R. M. Hare, The Language of Morals (1952)

2
IMPERATIVES AND LOGIC

2.1. In order to characterize clearly the difference between imperatives and indicatives, it will be helpful so to analyse the two types of sentence, as to make it plain what elements of meaning they have in common, and so isolate the essential difference. Since I have already attempted to do this in an article referred to above (1.4), I shall be as brief as possible.

We have noticed that the two sentences 'You are going to shut the door' and 'Shut the door' are both about the same thing, namely, your shutting the door in the immediate future; but that they are used to say different things about it. It is purely an accident of grammar that those parts of the spoken or written sentence which, in either case, refer to this thing that they are about, are not identical. Let us recast the sentences more clearly by writing in both cases an identical phrase for referring to this thing that they are both about. The phrase might be:

Your shutting the door in the immediate future.
We shall then have to add something, different in each case, which supplies the rest of what each sentence conveys. What we have so far tells us quite clearly what the sentences are about. It does not, however, tell us what the speaker is saying about it. We do not know whether he is stating that your shutting the door in the immediate future is what is going to happen or be the case, or whether he is telling us to make it the case, or something else. In order to complete the sentences, therefore, something has to be added to tell us this. We might complete the sentences as a command or a statement respectively, by writing:

Your shutting the door in the immediate future, please.
Your shutting the door in the immediate future, yes.
These two sentences would correspond to the normal English
Shut the door.
You are going to shut the door.

We shall need technical terms for referring to these different parts of sentences. The terms adopted in my article are not altogether satisfactory, and therefore I shall coin entirely new words. I shall call the part of the sentence that is common to both moods ('Your shutting the door in the immediate future') the phrastic; and the part that is different in the case of commands and statements ('yes' or 'please') the neustic. Readers of Liddell and Scott's Greek Lexicon will recognize the appropriateness of these terms. 'Phrastic' is derived from a Greek word meaning 'to point out or indicate', and 'neustic' from a word meaning 'to nod assent'. Both words are used indifferently of imperative and indicative speech. The utterance of a sentence containing phrastic and neustic might be dramatized as follows:

  1. The speaker points out or indicates what he is going to state to be the case, or command to be made the case;
  2. He nods, as if to say 'It is the case', or 'Do it'. He will, however, have to nod in a different way, according as he means one or other of these things.

2.2. Now clearly, if we are looking for the essential difference between statements and commands, we have to look in the neustic, not in the phrastic. But, as the use of the single word 'neustic' indicates, there is still something in common between indicative and imperative neustics. This is the common notion of, so to speak, 'nodding' a sentence. It is something that is done by anyone who uses a sentence in earnest and does not merely mention it or quote it in inverted commas; something essential to saying (and meaning) anything. The absence of inverted commas in written language symbolizes the element of meaning of which I am speaking; to write a sentence without inverted commas is like signing a cheque; to write it within inverted commas is like drawing a cheque without signing it, e.g. to show someone how to draw cheques. We could have a convention that, instead of putting inverted commas round sentences that we were mentioning and not using, we nodded, or made some special mark in writing, when we were using a sentence in earnest. The 'assertion symbol' in the logical system of Frege, and in that of Russell and Whitehead has, among other functions, this one of signifying the use or affirmation o a sentence.1 It could, in this function, be applied to commands as well as to statements. We may perhaps strain language slightly an use the word 'affirm' of both.

