C. D. Broad, Five Types of Ethical Theory, 1930
(A) LOGICAL ANALYSIS OF ETHICAL TERMS: (I) Ought and Right. The main discussion on this subject is to be found in Book I, Chap. III.
(1, 1) We must begin by distinguishing a narrower and a wider sense of "ought". In its narrower sense it applies only to actions which an agent could do if he willed. But there is a wider sense in which there is no such implication. We can say that sorrow ought to have been felt by a certain man at the death of a certain relation, though it was not in his power to feel sorrow at will. And we can say that virtue ought to be rewarded. 
(1, 2) There is another distinction to be drawn between what I will call the deontological, the teleological, and the logical application of "ought". Some people judge that there are certain types of action which ought to be done (or avoided) in all or in certain types of situation, regardless of the goodness or badness of the probable consequences. This is what I call the "deontological" application of "ought". Now there are people who would deny that they ever make such judgments as these. But such people may, nevertheless. make the judgment that every one ought to aim at certain ends without any ulterior motive, e.g., at his own greatest happiness, at the greatest happiness of all sentient beings, and so on. This is what I call the "teleological" application of "ought". Sidgwick suggests that many people who say that they have no notion of unconditional obligation merely mean that they never use "ought" in the deontological application though they may quite well use it in the teleological application. Lastly, it is conceivable that there are people who not only do not recognise any types of action as being obligatory apart from all consideration of the goodness of their consequences, but also do not recognise that there are any ends which every one ought to aim at. Every one must admit indeed that there are ends which are in fact ultimate for a given individual, i.e., things that he does in fact desire directly and not merely as a means to something else. But it might be said that there is nothing of which it could be held that every one ought to desire it as an end. Even so, as Sidgwick points out, there is an application of "ought" which such people would make. If a certain man does in fact take a certain end as ultimate for him then he ought to be consistent about it. He ought to take such means  as he believes will tend to bring it into being, and he ought not to do things which he believes will be inconsistent with its realisation. That people can and do will ends and then fail to will what they believe to be the right means to them is certain. And we do say that no one ought to act in this inconsistent way. This is the logical application of "ought"
It will be noted that I have been careful to talk of three different applications, and not of three different meanings, of "ought". We have now to consider whether these different applications do involve different meanings, and also how they are related to the distinction which we have already drawn between the wider and the narrower sense of "ought". The position seems to me to be as follows: (a) "Ought", when used in its teleological application, is used in its wider sense. For in this application we say that every one ought to desire so-and-so as an ultimate end. Now it is plain that we cannot desire this or that at will, any more than we can love this or that person at will. Thus to say that each ought to desire the happiness of all is like saying that every one ought to love his parents and is not like saying that every one ought to speak the truth. (b) "Ought", when used in its logical application, would seem to be used in its narrower sense. For we believe that it is within the power of any sane human being to be consistent if he tries. Thus to say that anyone who adopts an end as ultimate for him ought to adopt what he believes to be the means to it is like saying that every one ought to tell the truth and is not like saying that every one ought to love his parents. In fact it seems to me that the logical ought is just a special case of the deontological ought. Its main interest is that it is recognised by people who would not  admit that they could recognise any other instance of the deontological ought.
(1, 3) We must now say something about the relations between "right" and "ought". This will enable us to say something further about the relations between the narrower and the wider senses of "ought".
- Any action that I ought to do would be right for me to do. But there might be several alternative actions open to me all of which were equally right. In that case it cannot be said of any one of them that I ought to do it; it could only be said that I ought to do one or other of these actions, and that it was indifferent which I did.
- Even if only one course of action open to me were right, or if one alternative were more right than any of the others, we should not necessarily say that I ought to do that action. We tend to confine the word "ought", in its narrower sense, to cases where we believe that there are motives and inclinations against doing the rightest action open to the agent. Thus, as Sidgwick points out, we should hardly say of an ordinary healthy man that he ought, in the narrower sense, to take adequate nourishment; though we might say this of an invalid with a disinclination to take food or of a miser. And, although we hold that God acts rightly, we should hesitate to say that he always does as he ought or does his duty. Such notions would seem inappropriate to a being who is supposed to have no inclinations to do what is wrong or to leave undone what is right.
