Integrity and Virtue

Is integrity a virtue? I'm not so sure. The reason I'm not sure is that integrity seems to be a much broader concept than many of the other virtue concepts. Some, like Bernard Williams, have made a similar suggestion, although sometimes the worry looks to be that integrity is not a virtue because people with morally suspect (or even pernicious) commitments could have integrity by remaining "true to themselves." In their book Integrity and the Fragile Self, Damian Cox, Marguerite La Caze, and Michael Levine argue that integrity is a virtue, and while I am sympathetic with the idea that it doesn't make sense to say, full voice, that a person who is "true" to vicious commitments thereby manifests what we normally mean by integrity, I find much of their argument confusing. Consider, for example, their characterization of integrity:

As we conceive it, integrity is not a kind of wholeness, solidity of character or moral purity. It involves a capacity to respond to change in one’s values or circumstances, a kind of continual remaking of the self, as well as a capacity to balance competing commitments and values and to take responsibility for one’s work and thought. Understanding integrity involves taking the self to be always in process, rather than static and unchanging or containing an inner ‘core’ around which reasonably superficial changes are made. Rather than presenting integrity as a merely formal quality characterizing the ‘good order’ or ‘well-functioning’ of a person’s psychology, we take it to be a complex and thick virtue term. It stands as a mean to various excesses: on the one side, conformity, arrogance, dogmatism, fanaticism, monomania, preciousness, sanctimoniousness, rigidity; on the other side, capriciousness, wantonness, triviality, disintegration, weakness of will, self-deception, self-ignorance, mendacity, hypocrisy, indifference. (41)

Certainly, to possess the characteristics described by Cox et al would be a mark of virtue, but that is part of what confuses me. It seems that integrity, as they understand it, is virtue, or at least a large swath of it, and not simply a virtue. The fact that they locate integrity at the center of many excesses and deficiencies of character signals to me that integrity is a characteristic that captures a whole host of virtues. That is why I find it slightly awkward to say that it is a virtue. They also cannot (and do not) completely rule out the significance of the standard ways of conceiving of virtue: wholeness of character, resistance to compromise of one's commitments, and so on, are in many cases the features of a person's life and actions which prompt ascriptions of integrity.

I'm tempted to suggest that integrity is a "family resemblance" concept (in the manner of Wittgenstein); this would explain why attempts to provide accounts of integrity that reduce it to a particular trait or feature tend to generate counterexamples. Or maybe integrity is like porn: we know it when we see it.