Yesterday, my one time supervisor (Garber) was the external examiner of a PhD in my department (I was not on the committee). After, at the festive reception, I had the distinctive pleasure of introducing him to my first and most advanced PhD student (Van Strien); her public defense is scheduled in September. (He will not be involved in that.) Just as my dissertation had been partly on the edge and largely beyond my supervisor's area of expertise, her project covers territory that goes beyond stuff I would (or could) publish on. The advantage of such projects is that there is no competition between student and supervisor; it also means one can be very receptive because one is really learning from one's student. The obvious danger is that one risks missing some problems obvious to experts. One also has to navigate a supervisor's potential lack of interest. My supervisor did not expect his students to keep track of his publications (or drafts); the one seminar I took with him turned out to be on material he was teaching himself and that to the best of my knowledge he has not really published on.
Even so, through a funny kind of osmosis (written comments, reading groups, shared public space at workshops/talks, etc.), social mores and intellectual commitments get transmitted. With hindsight, it's clear to me that in my first efforts at publishing after I came out of graduate school, I was a 'contextualist' historian of philosophy, which treated natural philosophy as an integral part of its history. From the reactions of others, I inferred that, in fact, I was (legitimately) perceived as my supervisor's student. Ironically enough, a few years out of graduate school, after I realized that I might disagree with some of my supervisor's most important methodological commitments and the complex ways of characterizing the relationships between physics and metaphysics in the early modern period, I started reading his work with great care and in detail. It was, in fact, exhilarating to present the product of my engagement to audiences that included him. In my image of myself at the time, this involved 'finding my own voice.'