- It seems to me that, when I speak of anything as "right", I am always thinking of it as a factor in a certain wider total situation, and that I mean that it is "appropriately" or "fittingly" related to the rest of this situation. When I speak of anything as "wrong" I am thinking of it as "inappropriately" or "unfittingly"  related to the rest of the situation. This is quite explicit when we say that love is the right emotion to feel to one's parents, or that pity and help are the right kinds of emotion and action in presence of undeserved suffering. This relational character of rightness and wrongness tends to be disguised by the fact that some types of action are commonly thought to be wrong absolutely; but this, I think, means only that they are held to be unfitting to all situations. What I have just asserted is not, and does not pretend to be, an analytical definition of "right" and "wrong". It does bring out their relational character, and it correlates them with certain other notions. But the kind of appropriateness and inappropriateness which is implied in the notions of "right" and "wrong" is, so far as I can see, specific and unanalysable.
Now, so far as I can see, the wider sense of "ought" reduces to that of right, together with the associated notion that, if the right state of affairs were in the power of anyone to produce, he ought to produce it. Take, e.g., the statement that virtue ought to be rewarded. This means primarily that it is right that virtue should be accompanied by happiness, that the one is fitting to the other. In so far as it means more than this the further implication is that anyone who had it in his power to make the virtuous happy would be under an obligation to do so. I think therefore that there is no need to hold that "ought-to-be" is a third independent notion in addition to "right" and "ought-to-do". For it seems that "ought-to-be" can be analysed in terms of "right" together with a hypothetical reference to what a being who had it in his power to produce the right state of affairs "ought to do".
(d) "Ought", in the narrower sense in which in future  I propose to use it, seems to be bound up with the following facts.
- That a man's belief that a certain action which is in his power is right is a motive for doing it, and that his belief that a certain state of affairs which he could help to bring about would be good is a motive for aiming at it.
- That human beings are subject to other motives which may and often do conflict with this one. And
- that, in cases of conflict, it is right that this motive should win. When such a conflict is actually taking place we have a peculiar emotional experience which may be called a "feeling of obligation".
(1, 4) In the above discussion I have in places wandered far from Sidgwick, though I do not know that I have said anything that he would deny. We come now to a question which he discusses very fully: "Can the term 'right' be analysed into a combination of other, and not specifically ethical, terms?" To hold that it can is to hold a naturalistic theory as regards right. Sidgwick's method is to take the most plausible of the naturalistic analyses, and to try to show that they are inadequate. It of course remains possible that some day some more subtle naturalistic analysis may be proposed, and that this will be immune to Sidgwick's criticisms. But this has not in fact happened up to now. The objections have often been ignored, but they have never been answered.
Sidgwick takes four suggested analyses for discussion. (a) It might be suggested that when I say that X is right I mean simply that it excites in me a certain kind of feeling of approval. Since people certainly argue with each other about right and wrong, this can hardly be the primary meaning. But it might be said that this is all that they ever have any ground for asserting; and that they carelessly  put their judgment in an impersonal form, as a man might do if he said that the taste of onions is nasty, though he really means no more than that he dislikes the taste of onions. I think it is obvious that this extremely subjective view will not fit the facts. At the very least I must mean that X would evoke a feeling of approval in all or most people on all or most occasions when they contemplated it.
It is clear that the theory could be most satisfactorily refuted if it could be shown that I sometimes reverse the judgment about X whilst my emotion towards it remains unchanged, or that my emotion towards X sometimes changes its determinate form whilst my judgment about X remains unchanged. Sidgwick, however, does not claim that this happens. What he says is that my judgment may change from "X is wrong" to "X is right", and I may still feel towards X an emotion which resembles that which I formerly felt. But, on careful introspection, it is found to be no longer moral disapproval but a "quasi-moral feeling of repugnance". This fact is important in so far as it enables us to distinguish the feeling of moral approval and dis-~ approval from other pairs of opposed emotions which often accompany that feeling and are liable to be mistaken for it. It is, 6.g., clear that, in the case of unusual sexual practices, the majority of normal people constantly mistake what is in fact a quasi-moral feeling of repugnance for a genuine feeling of moral disapproval. But I cannot see that the fact is incompatible with the theory of the meaning of right" which Sidgwick is attacking. For in his example it is surely possible that at first I feel moral disapproval mixed with quasi-moral repugnance, and that later I feel moral approval mixed with quasi-moral repugnance. And  the supporters of the present theory could say that my first judgment expressed the fact that I was feeling moral disapproval; my second expresses the fact that I am feeling moral approval; and the constant factor of quasi-moral repugnance does not enter into either judgment. Sidgwick's conclusion that the moral emotion is causally determined by the moral judgment, and therefore cannot be the subjectmatter of the judgment, is compatible with the facts but is not necessitated by them.
