Ethics of care
I offer a definition to ensure that we all have the same thing in mind in talking of an 'ethics of care' (or to sort things out if we don't) :
The key idea is that the detached,
impartial observer ideal of morality, characteristic
of ethics since the enlightenment, is flawed and
inappropriate, particularly for women. In its place is
recommended an approach stressing involvement in
the situation, with an attitude of care for others also
involved. As such, the importance of relations
between people in their practical reasoning is
highlighted rather than the more common approach
stressing abstract principles. (Peter Allmark, 'Can There Be an Ethics of Care?', Journal of Medical Ethics, Vol. 21, No. 1 (Feb., 1995), pp. 19-24: 19.)
On any ordinary standard reading of 'relational' an ethics of care is relational. (I make no comment on the phrase, 'particularly for women'.)
Three senses of caring
Noddings distinguishes between two kinds of caring: "caring for"
and "caring about." Caring for, according to her, takes place on the occasions
in which one person, the carer, cares directly and in person for another, the
cared-for (2002a, 21). We care for people who belong to our "inner, intimate
circle" of family members, relatives, friends, acquaintances, and so on, but only
care about strangers or people with whom we do not have direct, face-to-face
encounters. Caring for, on the one hand, has a personal touch and is motivated
by natural affection, and therefore is done willingly and cheerfully. "Clearly, in
the deep human sense... I cannot claim to care for my relative if my caretaking is perfunctory or grudging" (9). On the other hand, caring about is, for the most
part, actuated by drawing upon ethical caring. According to Noddings, when
it comes to helping a needy stranger, although we may recognize the natural
internal imperative "I must," there is little cheerfulness or willingness to begin
with, so we have to appeal to an "ethical ideal" by asking ourselves how we
would behave if this stranger were someone we loved. "In doing this," says Nod-
dings, "we draw upon an ethical ideal-a set of memories of caring and being
cared for that we regard as manifestations of our best selves and relations. We
summon what we need to maintain the original "I must". (Shirong Luo, 'Relation, Virtue, and Relational Virtue: Three Concepts of Caring', Hypatia, Vol. 22, No. 3 (Summer, 2007), pp. 92-110: 93-4.)
The third sense of an ethics of care focuses on the contribution of the cared-for :
Although Noddings's emphasis on the contribution of the cared-for comple-
ments and broadens the virtue ethicist's perspective in new and important
ways, the question is: what is the nature of the contribution of the cared-for?
In addition to what she says above, her following remarks appear to adumbrate
an answer,
By recognizing the carer's efforts, by responding in some posi-tive way, the cared-for makes a distinctive contribution to the
relation and establishes it as caring. In this way, infants con-
tribute to the parent-child relation, patients to the physician-
patient relation, and students to the teacher-student relation.
(1984/2003, xiii-xiv)
From the care perspective, a huge thank-you goes to the responsive children, the students glowing with new learning, the feeble
elderly who can do little more than smile a thanks for effort at
care. We know just how great these contributions are when they
are withdrawn. (2002a : 19.)
Virtues - self- and other-regarding
I like the idea that all virtue is relational.
It seems to me that from your perspective it's only if you subsume all virtues under an ethics of care in any or all of these senses that you can reach the point that 'all virtue is relational'.
One block to this view, or difficulty in it, is that there are (or are usually judged to be) self-regarding virtues which are not in any standard sense necessarily 'relational' to other agents or their interests.
Virtues like courage, prudence, temperance, and so on, have traditionally
been distinguished from virtues like generosity, honesty and conscientiousness, and are often referred to as the self-regarding virtues, with the implication of course that the agent is regarding himself, is acting in his own interest
when he displays this kind of virtue. The explanation of why they are
virtues at all then often takes the form of claiming that each of them is
concerned with overcoming some specific passion (fear, lust and so on),
which would interfere with the pursuit of self-interest, but they are often
regarded as inferior and even somewhat dubious virtues. For convenience,
we shall keep the name 'self-regarding' to refer to them, but we want to
claim that they are not logically connected with the pursuit of self-interest
(nor for that matter do they consist of overcoming passions). They differ
from the other-regarding virtues, so far as self-interest is concerned, only
in the fact that they are not logically connected with benefiting others : a
man can, though he need not, display them in his own interest. He can act
courageously or prudently, say in the furtherance of his own career or in
carrying out a train robbery, but equally he may display courage or prudence
in the pursuit of world peace, or indeed any end at all that he regards as
worthwhile.
