There are two important elements that I want highlight in explaining why I have chosen to dedicate a whole chapter to Pierre Bourdieu. First, I want to demonstrate his proximity to a certain Structuralist way of thinking about systems—social, natural, and mathematical—that is no longer “fashionable” and, accordingly, has been exposed to a barrage of criticism. However, much of this criticism is both superficial and misplaced. Second, and for this very reason, I want to show that Bourdieu’s Structuralist anthropology is far less rigid and deterministic than is usually supposed. To this end, I want to trace two of the most significant influences over Bourdieu’s philosophical development by going back to the sociological work of Jean Piaget as well as Merleau-Ponty’s phenomenology of the flesh. Despite this structural flexibility, I still intend to distance myself from Bourdieu’s conceptual framework. On one hand, I want to raise doubts about Bourdieu’s conceptions of symbolic or cultural capital. Moreover, it is this very social notion of capital that has been taken up by many commentators on the digital economy, as evidenced by the work of Lissitsa (2015), and Hesmondhalgh (2006), whereas other authors writing about the digital economy, such as Costa (2013) or Bolin (2012), have drawn, respectively, on Bourdieu’s conception of habitus and field. On the other hand, I want to suggest that Bourdieu’s interpretations of mathematics, in particular, can be accused of being somewhat rigid and outdated. In this domain, Bourdieu’s structuralist orientation takes on a form that is especially conservative and restrictive in its effects. To this end, I have drawn on Merleau-Ponty’s philosophy of the flesh as a counter-foil to Bourdieu’s own reflexive sociology. Nevertheless, even Merleau-Ponty’s philosophy is found to be wanting although, in this case, an efficacious remedy can readily be prescribed.