Originally published in Mind, vol LXXIX, No 315, July 1970, pp 385--394
This is a sequel to Aaron Sloman How to derive ``better'' from ``is'',
in American Philosophical Quarterly, Vol 6, Number 1, Jan 1969, pp 43--52.

Re-formatted: 24 Jan 2016

This file is http://www.cs.bham.ac.uk/research/projects/cogaff/sloman-ought-and-better.html
Or PDF http://www.cs.bham.ac.uk/research/projects/cogaff/sloman-ought-and-better.pdf
One word has been changed in this version of the paper, on aesthetic grounds.


Aaron Sloman
School of Computer Science, University of Birmingham.
(Originally written at University of Sussex)

A. Some problems

It is often said that `ought' implies `can', yet it is clear that one can say without contradiction such things as `The government ought to build more primary schools, but lacks the means', or `Ideally, you ought to pay for the damage you have done, though I know you cannot afford it'. Must this be a peripheral or "weakened" sense of `ought'? (Cf. R. M. Hare, Freedom and Reason, ch. 4.)

Modus ponens is a valid principle of inference, yet one can accept (i) `If William is the mayor then he ought to attend the meeting in the Town Hall today' and (ii) `William is the mayor', yet reject (iii) `William ought to attend the meeting in the Town Hall today', e.g. if William's wife is ill. Must we construe this as either a case of inconsistency, or a case of ambiguity of' ought' ?

Sentences using `ought' appear to have some kind of non-descriptive force (e.g. commending, guiding actions, committing the speaker), in which case it would seem that no `ought' statement can follow logically from purely factual statements lacking such force. Yet from factual statements about slowness and liability to breakdown of alternative means of transport it seems possible validly to infer: `In order to get to London by noon you ought to go by train'. Does `ought' sometimes follow from `is'?

'Ought' can be used to say what is highly likely, as in `Judging by those clouds, it ought to rain this afternoon'. Most philosophical analyses of `ought' don't seem to apply to this use: is this because it is simply a different meaning of the word, with no connection between the various uses? Then isn't it odd that `should', `must' and `may' (as well as many other words) have a similar ambiguity? Can we find no unitary analysis to cover: `You ought to tell the truth' and `It ought to rain today'?

It seems to be possible to deal with these problems by investigating the hidden logical structure of `ought' statements, and bringing out the connection between `ought' and `better'.

B. The hidden structure of `ought' statements

Philosophers generally discuss uses of `ought' in sentences of the form:

 (1)  A ought to do X.

But this is only a special case of the more general form:

 (2)   It ought to be the case that p,

where p is a possible state of affairs. For (1) is surely equivalent to:

 (3)  It ought to be the case that A does X.

Note that this does not mean the same as `someone ought to bring it about that A does X'.

What does the general form (2) mean? It could say that p is likely or probable: this interpretation will be discussed later, so let us ignore it for the present. Or it could say that possibility p is better than the alternatives, for someone who said `p ought to be the case, but it would be better if q were the case', where p and q are incompatible, would be contradicting himself. But better than what alternatives? After all, p might be the best member of one class of possibilities yet only the third-best member of another class. So the relevant comparison class of possibilities must be made explicit if ambiguity is to be avoided, thus:

 (4)  p is better than the alternative possibilities in the class Z, or, equivalently,

 (5)   Among the possibilities in Z, p ought to be the case.

However, (2) could be said when p is not itself the best of the possibilities under consideration, but is a logically or causally necessary condition for the best possibility. The best way of curing a certain patient may be giving him drug P and drug Q simultaneously (even though either alone might be fatal): this implies that he ought to be given drug P and drug Q, but it also implies that he ought to be given drug P. So a more general interpretation of (2) would be:

 (6)  p is, or is a necessary condition for, the best of the possibilities in the class Z.