It follows that the self-regarding virtues cannot be distinguished from
each other as the other-regarding virtues are, by the nature of the benefit
the agent believes will come of his action. What distinguishes, say, a courageous and a prudent action is not the sort of reason the agent may have
for doing the action but the sort of reason there is in his view for not doing
it, or, as we could put it, the nature of the temptation not to do it. I act
courageously if I do what I believe to be dangerous but nevertheless worth
doing; if I do what I believe involves giving up a physical pleasure but is
nevertheless worth doing, then I display the virtue of temperance, or again
if I give up some immediate advantage or pleasure for the sake of a long-
term end, it is prudence I show. The virtue, of course, lies not in doing
what is dangerous, abstaining from what is pleasant and so on, but in doing
so when it seems worthwhile, when there is a reason for doing so which
overrides the initial reason against the course of action in question. And
conversely it is cowardly not to do a dangerous action or imprudent not to give up an immediate advantage only when it would, in one's own view,
be worth doing. (Gabriele Taylor and Sybil Wolfram, 'The Self-Regarding and Other-Regarding Virtues', The Philosophical Quarterly (1950-), Vol. 18, No. 72 (Jul., 1968), pp. 238-248: 244-5.)
The conclusion is that the self-regarding virtues may be relational, when exercised in the interests of others, but that temperance, say, or courage, are virtues of the individual which, while they may perfectly well be used to help others, have no inherent relation to anyone except the agent.
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After-thoughts
Not every self-regarding trait or habit can count as a self-regarding virtue. I used the examples of courage, prudence, temperance (self-control). We regard these as admirable traits of the persons who have them. I didn't intend to suggest, in case anyone may suppose this, that just any habit or trait that serves my own interests, no matter how vile that habit or trait may be, is a virtue, a self-regarding virtue. Perhaps no-one has drawn this inference but I want to block it anyway.
I can see how the exercise of a self-regarding virtue could produce extremely undesirable states of affairs or consequences. One needs courage to do any number of bad actions. But I'd add that other-regarding virtues can also produce extremely undesirable states of affairs or consequences. An ethics of care - of caring for or caring about - can generate behaviour that over-protects and stifles the autonomy and moral development of the object of care. Honesty and generosity - which also are other-regarding virtues - can produce extremely undesirable states of affairs and consequences. Generosity to a drug addict can kill them if they mis-spend the money you give them. Honesty can produce devastasting consequences if, say, it involves disclosing a secret one was trusted to keep. I say this to keep the balance level between the self- and the other-regarding virtues : to emphasise that any virtue of whatever kind is capable of generating morally undesirable states of affairs and consequences.
What is needed (deep breath) in the exercise of all the virtues is the aisthesis or moral insight of Aristotle's phronimos or person of practical wisdom (phronesis) who can measure and adjust their decisions and actions to the exact circumstances of the situation. There is no algorithm for this; it requires (if it's to be possible at all) the intimate and intelligent understanding of a tradition of morality. I don't exclude the guidance of conscience in the manner of Joseph Butler's ethics or some other source of moral insight. I simply align myself with the Aristotelian approach.
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References
Noddings, Nel. 1984/2003. Caring: A feminine approach to ethics and moral education.
Berkeley and Los Angeles: University of California Press. 2000.
Two concepts of caring. In Proceedings of the 1999 annual meeting of the
Philosophy of Education Society, ed. Randall Curren. Urbana, Ill.: Philosophy of
Education Society. http://www.ed.uiuc.edu/EPS/PES-yearbook/1999/noddings.asp.
2002a. Educating moral people: A caring alternative to character education. New
York: Teachers College Press.
2002b. Starting at home: Caring and social policy. Berkeley and Los Angeles:
University of California Press.