Closely allied to such an affirmation sign would be a sign for agreement or assent for use by a hearer. To use such a sign of assent would be tantamount to repeating the sentence with the pronouns, &c., changed where necessary. Thus, if I said 'You are going to shut the door', and you answered 'Yes', this would be a sign of assent, and would be equivalent to 'I am going to shut the door'. And if I said 'Shut the door', and you answered 'Aye, aye sir', this likewise would be a sign of assent; if we wished to express what it is equivalent to, we might say 'Let me shut the door' or 'I will shut the door' (where 'I will' is not a prediction but the expression of a resolve or a promise). Now this should give us a clue to the essential difference between statements and commands; it lies in what is involved in assenting to them; and what is involved in assenting to them is, as I have said, closely allied to what is involved in affirming them in the first place.2

If we assent to a statement we are said to be sincere in our assent if and only if we believe that it is true (believe what the speaker has said). If, on the other hand, we assent to a second-person command addressed to ourselves, we are said to be sincere in our assent if and only if we do or resolve to do what the speaker has told us to do; if we do not do it but only resolve to do it later, then if, when the occasion arises for doing it, we do not do it, we are said to have changed our mind; we are no longer sticking to the assent which we previously expressed. It is a tautology to say that we cannot sincerely assent to a second-person command addressed to ourselves, and at the same time not perform it, if now is the occasion for performing it and it is in our (physical and psychological) power to do so. Similarly, it is a tautology to say that we cannot sincerely assent to a statement, and at the same time not believe it. Thus we may characterize provisionally the difference between statements and commands by saying that, whereas sincerely assenting to the former involves believing something, sincerely assenting to the latter involves (on the appropriate occasion and if it is within our power), doing something. But this statement is over-simplified, and will require qualification later (11.2).

In the case of third-person commands, to assent is to join in affirming. In the case of first-person commands ('Let me do so and so') and resolves ('I will do so and so'), which are closely similar to one another, affirmation and assent are identical. It is logically impossible for a man to dissent from what he himself is affirming (though of course he may not be sincere in affirming it).

2. 3. It must be explained that, as I am using the word affirm, it is not the opposite of 'negate'. It is possible to affirm either an affirmative sentence or a negative one. The sign of negation, 'not', is normally part of the phrastic of both indicatives and imperatives; thus, instead of 'You are not going to shut the door' we should write 'Your not shutting the door in the immediate future, yes'; and instead of 'Do not shut the door', we should write 'Your not shutting the door in the immediate future, please'. Modal sentences containing the word 'may' could, it seems, be represented by negating the neustic; thus 'You may shut the door (permissive) might be written 'I don't tell you not to shut the door' and this in turn might be rendered 'Your not shutting the door in the immediate future, not-please'; and similarly, the sentence 'You may be going to shut the door' might be rendered 'I don't say you aren't going to shut the door' or 'Your not shutting the door in the immediate future, not-yes'. But these are complications into which we need not enter.

I have indicated in the article already referred to that in their ordinary uses the common logical connectives 'if', 'and', and 'or', like the sign of negation, are best treated as part of the phrastic of sentences. This means that they are common ground between indicatives and imperatives. The same is true, with a certain qualification to be mentioned later (11.5), of the quantifiers 'all' and 'some'. I am not now so sure that in ordinary language these words behave, logically, in exactly the same way in imperatives as they do in indicatives; but be this as it may, the differences are purely an accident of grammar. By using the ordinary logical connectives, as they are used in the indicative mood, in the phrastics of our remodelled imperative sentences, we could do with the revised imperative mood everything that we now do with the natural one. This is clear from the fact that, by a circumlocution, we couid always, instead of a simple command (e.g. 'Shut the door or put the door-stop in position', said to Jones) substitute the command to make an indicative sentence true (e.g. 'Make the sentence "Jones is going to shut the door or put the door-stop in position" true'). This, however, is not to be construed as an admission of the logical primacy of the indicative mood (whatever that might mean); for we could do the same the other way round -- e.g. by saying, instead of 'Jones shut the door at 5 p.m.', 'The command [actual or imagined] "Let Jones shut the door at 5 p.m." was obeyed'. The only restriction on this procedure is due to the fact, referred to later (12.4), that the imperative mood is much less rich than the indicative , especially in tenses.