Strictly, we should also allow for the possibility that several members of Z, namely q, r,... s, are equally good and all better than other members of Z: in this case p would be, or be a necessary condition for, the exclusive disjunction of q, r,... and s. (inclusive, in case the combination of two possibilities is worse than either alone.) I shall ignore such complications for present purposes, and assert as my main thesis that (2) can be regarded as elliptical for (6). In section D, I shall discuss the conditions under which (6) (and therefore (2)) could be assertive, i.e. could express a true or false proposition. We shall see that this would require (6) to have a still more complicated hidden structure. Meanwhile, let us look a bit more closely at the notion of a comparison class.

C. Types of comparison class. 'Ought' and `Can'

It would be rash to claim that anyone who makes an `ought' statement must always have some definite comparison class of possibilities in mind. Instead, I claim merely that the less clear one is about which range of alternatives is under consideration when one is singled out as best, or what ought to be, the less clear it is what the implications are of what one is saying: e.g. was the possibility q rejected as inferior to p, or was q simply not considered as a possibility? In ordinary discourse, the relevant comparison class Z is very rarely made explicit, since it can often be inferred from the context of discussion. If it were made explicit it might be of any of the following types:

(a)   Z could be any arbitrary collection of possible states of affairs, though if wholly arbitrary it would be of little interest.

(b)   Z may contain just two possibilities, p and not-p, e.g. 'the existence somewhere, sometime, of human beings' and `the non-existence anywhere of human beings'. Here `p ought to be the case' amounts to `p is (or would be) better than not-p'. However, if a more extensive class of possibilities is taken into account, then thinking p to be better than not-p does not justify saying that p ought to be the case, for another possibility q, incompatible with p, may be better than p. (E.g. p = A gives exactly 7/8 of what he can spare to good causes, q = A gives all he can spare to good causes. Prior assumption: all proportions are equally likely.)

(c)   The most common type of comparison class is one which contains possible developments of some particular situation q, i.e. possible states of affairs or sequences of events which could succeed the state of affairs q. Thus q might be the economic and political situation in some British colony in 1910, and Z the class of logically possible subsequent states of affairs.

(d)   Instead of including all the logically possible developments of a situation q, Z may be restricted to include only those which could be brought about by some specified agent. This restriction may be implied by making an agent the subject of `ought' as in `You ought. . .', `America ought. . .'.

(e)   The class of possible developments of a situation might be restricted in other ways, e.g. (i) by considering a narrower type of possibility than logical possibility, such as physical, psychological, economic or sociological possibility, so that some logical possibilities are ruled out of the comparison class Z on the basis of known scientific laws; or (ii) by ruling out some possibilities as improbable, so that only developments whose probability relative to evidence available at the time of discussion exceeds some specified minimum are included in Z; or (iii) by restricting Z in case (d) to include only developments which would lie within the power of a normal agent of the type under consideration.

(f) The comparison class Z may, in addition be restricted by some constraint, i.e. a condition which all its members must satisfy, such as: bringing about a certain specified result in a fixed time; or involving the death of no innocent persons; or maintaining certain variables {e.g. temperature, cost of living, amount of effort expended) within certain bounds; or not interfering with some specified programme.

Although the above is not an exhaustive or systematic classification of types of comparison class, it does illustrate the variety of ways in which the possibilities under consideration may be restricted. Of course, some race of supermen might always consider all possibilities when trying to decide what ought to be the case, or what ought to be done. But our considerations are limited, not only by the bounds of our own imagination and knowledge, but also by the structure of the practical situations in which we are faced with such questions: our prior decisions, principles, commitments, etc., impose restrictions or constraints on the possibilities we can consistently take into account.