(b) The second analysis is that when I say that X is right I mean that I have a feeling of approval towards it and also sympathetic representations of other men's similar feelings. To this Sidgwick answers that I may begin to feel moral disapproval of an action which I once approved, whilst my fellow-men continue to feel moral approval of it. Or, again, I might go on feeling moral approval after other men had begun to feel moral disapproval. In such cases the sympathetic representation of other men's similar -feelings has ceased. Nevertheless I should begin to judge that the action is wrong in the first case, and I should continue to judge that it is right in the second case. It is of course true that the sympathetic representation of the similar feelings of others generally accompanies and supports my moral judgments. But this is because my judgments generally agree with those of others, and this agreement increases my conviction of the truth of my own judgments.
(c) The third analysis is that when I say that X is right I mean that other men will feel approval towards me if I do X and will feel disapproval towards me if I omit to do X. This theory, as Sidgwick says, does bring out a certain analogy between moral and legal right. An action is legally wrong if it will be punished by the law; and, on this theory,  it is morally wrong if it will be punished by the pains of public disapprobation. But it is plain that the analogy is only partial, and that the theory is inadequate. For we admit that there are things which it is right to do, but which will call forth public disapproval; and conversely. We often hold that public opinion distributes its approvals and disapprovals wrongly; and it seems clear that such judgments involve a sense of "wrong" which cannot be analysed in terms of public approval and disapproval. Lastly, if I say to a man: "You will be wrong if you do so and so, and public opinion will be against you," the second part of my admonition is clearly not a mere repetition of the first, as it should be on the present theory. It is true that there are quasi-moral judgments, just as there are quasi-moral emotions. The words "right" and "wrong" in such judgments do mean no more than "evoking social approval" and "evoking social disapproval" respectively. The codes of honour, of fashion, etc., consist of such judgments. And unreflective people do not sharply distinguish them from genuine moral judgments. But, when Me reflect, we do seem to see that there is a fundamental difference between the quasi-moral judgment: "It is wrong to wear brown boots with a morning-coat" and the genuinely moral judgment: "It is wrong to inflict pain on innocent persons except as a means to removing some greater evil." The distinction becomes most clear when one and the same action is the object of moral approval and quasi-moral disapproval, or conversely. This difference seems plainly to exist within my experience; but I cannot help being somewhat perturbed to find that there are important departments of conduct in which judgments which seem to most people to be clearly moral seem to me equally clearly to be  only quasi-moral. I have no doubt that they are mistaken in thinking these judgments moral (though it is of course possible that I suffer from moral obtuseness), but I cannot help wondering whether the few judgments which seem to me so clearly moral may not really be only quasi-moral judgments which have so Or resisted my attempts at ethical scepticism.
(d) The fourth analysis is that to say that X is right or that it is wrong means respectively that one will be rewarded or punished by God if one does it. To this Sidgwick answers that people certainly make moral judgments and feel moral emotions without holding this particular form of theism. Moreover, those who believe that God will in fact reward certain actions and punish certain others generally believe that he will do so because the former are independently right and the latter independently wrong. Lastly, although we should not say that it is God's duty to act justly, because we think of him as not subject to any opposing impulses, we should say that it is right for him to do so. And we certainly do not mean that he will be punished by himself if he does not.
Sidgwick concludes that the notions of right and wrong are probably logically simple and so incapable of analysis. Even if his list of attempted analyses covers all the possibilities, which we cannot safely assume, there remains a point of formal logic to be mentioned. Strictly speaking, he has shown only that "right" does not always mean any one of these. It remains logically possible that it always means one or other of them, sometimes one and sometimes another. If so, it is a fundamentally ambiguous word. What he needs to show is that there is a meaning of "right" which does not coincide with any of these alternatives, and that it is used with this sense in ethical iudgmentg. I am inclined  to think that this is true; but Sidgwick's argument does not strictly suffice to prove it.