The imperative and the indicative moods also have in common, because of their common phrastic element, everything to do with their reference to actual or possible states of affairs. There is a possible state of affairs referred to by the phrastic 'Your shutting the door in the immediate future'. This reference is not affected by what comes after. Both imperatives and indicatives have to refer to the state of affairs which they are about. This means that imperatives, like indicatives, can suffer from the malady to which the so-called verification theory, of meaning draws attention; for this malady, being a malady of the phrastic, has nothing to do with statements as such; those who thought so were misled. One of the ways in which a sentence can fail to signify is for it to refer to no identifiable state of affairs. Thus the sentences 'The Absolute is green' and 'Let the Absolute be made green' are meaningless for the same reason, namely, that we do not know what is referred to by 'The Absolute being green'. Sentences may also for this reason fail to be understood by one person, though perfectly significant to another; thus the command 'Luff' is meaningless to those who do not know what luffing consists in. It would be unfortunate if the verification criterion were thought to impugn the meaningfulness of all but indicative sentences -- as if 'Shut the door' was as meaningless as 'Frump the bump'.

There is another malady to which imperatives, like indicatives, are liable, owing to the presence of logical connectives in the phrastics of both of them. This is called, in the case of indicatives, self-contradiction; and the term is equally applicable to imperatives. Commands as well as statements can contradict one another. Even if this were not a normal way of speaking, we might well adopt it; for the feature to which it draws attention in commands is identical with that which is normallv called contradiction. Consider the following example, taken from Lord Cunningham's autobiography.3 The admiral and the captain of a cruiser which is his flagship shout almost simultaneously to the helmsman in order to avoid a collision, one 'Hard 'a port' and the other 'Hard 'a starboard'. Lord Cunningham refers to these two orders as 'contrary'; and so they are, in the proper Aristotelian sense.4 It follows that the two orders contradict one another in the sense that the conjunction of them is self-contradictory; the relation between them is the same as that between the two predictions 'You are going to turn hard 'a port' and 'You are going to turn hard 'a starboard'. Some orders can, of course, be contradictory without being contrary; the simple contradictory of 'Shut the door' is 'Do not shut the door'.

It might be held that the law of the excluded middle does not apply to commands. This, however, is a mistake if it is implied that commands are peculiar in this respect. It is quite clear that if I do not say 'Shut the door' this does not compel me, logically, to say 'Do not shut the door'. I can say 'You may either shut the door or not shut the door'; or I can say nothing at all. But similarly, if I do not say 'You are going to shut the door', this does not compel me logically to say 'You are not going to shut the door'. I can say 'You may be going to shut the door, and you may be going not to shut the door', or I can say nothing at all. But if asked 'Am I going to shut the door or not?' I have to answer, because of the terms of the question, either 'You are going to shut the door' or 'You are not going to shut the door' unless I refuse to answer the question at all. 'You may be going to' is not an answer to this question. And similarly, if I am asked 'Shall I shut the door or not?' I have to answer, if I answer the question at all, either 'Shut it' or 'Don't shut it'. The truth is that our language possesses ways of speaking in a three-valued way and ways of speaking in a two-valued way; and these two ways are available in both the indicative and the imperative moods.

Another way of showing that simple imperatives are normally two-valued is to point out that the advice (to a chess player) 'At your next move, either move your queen or don't move your queen' is analytic (I define this term below (3.3)). It gives the player no positive instructions whatever as to what he is to do, just as the sentence 'It is either raining or not raining' tells me nothing about the weather.5 If the logic of simple imperatives were three-valued, the sentence quoted would not be analytic; it would positively exclude a third possibility, that of neither moving the queen nor not moving her. Imperative disjunctions of this form are not always analytic; for example 'Either stay in or don't stay in' would naturally be taken to imply 'Don't stand blocking the doorway'; but this has nothing to do with the imperative as such; it is a feature of the phrastic of the sentence, as is shown by comparing the parallel indicative sentence 'You're going either to stay in or not stay in (sc. you're not going to stand dithering there in the doorway)'.