In particular, in a context in which an `ought' statement is made with the obvious intention of giving relevant practical advice to some individual, the comparison class Z must be restricted to what is a practical possibility for him, i.e. to what he can do or bring about, otherwise the statement will lose its point. In other words, the giving of advice or recommendation implies that practical possibilities are being advocated, so only the relative merits of these need to be considered. This is all that lies behind the dogma that `ought' implies `can'. But why should we not also compare wider ranges of possibilities and say which we think is best? This is not excluded by the meaning of `ought'. The word does not have to be used to give immediately relevant practical advice or criticism, and it is easy to prevent any such interpretation with the aid of such expressions as `ignoring the practical difficulties in the situation', or `ideally'. Indeed such relatively unrestricted `ought' statements can even have an indirect practical relevance, for our deliberations or advice about what ought to be done in actual situations may well be clarified, or even inspired, by considering some impractical possibilities. I conclude that although `ought' implies `logically can', it does not imply `practically can', though the latter implication is sometimes generated by the context. Where others claim to see differences in meaning of `ought', we now see differences in the comparison class.

D. The basis of comparison

Returning now to (6) of section B, which I claimed revealed the hidden structure of `ought' statements, let us consider under what conditions it can assert something true or false. It is clear that one thing cannot simply be better than another : it must be better at or for something, or better in relation to some basis of comparison. Of course, one of the two can simply be preferred, or recommended, or prescribed: but that does not amount to being better. Of any two things each will be better in relation to some basis or other. For instance, of two incompatible policies one may be better at promoting economic growth while the other is better at reducing crime. This illustrates the general point that unless some basis of comparison is specified, the question `Which is better?', or the statement `This is better than that' must be incomplete. This implies that (6) (and therefore also (2)), if it is to assert something unambiguously, must be elliptical for something like:

  (7)   p is, or is a necessary condition for, the best, relative to the basis B, of the possibilities in the class Z.

In terms of `ought' this would be:

  (8)   Considering the possibilities in Z, p ought to be the case relative to the basis B,

or, symbolically: `Ought (p, Z, B)'. Here `ought' is effectively an operator on three arguments, even though this may be concealed in ordinary forms of expression.

In the simplest cases, the basis B will specify some condition, such as `promoting happiness', or `getting to London within 2 hours', and to say that something is better, or best, in relation to B will then be (roughly speaking) to say that it is more, or most, conducive to satisfaction of that condition. In more complex cases of comparison, `more conducive' may be qualified by reference to other factors, e.g. 'more conducive in respect R, in circumstances S'. Thus a more explicit representation of the most general form of (7) would specify that the basis B necessarily includes a condition C, which I call the "reference condition", and possibly also other factors such as R and S.

However, we need not go into such details here. (For further details, and a demonstration that all these concepts can be defined in purely logical terms, see 'How to derive "Better" from "Is"', in American Philosophical Quarterly, January 1969.)

If a basis of comparison is specified, the statement that one thing is better than another relative to that basis is a purely factual true or false statement, such as `Willie is better than Winnie at standing on one leg', `Smoking brand X is better than smoking brand Y if you want to contract lung cancer as soon as possible'. In so far as `ought' statements can be analysed in terms of `better' they too are factual statements when a basis of comparison is explicit, as in `In order to get to London by noon, you ought to go by train'; hence they may be logically derivable from other factual statements. However, in suitable contexts, for instance where the basis specifies some condition C which the hearer wants satisfied, interaction between the basis and the context can generate non-descriptive (e.g. action-guiding) force: thus, the hearer may be given reason (or more precisely prima facie reason) to prefer something or choose it. To say what is better, or what ought to be, relative to a basis B specifying a condition which someone (speaker, hearer, the majority of people, everyone, etc.) wants satisfied, or might want satisfied in certain circumstances, may have a practical point. As noted in section C, the extent to which it is immediately relevant in a practical way, can depend not only on the basis, but also on whether the comparison class Z is restricted to practical possibilities. However, on our analysis, it is not part of the meaning of `ought' that it should have any immediate practical relevance. Where others claim to see differences in meaning of `ought', we can now see differences in basis of comparison, as well as differences in comparison class.

