A significant part of Henry Sidgwick's The Methods of Ethics is a critical discussion of topics raised in Whewell's moral philosophy, although he does not explicitly call attention to the fact that this is what he is doing. Thus he has significant sections devoted to Whewell's Five Virtues, including Purity. ('Virtue' in both Whewell and Sidgwick is perhaps not quite what we usually mean by 'virtue'; we should perhaps think of a Virtue in their sense as being a value exemplified by a good character. In Whewell, at least, what we would often think of as the virtue is closer to what Whewell instead calls the Spirit of the Virtue.) However, Sidgwick makes a significant change when he talks about it, one that distorts the discussion considerably. In Whewell, Purity is concerned with the idea that we should not act like mere beasts; in particular, our 'lower' parts (like bodily desires) should be subordinated to our 'higher' parts (like our moral capacities). This is quite general, and forms subordinate Virtues depending on the kinds of bodily desires, like Temperance for food and drink, Chastity for sex, Modesty as an offshoot of Chastity concerned with attitude. All of these are governed by a unified principle. And this is essential for Whewell, because he is in turn responding to Bentham who rejects both as forms of 'asceticism' (the ultimate evil in Bentham's hedonistic utilitarianism). Sidgwick, however, more or less identifies Purity with Chastity. This ends up creating a number of problems.
(1) First, Temperance is divided from Chastity, and the two are no longer seen as having a common root and end. True, Sidgwick does recognize that there is a practical convenience in treating the two together, but the internal unity between the two is broken. The breaking of the unity has the further effect that the role of Purity in Whewell's response to the utilitarians is obscured, and the further clarification of the idea that could come from Whewell's argument against Bentham is ignored.
(2) Further, it leads Sidgwick to think of Purity/Chastity not as a Virtue concerned with our priorities in all life but as concerned with interpersonal relations. He denies, for instance, that Purity is a self-regarding Virtue (which is certainly not wholly true in Whewell's scheme), and talks about it almost entirely in terms of sexual intercourse, despite the fact that Purity is usually not considered (by Common Sense or by Whewell) to be solely concerned with the actual sexual deed. This creates a muddle. In Methods III.ix, when he first discusses it, Sidgwick is in the process of arguing that 'Common Sense Morality' provides no definite, precise rules for moral life, using Whewell's scheme of the Virtues to structure his argument. Unsurprisingly, he finds that Common Sense is very imprecise about Purity -- but all of the imprecision arises in contexts concerning interpersonal relations, and thus from Sidgwick's own modification of the idea, whose attribution to Common Sense is never really justified and which is simply unjustifiable in the context of Whewell's overall scheme. Whewell is very clear (and Sidgwick is very aware) that our sexual morality does not unfold entirely out of Purity, but depends very heavily on another of the Five Virtues, Order, which concerns Law. It is Order, not Purity, that primarily concerns sexual matters as matters of interpersonal relation, because it is interpersonal relations in particular that require definite standards. Much of Sidgwick's criticism of Purity as a source of definite guidance really boils down to the claim that you can't get the Order parts of sexual morality out of Purity alone. This is true, but doesn't actually tell us much of anything about Purity itself.
(3) Sidgwick notes a distinction in Common Sense Morality between a 'stricter' and a 'laxer' view of Purity; the stricter holds that sexual appetite should be indulged only for procreation and the laxer that it should be indulged only for increasing mutual affection in a permanent union. Part of his argument that Purity provides no precise guidance is that these are two very different views. But throughout, Sidgwick is assuming that sexual appetite can have only one end, which is not at all what Whewell's characterization of Purity implies. And we already know that Common Sense Morality does not assign sexual appetite one end. Sidgwick has admitted it himself. He takes this to be a sign that Common Sense Morality is not definitively decided on the topic, but in reality nothing requires that either end be taken exclusively, and it is plausible that Common Sense Morality rejects rather than assumes the idea that indulgence of sexual appetite can't have more than one end consistent with Purity.
(4) One of the most important claims Sidgwick makes is, "But it may be observed that any attempt to lay down minute and detailed rules on this subject seems to be condemned by Common Sense as tending to defeat the end of purity; as such minuteness of moral legislation invites men in general to exercise their thoughts on this subject to an extent which is practically dangerous" (III.ix.3). This is a claim that Sidgwick can make only because he conceives Purity so narrowly, as pretty much entirely concerned with the sexual act itself. Thus any extensive attempts to work out what is required to be 'pure' requires extensively thinking about sexual acts. But Purity as Whewell describes it does not work this way; it covers many things that are not sexual at all, and those things that it covers that are sexual are not all of the same kind, some of them being with secondary matters. Purity conceived this way does not require 'minute legislation' on how to have sex; it concerns things like how to treat people you are sexually attracted to, how to behave in romantic situations, how to act with good manners to members of the opposite sex in situations where sex might be relevant, and what should take precedence over any sexual behavior at all. These things will often not require thinking about any sexual act at all, because they concern things well upstream. What is more, it's not only that Sidgwick is certainly not getting Whewell right here; he is also certainly not getting Common Sense right. Is it really true that "any attempt to lay down minute and detailed rules" on sexual matters is condemned by Common Sense when the vast majority of societies that have ever existed have fairly minute and detailed rules about how men and women, and especially young men and women, should behave around each other? The existence of marriage and virginity customs are fairly close to universal; gossip about scandals is pretty much all the world over concerned with sex; people are very opinionated (and reasonably so) about how they should be treated in any matter even remotely concerned with sex.
Thus the entire discussion of Purity in Sidgwick attributes to Common Sense Morality on the subject of Purity a set of confusions and limitations that arise entirely from Sidgwick's never-justified modification.
While most of it is concerned with issues orthogonal to those considered here, Francesco Orsi has an interesting discussion of Sidgwick's comments on Purity: Sidgwick and the Morality of Purity.