2.4. It follows, from the fact that commands may contradict one another, that in order to avoid self-contradiction, a command, like a statement, must observe certain logical rules. These rules are the rules for the use of all the expressions contained in it. In the case of some expressions -- the so-called logical words -- these rules are what give the expressions all the meaning they have. Thus to know the meaning of the word 'all' is to know that one cannot without self-contradiction say certain things, for example 'All men are mortal and Socrates is a man but Socrates is not mortal'. If the reader will reflect, how he would tell whether someone knew the meaning of the word 'all', he will see that the only way he could do it would be by finding out what simpler sentences that person thought were entailed by sentences containing the word 'all'. 'Entailed' is a strong word, and logicians nowadays are not given to using strong words; a full discussion of its meaning, especially in mathematical contexts, would occupy many pages; but for my present purposes it may be defined accurately enough as follows:

A sentence P entails a sentence Q if and only if the fact that a person assents to P but dissents from Q is a sufficient criterion for saying that he has misunderstood one or other of the sentences.6
'Sentence' here is an abbreviation for 'sentence as used by a particular speaker on a particular occasion'; for speakers may on different occasions use words with different meanings, and this means that what is entailed by what they say will also differ. We elicit their meaning by asking them what they regard their remarks as entailing.7

Now the word 'all' and other logical words are used in commands, as in statements. It follows that there must also be entailment-relations between commands; for otherwise it would be impossible to give any meaning to these words as used in them. If we had to find out whether someone knew the meaning of the word 'all' in 'Take all the boxes to the station', we should have to find out whether he realized that a person who assented to this command, and also to the statement 'This is one of the boxes' and yet refused to assent to the command 'Take this to the station' could only do so if he had misunderstood one of these three sentences. If this sort of test were inapplicable the word 'all' (in imperatives as in indicatives) would be entirely meaningless. We may therefore say that the existence in our language of universal sentences in the imperative mood is in itself sufficient proof that our language admits of entailments of which at least one term is a command. Whether the word 'entail' is to be used for these relations is only a matter of terminological convenience. I propose so to use it.8

I gave, in the article quoted, a number of examples of entailments whose conclusions are commands. It would seem possible in principle, since the ordinary logical words occur in the phrastics of imperatives, to reconstruct the ordinary sentential calculus in terms of phrastics only, and then apply it to indicatives and imperatives alike simply by adding the appropriate neustics.9 It would remain to be determined to what extent the calculus, as so reconstructed, would correspond to our ordinary language; this is a familiar problem in the case of indicative logic, and its solution depends on patiently investigating, whether the logical signs in the calculus are bound by the same rules as determine the meanings of the logical words which we use in our normal speech. It might be found that ordinary speech has a number of different rules for the use of the words 'if, 'or', &c., in different contexts; and in particular their use in indicative contexts might differ from their use in imperative contexts. All this is a matter for inquiry; but it does not in the least affect the principle that, provided that we either find out what the rules are, or lay down what they are to be, we can study the logic of imperative sentences with as much assurance as that of indicatives. There can be, here as elsewhere, no question of 'rival logics', but only of alternative rules determining the use (i.e. the entailment-relations) of our logical signs; it is a tautology to say that so long as we continue to use our words in the same sense, their entailment-relations will remain the same.10

2. 5. Here we need not go into these complications. We shall need, in this inquiry, to consider only the inference from universal imperative sentences, together with indicative minor premisses, to singular imperative conclusions. I have already given an example of such an inference, and maintained that, if it were impossible to make inferences of this kind, the word 'all' would have no meaning in commands. But this type of inference does raise a further difficulty, because one of the premisses is in the indicative, and one in the imperative. The inference is:

Take all the boxes to the station.
This is one of the boxes.
∴ Take this to the station.
It might be asked how we are to know, given two premisses in different moods, in what mood the conclusion is to be. The problem of the effect upon inferences of the moods of premisses and conclusion has been ignored by logicians who have not looked beyond the indicative mood; though there is no reason why they should have ignored it; for how should we set about demonstrating that the conclusion from a set of indicative premisses must also be in the indicative? But if, as I do, we regard the entailment-relations of ordinary logic as relations between the phrastics of sentences, the problem becomes pressing. Granted that the reason for the validity of the above syllogism is that the phrastics 'Your taking all the boxes to the station and this being one of the boxes' and 'Your not taking this to the station' are logically inconsistent with one another, because of the logical rules governing the use of the word 'all', how are we to know that we cannot add neustics in a different way from the above? We might write, for example:
Take all the boxes to the station.
This is one of the boxes.
∴ You are going to take this to the station.
and call this a valid syllogism, which it plainly is not.

