Postdisciplinarity has a small but growing fellowship of interest in the academy. Defining postdisciplinarity as shorthand for all the conversations we need to have once we have come to terms with disciplines as neither natural nor inevitable, in this chapter we deconstruct some of the key epistemic assumptions that help to keep disciplinarity in place as the reigning imagined order of contemporary knowledge production. Specifically, we assert three epistemic premises undergirding disciplinarity, which rarely go unquestioned: that depth is superior to breadth, that expertise equals specialization, and that discovery and originality are the knowledge functions characterizing true research advancements. These premises are, in turn, supported by a widespread adherence to the principle of reductionism across the academy. Working in concert, this set of assumptions is embedded into the material and intersubjective dimensions of academic life, and even into the psyches of individual scholars. Ultimately, we return to the quest of the individual scholar within this system, arguing that the experience of running up against the limits of the disciplines within which we work is not a failure to be feared, but a triumph to be celebrated, as we move towards a greater sense of purpose in our work. We then suggest postdisciplinary webs rather than walls guarding disciplinary towers as an alternative metaphor for knowledge production, contemplating the special properties of webs and those who weave and watch them, and then exploring the examples of the Open movement and Slow Science as important allies in advancing the postdisciplinary project.