E. `Ought' and `must'

It is worth comparing statements about what ought to happen or be done with statements about what is obligatory, essential, or what must happen or be done. Where the former kind of statement says (what is a necessary condition for) what is best, or better than all alternatives, the latter picks out the only candidate (or a necessary condition for it). For instance `If you want to get to London by noon, then you ought to go by train' picks out the best means without excluding the possibility of others, whereas `If you want to get to London by noon then you have to (must, will be obliged to etc.) go by train' implies that no other means exists. (Cf. `On being obliged to act', by A. R.. White, in The Royal Institute of Philosophy Lectures (1966-67, ed. G. N. A. Vesey.) With `must', `obliged' and equivalents, as with `ought', no true or false assertion can be made unless a basis is specified as the source of the obligation or necessity: e.g. the achievement of some goal, or the satisfaction of some other condition, such as getting one to London by noon. Where no basis is made explicit, such statements must be regarded as elliptical or incomplete, unless they have some purely non-assertive (e.g. imperative) force.

Relative to a given basis B we can compare a number of different possibilities, and subdivide them into the following categories. First there are the alternatives which are necessary relative to the basis: these are what must be or be done. Then there are those whose negations are necessary: these are wrong, or prohibited. Those whose negations are not necessary are permitted, or what may be. Amongst the latter, the possibility which is best relative to B, is the one which ought to (or should) happen or be done. This contrast between `ought' and `must' is obliterated by referring to both as cases of "obligation", or by attempting to define `ought' in terms of `not permitted not to', or `what is required, or demanded'. Perhaps this is a symptom of a perfectionist approach, which requires every basis of comparison to demand that "only the best is good enough", or "nothing but the best will do". However, it is quite possible for a moral code for instance to make a distinction between minimum standards of behaviour, i.e. what one must do, and the highest standards, i.e. what one ought to do. Only a primitive moral code need be composed merely of commandments.

F. Apparent breakdown of logical principles

We have noted that without a basis of comparison, a sentence using `ought', `must', etc. cannot express a complete true or false proposition. As previous illustrations show, there are various ways in which a basis may be explicit, including the use of such phrases as `From the point of view of.. .', `In order to achieve ...','If you want...', `If you're the mayor ...', or `If there's to be . . .'. Where an `if' clause specifies a basis of comparison, as in `If you want to travel safely you ought to buy seat belts', then the statement thus made is not really a conditional statement, since the apparent consequent does not express a complete proposition on its own. This explains why the attempt to apply logical principles of inference which work for genuine conditional statements breaks down where `ought' and `must' are involved. Thus, if modus tollens were applicable one could infer from `You ought not to buy seat belts' and the above statement to `You don't want to travel safely'. Transposition of the original example would lead to the nonsensical `If you ought not to buy seat belts then you don't want to travel safely'. There is a stronger temptation to apply modus ponens, using a second premiss `You want to travel safely', to infer `You ought to buy seat belts'. But this is illegitimate since the latter does not express any complete statement on its own—unless it is elliptical for our original sentence with the `if' clause. Similar remarks can be made about `If you want to travel safely then you must buy seat belts'.

There are other forms of inference which appear to break down when we use methods of indicating the basis of comparison which disguise the logical structures involved. For instance, in `A carving knife ought to be very sharp', `Anyone who wants to win ought to train hard', or `Teachers ought to prepare their lessons in advance', we do not have universal statements of the form `All A are B' where `A' and `B' are complete predicates. `All A's ought to be X' must be construed as being of the form `The best way to fulfil the (normal or standard) role of an A is to be an X'. Thus the appearance of validity of:


Teachers ought to prepare their lessons in advance.
Miss W is a teacher
Therefore, Miss W ought to prepare her lessons in advance.

is deceptive. The "conclusion" is not a complete true or false statement, unless it is elliptical for something like `In order to teach successfully Miss W. ought to prepare her lessons in advance', or `Preparing her lessons in advance would be the best way for Miss W. to become a successful teacher', in which case it follows without the second premiss of (I). Suspecting something odd about such inferences, it is tempting to diagnose the invalidity as due to a change in the meaning of `ought', e.g. from "prima facie" force in the first premiss to an "overriding" force in the conclusion. However, our analysis shows that this temptation can be resisted. Neither do we need to say that logical principles of inference sometimes break down: instead we conclude that statements which appear to be of the forms to which such principles apply really have different logical forms. Of course, in other cases, principles of inference may appear to break down because of unacknowledged slides from one basis, or comparison class, to another, or because of slides between assertive and non-assertive uses of `ought', to be discussed below.

