In context:
When I began this book, I intended to update Steven Marcus’s classic psychoanalytic and thematic reading of obscene writing in The Other Victorians by giving greater attention to the historical circumstances of the nineteenth-century British trade in obscene publications.2 It soon became apparent that the topic was not conducive to positivist historiography. The frontiers of obscenity, then as now, are never clear-cut. It has no stable definition: the surfeit of terms – obscenity, pornography, erotica, and smut – reveals the extent of the confusion and the problem endemic to the field.
The author seems to be questioning whether a historical method founded on positivism can really work for something so subjective as "obscenity." Positivism, I think, demands a kind of universality, and appeal to unambiguous fact/information, that is ill-suited to studying something so inherently subjective (or so claims the author you are quoting there). The fact that there is such difficulty even defining the basic terms associated with the topic are evidence of this to the author. The bounds of what even constitute what is being studied are unclear.
I tend to associate positivism with certain sorts of sociology, the desire to ascribe "laws" to how societies work that are derived from a dispassionate/rational/logical analysis of the information. This has been applied to the study of history as well, of course. My general feeling is that pure positivism doesn't currently hold a ton of cache among historians. Clearly we have all embraced elements of positivism. If your work is not rooted in some kind of documentation/sources somewhere then you aren't going to get very far. However, I think we also, as a field, understand the importance of the historian herself in the writing of history.
I'd be interested in discussing the matter really.