(1, 5) It remains to be noticed that Sidgwick clearly points out that the logical simplicity of the term right neither entails nor is incompatible with the psychological primitiveness of the notion of right in the human mind. It is quite possible that the notion may have arisen in the course of evolution, and that we can point out the other notions which have preceded it. Some people have imagined that, if this could be done, it would follow that right cannot be logically simple but must be composed of the terms which are the objects of these psychologically earlier notions. This, as Sidgwick remarks, is to carry over to psychology the chemical theory that the resultant of the interaction of several elements is composed of those elements, still persisting in a disguised form, and of nothing else. Even in chemistry this is a bit of highly speculative metaphysics, if taken literally. But at least it is a convenient way of summing up certain important observable facts, such as the constancy of mass, the fact that a compound can be repeatedly generated by the disappearance of its elements and the elements be regenerated by the destruction of the compound, and so on. There are absolutely no facts in psychology which bear the least analogy to these; and so there is no justification for treating the products of psychological development as if they were compounds containing their antecedents as elements.
(2) Good. Sidgwick does not treat the term Good until Book I, Chap. IX is reached. But this seems to be the proper place to deal with it.
(2, 1) The first question to be considered is whether "goodness" can be defined in terms of pleasantness. In  this discussion it will be well to remember the distinction which I drew, in connexion with Hume's theory, between non-causal pleasantness, which can belong only to experiences and which makes such experiences pleasures, and causal pleasantness, which can belong to other things beside experiences. It will be remembered that the statement that X is "causally pleasant" means that there is at least one mode of cognising X which is at most times and for most men a pleasant experience.
Now, when we talk of "good" wine or "good" pictures, it does seem at first sight that we mean simply wine which is pleasant to taste or pictures which are pleasant to see. And so it seems as if "goodness", in these cases at any rate, could be identified with causal pleasantness. But, even when we confine ourselves to such things as wines and pictures, there are serious difficulties, which Sidgwick points out, in this view. We distinguish between good and bad taste in such matters. A "good" picture could hardly be defined as one which most men at most times find it pleasant to contemplate. We should rather be inclined to say that it is one which persons of good taste in such matters find it pleasant to contemplate. But then we are defining "goodness", as applied to pictures, not simply in terms of causal pleasantness, but in terms of this and "goodness" as applied to taste. And it seems as if "goodness", in the latter sense, involved some reference to a supposed objective standard, and could not itself be defined in terms of causal pleasantness. Then, again, it must be admitted that a bad picture or wine may not only please more people than a better one, but may also give more intense pleasure to those whom it pleases. The blase expert may get very little pleasure from seeing pictures or tasting wines which  he recognises to be very good, whilst he may get acute discomfort from wines and pictures which give intense pleasure to less sophisticated people of crude tastes and strong susceptibilities.
Suppose now that we pass regretfully from wines and pictures to character and conduct. If we say that a "good" character means one which spectators find it pleasant to contemplate, we shall be back in the difficulties which arose over wines and pictures. We shall have to say that the pleasure must be of a certain specific kind, that it will be felt only by people of good moral taste, and that even in them it may not excite a degree of pleasure proportional to its goodness. It seems almost certain that the contemplation of the character and conduct of the heroes and heroines of the films has given far more intense and widespread pleasure than the contemplation of the character and conduct of Socrates or St. Paul. If, on the other hand, we take a wider definition, and say that "good" character or conduct means character or conduct which is either immediately pleasant or productive of pleasure on the whole and in the long run, we seem to be asserting that the fundamental doctrine of Hedonism is a tautology like the statement that the rich and only the rich are wealthy. Now Hedonism, whether true or false, has seldom seemed to its supporters and never to its opponents to be a mere tautology which is true ex vi termini.