G. Other uses of `ought'

No claim has been made that every use of `ought' conforms to the analysis presented here, neither have general criteria been given for recognizing uses which do conform. At best we can only ask: `Is this use intended to convey something which could be said equally well, or perhaps even with greater clarity, by saying that such and such is (would be, would have been) better (relative to such and such a basis of comparison) than any other of the alternatives under consideration?' Clearly there are some uses of `ought' which do not fit this analysis. For instance there are some non-assertive uses of 'ought' (and `better') related to expressing a preference, or recommending: and here no basis of comparison is needed to complete the meaning. (An analysis in terms of imperatives would be more appropriate to `must' than `ought', unless the imperative uses some such construction as `Preferably do X', which implies that although alternatives to X are regarded as inferior they are not absolutely ruled out.) Secondly, there appear to be some "naturalistic" uses where the meaning of `ought' (and `better') includes some particular basis of comparison, such as generally accepted moral principles, or standards of etiquette, of the speaker's society. Hare calls this an inverted commas use. (The Language of Morals, p. 124.) In this use no basis need be made explicit to complete the statement, for it would either be redundant or generate a contradiction. Thirdly, there is a metaphysical use of `ought' (and `better') which is based on a fairly common (though in my view hopelessly confused) belief that there is some sort of "absolute basis" of comparison which necessarily gives some kind of imperative force to all comparisons or `ought' statements referring to it. No doubt there are also mixtures of these uses. A full explanation of the apparent differences between `prima facie' and `over-riding' uses of `ought' would require an analysis of the ways in which we slide between assertive and non-assertive uses.

Since what has just been said about different uses of `ought' applies equally to `better', the first part of my analysis of the former in terms of the latter, i.e. sections B and C above, survives all these variations of sense. The remarks in section D and after, about bases of comparison, apply only to considered attempts to say something true or false. (However, I should point out that I regard it as less important here to give a strictly accurate account of what people actually do say than to suggest what they might say if only they knew how.)

Finally, we come to uses of `ought' in statements about what is likely or probable, as in `Judging by the weather charts, it ought to be fine this afternoon', or `The book ought to be where I left it, on the top shelf'. The contrast between `ought', `must' and `may' pointed out in section E holds in this sort of use also. `It must be fine this afternoon' rules out alternatives left open by `It ought to be fine', while `It may be fine' merely picks out one alternative which is not ruled out, without implying that it is the only or the best one. This shows that this use of `ought' is closely related to the uses discussed previously: it is not simply ambiguous. Can we say anything more than this? Can this use be analysed in terms of `better' or `best'? Professor Alan White has suggested in the paper referred to in section E that a unitary analysis can be given in terms of `best reasons', i.e. `best reasons for doing X' and `best reasons for thinking that p'. This has the disadvantage of not covering such uses as `There ought to have been less suffering in the world', where no suitable `doing X' or `thinking that p' can be found. However, it does seem that an analysis of `It ought to be the case that p' in terms of `best' can be found along one of the following lines:

  (9) Among the possible alternatives, p is the one which best fits the available evidence (or known facts).

Or, perhaps:

  (9') Among the possible alternatives, p is the best one to believe (or act on).

(Or, more generally: `p is or is a necessary condition for . . .') Since these are special cases of the general schema (7), of section D, it turns out that there is no need to postulate a different sense of `ought' when it is used to say what is most probable. However, it may be that in addition this use can be construed as having overtones to the effect that nature, or the world (or God?) is some sort of agent which ought to produce this particular state of affairs in order to keep its promises to us!

University of Sussex (Author now at School of Computer Science The University of Birmingham)