The third criterion candidate which Mogensen puts to the test lies in “depth and breadth of influence”. In reference to a complex system, a factor possessing such a quality would expectedly play “a uniquely important role in controlling the overall behaviour of the system” (p. 13). According to a systemic analysis of this kind, the centrality of a trait would follow from the number of functions for which it is responsible as well as the amount of influence it exhibits towards other traits and their dependent functions. In short, can the former override the latter in case of tension, conflict or mere priority?
Mogensen holds up hierarchical ordering as a potential pattern of depth and breadth of influence:
Our psychological states often exhibit a hierarchical ordering, with downstream beliefs and desires dependent on more fundamental upstream attitudes. Identity centrality might be partly a matter of a trait’s elevated position in this kind of chain-of-command (p. 13).
On such a pattern, the number of downstream beliefs subject to the trait under consideration (e.g. religion, nationality, sexuality, etc.) would decisive in determining a trait’s centrality. While impossible to set an invariable threshold figure, we can nevertheless understand the appeal of having rough guidelines of this kind. (Although it remains an open question whether a person’s beliefs could be sufficiently catalogued so as to be put to a test of this kind.
Yet the author recalls that considerations need not only be quantitative. Questions of centrality could also set out from considerations of the variety of fields subject to the influence of a given trait, independent of purely numerical relations. Such an idea “may suggest that part of what makes certain traits central to who we are is their capacity to shape our thoughts and activities across diverse domains of social behaviour” (p. 14).
In other words, the more central the trait, the more likely we are to see its manifestation in such different fields as work and family life, religion and politics, creative endeavors and leisure. Were a trait (e.g. religion, nationality, sexuality, etc.) to play a preponderant role in determining even some of the actions taken by the person within these fields, we could reasonably see it as having a breadth analogous to the depth seen in the hierarchical version.
Despite the currency of depth and breadth of influence accounts among contemporary philosophers, Mogensen finds the candidate criterion not without its flaws. The first owes to inclusivity:
One problem for this kind of view is that it seems too inclusive. It threatens to count as central certain traits that seem too basic and low-level to form part of our identity: the sort of core background processes that are necessary for getting by in day-to-day life. (p. 14)
The author finds this worrisome in that this criterion might apply to other traits or bundles of traits which, while imperative for functioning in a number of different fields, cannot properly be thought to fall under the heading of identity. By way of example, Mogensen illustrates how folk psychology, i.e. the processes by which those untrained in social sciences go about attributing mental states to others, are vital to our everyday functioning at work, in the community, and with the family. If they thus evince a certain breadth of influence, they cannot, however, count towards our identity in any relevant sense.
As an extension of Mogensen’s critique, we would only need add that unconscious brain processes demonstrate much the same. Insofar as these processes condition or provoke certain actions, reactions or dispositions in different fields, they might likewise benefit from the same breadth of influence. Yet they are, by definition, unavailable to conscious processes or correction.
For all these reasons Mogensen suggests of such complexes that:
They are more like the background against which my life takes shape than a proper part of it. In some sense, of course, they belong to the central elements of my mind. It’s just not the sense that interests us (p. 15).
A second problem would lie in the relation between depth and breadth accounts and the ethics of authenticity. For it is entirely conceivable that a central element of a person’s identity, whether from lack of opportunity or repression, may not receive expression in thought, speech or deed and would, by extension, not be considered to have the requisite depth or breadth in spite of its centrality.
An inauthentic life of this kind would seem to be defined precisely by the failure of the person’s true self to achieve the kind of depth and breadth of influence that some authors believe to be partially constitutive of identity centrality. It’s difficult to understand how a person could be said to mask an important facet of herself in this way if what makes a given trait central to who she is gets determined to a large extent by the degree to which it resonates throughout a wide range of her behaviours (p. 15).
Given the difficulty in squaring negative instantiations of the ethics of authenticity and depth and breadth accounts, considerable effort would need to go into making room for failed depth and breadth of the kind seen above. One possibility, as noted by the author, consists in weakening the claims to centrality as determined by depth and breadth accounts. These might then become just one more such tool in arbitrating identity centrality. But, in losing that explanatory strength, they also lose interest for inquiry.