Social epistemologists should be well-equipped to explain and evaluate the growing vulnerabilities associated with filter bubbles, echo chambers, and group polarization in social media. However, almost all social epistemology has been built for social contexts that involve merely a speaker-hearer dyad. Filter bubbles, echo chambers, and group polarization all presuppose much larger and more complex network structures. In this paper, we lay the groundwork for a properly social epistemology that gives the role and structure of networks their due. In particular, (...) we formally define epistemic constructs that quantify the structural epistemic position of each node within an interconnected network. We argue for the epistemic value of a structure that we call the (m,k)-observer. We then present empirical evidence that (m,k)-observers are rare in social media discussions of controversial topics, which suggests that people suffer from serious problems of epistemic vulnerability. We conclude by arguing that social epistemologists and computer scientists should work together to develop minimal interventions that improve the structure of epistemic networks. (shrink)