Let me first state two of the rules that seem to govern this matter; we may leave till later the question of their justification. The rules are:

  1. No indicative conclusion can be validly drawn from a set of premisses which cannot be validly drawn from the indicatives among them alone.
  2. No imperative conclusion can be validly drawn from a set of premisses which does not contain at least one imperative.

It is only the second rule which will concern us in this inquiry. There is a very important apparent exception to this rule, the so-called 'hypothetical imperative', with which I shall deal in the next chapter. For the moment, however, let us take the rule as it stands. It is of the most profound importance for ethics. This will be clear if I give a list of some famous arguments in ethics that seem to me to have been wittingly or unwittingly founded upon it. If we admit, as I shall later maintain, that it must be part of the function of a moral judgement to prescribe or guide choices, that is to say, to entail an answer to some question of the form 'What shall I do?' -- then it is clear, from the second of the rules just stated, that no moral judgement can be a pure statement of fact. On this foundation rests, indirectly, Socrates' refutation of Cephalus' definition of justice as 'speaking the truth and giving back anything that one has received from anyone', and of all Polemarchus' subsequent modifications of this definition.11 Aristotle was appealing indirectly to this rule when he made his most decisive break with Platonism, his rejection of the Idea of the Good; he gave, among other reasons, the reason that if there were such an Idea, sentences about it would not be action-guiding ('it would not be a good that you could by your action bring into existence').12 In the place of a factual, existing good, knowable by a kind of supra-sensible observation, Aristotle puts a 'good to be achieved by action' or, as he usually calls it, an 'end'; that is to say, he implicitly recognizes that, if to say something is good is to guide action, then it cannot be merely to state a fact about the world. Most of his ethical differences from Plato can be traced to this source.

In this logical rule, again, is to be found the basis of Hume's celebrated observation on the impossibility of deducing an 'ought'-proposition from a series of 'is'-propositions -- an observation which, as he rightly says, 'would subvert all the vulgar systems of morality', and not only those which had already appeared in his day.13 Kant, too, rested upon this rule in his polemic against 'Heteronomy of the will as the source of all spurious principles of morality'. There he says 'If the will . . . going beyond itself seeks this law in the character of any of its objects -- the result is always heteronomy'.14 The reason why heteronomous principles of morality are spurious is that from a series of indicative sentences about 'the character of any of its objects' no imperative sentence about what is to be done can be derived, and therefore no moral judgement can be derived from it either. In more recent times this rule was the point behind Professor G. E. Moore's celebrated 'refutation of naturalism', as we shall later see (11. 3). It was also the point behind Prichard's attack upon Rashdall.15 Prichard in effect argues that the goodness of a situation (which both he and those he is attacking regard as a fact about the situation) does not by itself constitute a reason why we ought to try to bring that situation into being; we need also what he (somewhat misleadingly) calls 'the feeling of imperativeness or obligation which is to be aroused by the thought of the action which will originate it'. And indeed, if the word 'good' is treated in the fashion that many intuitionists have treated it, this argument is perfectly valid; for sentences containing the word as so understood will not be genuine evaluative judgements, because no imperatives can be derived from them.16 But this objection applies, not only to the intuitionist theory of 'good', but to all who insist on the solely factual character of moral judgements; it applies to Prichard himself. Professor Ayer17 uses an argument against intuitionists in general which is based upon this fundamental rule. But in all these cases the appeal to the rule is only implicit. I know only two places in which the rule is explicitly stated; the first is by Poincare,18 who, however, makes what seems to me an illegitimate use of it, as will be apparent from the preceding argument; the second is by Professor Popper.19 Popper rightly refers to the rule as 'perhaps the simplest and the most important point about ethics'. A judgement is not moral if it does not provide, without further imperative premisses, a reason for doing something.

