In this paper, I attempt to explain how existing work in the science and technology studies (STS) sub-field of public engagement with, or participation in, public issues involving science and technology, has performed a serious category mistake in allowing itself to be called `public participation in science' research. This requires us to reflect more systematically upon how our assumed objects, here the public issues we think we are dealing with, come to be `objectified' in the forms which they do. Using the three sister papers, I make some conceptual distinctions which carry important political implications and corresponding analytical implications for STS. I suggest that the typical reduction of participation questions to ones of `what qualification do publics have for engagement in expert practices?' is a mistaken distraction from more important questions which not only much analytical work, but also dominant practice, continues to ignore. This reductionist tendency even in social science and STS may tend to intensify, the more the issues reach across global networks and arenas. Finally, I suggest that STS work on public participation needs to enrich itself with some relevant political theory and philosophy, which would throw due historical perspective on the deeper forces shaping scientific understandings and normative representational performances of its `democratic' publics.