This article concentrates on the dissertation or thesis as a form of argumentation common in postgraduate experience. The nature and history, as well as the social and political context of the dissertation/thesis are explored. Its basic structures are discussed; and three dissertations are examined to test the degree to which they embody argumentation and criticality. A particular dimension is explored as part of the article, in relation to current thinking in the UK about postgraduate research student skills training: to what extent does the genre of dissertation or thesis encourage, support and/or inhibit what has come to be known as "critical thinking" i.e. thinking that is aware of its relativity, has "edge" and is aware of itself as a process? It is found that guidelines for such research student training fail to give argumentation its due in postgraduate education. (Contains 1 table and 2 figures.)