Notes

1 See Russell and Whitehead, Principia Mathematica, i. 9.

2 For some interesting remarks about the kindred notions of 'admitting' and 'confirming', see P. F. Strawson, 'Truth', Analysis ix (1948-9), 83, and Aristotelian Society, Supplementary vol. xxiv (1950), 129.

3 Viscount Cunningham, A Sailor's Odyssey, p. 162.

4 Categories, 6a 17.

5 Wittgenstein, Tractatus, 4.461.

6 More complicated entailments, such as those in mathematics, might be covered by extending this definition as follows: the definition given would be treated as a definition of direct entailment, and indirect entailment would be defined as holding between two sentences P and R when there is a series of sentences Q1, Q2 . . . Qn such that P directly entails Q1, Q1 directly entails Q2, &c, and Qn directly entails R. But even this may not be sufficiently exact.

7 For an indication of how logical symbols may be defined in terms of the entailment-relations of sentences containing them, see K. R. Popper, 'New Foundations for Logic', Mind, lvi (1947), 193, and 'Logic without Assumptions', Aristotelian Society xlviii (1946-7), 251.

8 The reasons why many people have wished to deny that commands can entail or be entailed are mainly historical. But Aristotle speaks of practical as well as theoretical syllogisms (Movement of Animals, 701a 7 ff., Nicomachean Ethics, 1144a 31). He treated the major premiss of the former as a gerundive or a 'should'-sentence or in other ways, but never seems to have realized how different these forms are from normal indicatives. Moreover he says that the conclusion is an action (not an imperative enjoining an action). He finds the principal logical difference between practical and theoretical reasoning not in the prescriptive character of the former (which he recognizes) but in the fact that, having to conclude in an action, it has to refer to contingent particulars, which theoretical syllogisms (for reasons which we should question) are not by him allowed to do (Nicomachean Ethics, 1129b 19 ff., 1140a 31 ff., 1147a 2). This led him to assign a logically inferior status to practical inferences, though they are fundamental to his whole ethical theory; and his work on them has been strangely neglected. It is interesting that his general definition of syllogism, though always given in an indicative context, is sometimes (though not always) put in a form which could apply equally to imperatives: 'Syllogism consists in saying, given certain things, something further which follows necessarily from them' (Sophistical Refutations, 161a 1; cf. Topics, 100a 25, Prior Analytics, 24b 18).

9 An attempt on these lines has already been made by A. Hofstadter and J. C. C. McKinsey, 'On the logic of Imperatives', Philosophy of Science, vi (1939), 446 ft.; but see comments by A. Ross, 'Imperatives and Logic', ibid, xi (1944), 30 ff.

10 For a discussion of possible differences between imperative and indicative logic, see G. H. von Wright, 'Deontic Logic', Mind, lx (1951); it is important to realize that modal imperative logic is as distinct from the logic of simple imperatives as in the case of the indicative mood.

11 Plato, Republic, 331 c ff.

12 Nicomachean Ethics, 1096b 32.

13 Treatise, iii. 1, i.

14 Groundwork of the Metaphysic of Morals, tr. H. J. Paton, pp. 108 ff.

15 Moral Obligation, p. 4.

16 For a similar view, cf. W. K. Frankena, in The Philosophy of G. E. Moore, ed. P. Schilpp, p. 100.

17 'On the Analysis of Moral Judgments', Philosophical Essays, p. 240.

18 Dernieres pensees, p. 225.

19 'What can Logic do for Philosophy?', Aristotelian Society, Supplementary Vol. xxii (1948), 154; cf. The Open Society, ii. 51 ff.