I am not prepared to accept this last argument of Sidgwick's, for I believe that it rests on a very common confusion between analytical propositions and verbal or tautological propositions. It seems clear to me that a term may in fact be complex and in fact have a certain analvsis, and that people may vet use it in the main correctly  without recognizing that it is complex or knowing the right analysis of it. In that case the proposition which asserts that it has such and such an analysis will be analytic, but will not be tautologous. It therefore seems to me that "good" might mean immediately pleasant or conducive to pleasure in the long run, and yet that people who use the word "good" correctly might quite well fail to recogmse that this is the right analysis of the term which the word denotes. I agree with Sidgwick in thinking that this is not in fact the meaning of the word "good", but I deny that his argument proves his conclusion.
(2, 2) We pass now to a second suggestion, viz., that "good" can be defined in terms of desire. In this connexion Sidgwick makes a very important point which he hardly stresses enough, so that the reader may easily overlook it. I will therefore begin by making this point quite explicit. It concerns the ambiguity of the word "desirable In criticizing Mill at our mother's knee we all learnt one ambiguity of this word, viz., that it may mean capable of being desired or fit to be desired. The first meaning might be called the "purely positive meaning" and the second might be called the "ethically ideal meaning". The important point which Sidgwick makes is that there is a third sense, which might be called the "positively ideal meaning". In this sense "X has such and such a degree of desirability for me" means that I should desire X with such and such an intensity if I knew that it were attainable by voluntary action and if I could forecast with complete accuracy what my experience would be on attaining X. We must now notice that what is highly desirable, in this sense, if it could be got apart from its consequences, might have highly undesirable results. Among these results is the fact that  the indulgence of desire A may strengthen it and cause desire B to weaken or vanish; and yet B may be a more desirable desire, in the sense defined, than A. We thus come to the notion of "the most desirable future for me on the whole from now on".
This, according to Sidgwick, may be defined as that state of affairs which I should now choose in preference to any other that I could initiate at the time, provided that I had completely accurate knowledge of this and of all practically possible alternatives, and provided that I could accurately forecast what my experiences would be on the supposition that each alternative were realised. It will be noted that this would involve a knowledge of how my desires and feelings are going to alter in the course of my life, either as a result of my present choice or from causes outside my control. It is evident that this notion is "ideal", in the sense in which the notion of a perfect gas or a frictionless fluid is ideal. But, like those notions, it is purely positive; it involves in its analysis no reference to obligation or fittingness. The suggestion is that this is what is meant by "my good on the whole". He says that it seems paradoxical to suppose that "my good on the whole" can mean anything so complicated as this. And yet (Methods of Ethics, Sixth Edition, p. 112) he seems inclined to think that this may be the correct analysis of the term. And, for reasons which I have already given, I see no objection to the view that a term with which we are quite familiar may in fact have a very complicated and unfamiliar analysis.
In the second paragraph of the same page he goes on to say: "It seems to me, however, more in accordance with common-sense to recognise, as Butler does, that the calm  desire for my good on the whole is authoritative; and therefore carries with it implicitly a rational dictate to aim at this end, if in any case a conflicting desire urges the will in an opposite direction." It is not perfectly clear to me what he wishes us to infer from this statement. He might mean (a) that the purely positive, though ideal, definition of "my greatest good on the whole" is adequate; but that it is a synthetic and necessary proposition that I ought to desire my greatest good on the whole, thus defined. Or (b) he might mean that the purely positive definition is not adequate, and that "good" cannot be defined without reference to the ethical notion of "ought" or "right". It seems fairly clear from the latter part of this paragraph that he takes the second view. "My greatest good on the whole" is what I ought to desire, assuming that only my own existence were to be considered. And "the greatest good on the whole" is what I ought to desire when I give the right amount of importance to all other individuals as well as myself. (Sidgwick says "equal importance". But this prejudges the question whether equality is the right relative importance of myself and others.)
This seems to be Sidgwick's conclusion, but I must confess that I find his discussion very complicated and the result not very clearly stated. Assuming this to be the right interpretation, there remains one further question to be raised. It follows, no doubt, that a purely positive definition of "good" has been found to be impossible. But is any definition possible? Granted that the two propositions "X is the greatest good on the whole for me" and "X is what I ought to desire when I take account only of my own existence" are logically equivalent, is the second an analysis of the first? This does not seem to me at all obvious. It is surely possible that both "good" and "right" are indefinable, as both "shape" and "size" are, and yet that there is a synthetic, necessary, and mutual relation between them, as there is between shape and size.