemata the corresponding inferences from O(A) to A and from A to P(A) are clearly invalid, and are properly excluded in axiomatizations such as Prior’s. But Fisher argues that where deontic operators are regarded as having imperative schemata as operands the inferences are valid. For he reasons that one who has asserted O(A!) has committed himself to commanding A!. If I were to assert ‘X, you ought to do A’ I would thereby commit myself to commanding ‘X, do A’. To refuse to issue the command would be inconsistent with my assertion. Similarly, the inference from A! to P(A!) is valid, since it would be inconsistent to deny that a certain action is permissible after having commanded someone to perform it.14

But this reasoning is based on the dubious assumption that the com- mitments of the speaker can provide the sole condition for the logical validity of an inference. The assumption certainly does not hold for a wide range of valid indicative inferences. One who has asserted ‘Peter is tired’ can be said to commit himself to also asserting ‘Peter exists’ and ‘I believe that Peter is tired’. To deny the latter would be inconsistent with the assertion of the former. But it is widely (and rightly) accepted that these conclusions cannot be logically inferred. Speaker commitment may be a necessary condition for validity, but it is not sufficient. It must be sup- plemented by the requirement that satisfaction of the premisses guarantees satisfaction of the conclusion. This second requirement is clearly not met by the inference from O(A!) to A!, since it is possible for it to be true that A! ought to be obeyed and for A! to be in fact disobeyed. Similar considerations hold for the inference from A! to P(A!). From the fact A! is obeyed, it does not follow that obeying A! is permitted, and this inference should also be evaluated as invalid. We should thus reject, I think, this attempt to reintroduce a parallel to valid modal inferences. Instead, we are left in deontic logic with the weakened inference from O(A!) to P(A!) licensed in the standard formalizations. If our analysis is correct, normative propositions are in a sense “prescriptive,” but not in the sense of entailing prescriptions.

There are thus minimal modifications required by the prescriptional analysis of the standard formalizations of deontic logic. Retained is the

31

rejection of O(A!)>A! and A!>P(A!) in favor of the weakened axiom O(A!)>P(A!). Excluded are reiterated deontic modalities and the implication O(A>B!)>(O(A)>O(B!)). In place of the latter we have instead O(A>B!)>(A>O(B!)) from which can be derived the equivalence O(A>B!)

A>O(B!). That these modifications accord with our intuitions and allow the resolution of the two paradoxes discussed above can be claimed as a significant corroboration of the analysis.15

NOTES 1P.T. Geach, “Imperatives and Deontic Logic”, Analysis, 18 (1958),

2H. N. Castaneda, “Note on Imperative Logic”, Philosophical Studies, 6 (1955), pp. x 1-4 and “The Logical Structure of Action”, Theoria, 26 (1960), pp. 151-182. The view can perhaps be traced to the distinction in A. Ross, “Imperatives and Logic”, PhiZosophy of Science, 1 1 (1 944), pp. 30-46 between the “validity” and “satisfaction” of an imperative. See also E. J. Lemmon, “Deontic Logic and the Logic of Imperatives”, Logique e f Analyse, 8 (1965), pp. 39-71 for an analysis of ‘ought’ sentences in terms of an imperative being “in force.” The view is also suggested in R. M. Hare, “Some Alleged Differences between Indicatives and Imperatives”, Mind,

3G. H. Von Wright, “Deontic Logic” in Logical Sfudies (London, 1957).

4E. Stenius, “The Principles of a Logic of Normative Systems”,Acta Philosophica Fennica, XVI (1963), pp. 247-260.

5Cf. Castaneda, “Imperatives, Decisions, and ‘Oughts’ ” in Castaneda and Nakhnikian (ed.), Morality and the Language of Conducf (Detroit, 1963). Here the claim that normatives are meta-linguistic is qualified. A normative is said to be an “image” of a meta-linguistic sentence about an imperative, but distinguished from it in its use to directly guide behavior.

6A. N. Prior, Formal Logic, 2nd ed. (Oxford, 1962), pp. 220-229. 7Cf. M. Fisher, “A System of Deontic-Alethic Modal Logic”, Mind,

8These consequences are drawn in Castaneda’s axiomatization in “Acts, the Logic of Obligation, and Deontic Calculi”, Philosophical Sfudies, 29 (1968), pp. 13-26.

gStenius, op. cif. and J. Hintikka, “Some Main Problems in Deontic Logic” in R. Hilpinen (ed.), Deonfic Logic (Dordrecht, 1971).

1oR. Chisholm, “Contrary-to-Duty Imperatives”, Analysis, 24 (1 963), pp. 34-35.

IICastaneda, “On the Semantics of the Ought-to-Do” in Davidson and Harman (ed.), Semantics of Natural Language (Dordrecht, 1972). For Aqvist’s formulation of the paradox see “Good Samaritans, Contrary-to- Duty Imperatives, and Epistemic Obligations”, Nous, I (1967), pp.

pp. 49-56.

LXXVI (1967), pp. 309-326.

LXXI (1962), pp. 231-236.

361 -379.

32

12Cf. Castaneda, op. cit. 13~rior, op. cit. 14Fisher, op. cit. 151 am grateful to R. M. Hare for criticisms of an earlier draft of this

paper.

33

the prescriptional analysis of normatives

Documents