During the first decade of the twenty-first century, neopositivist claims made about the nature and validity of knowledge in the debates about scientifically based research were countered by educators who, decades earlier, had made various turns away from positivism and were surprised by its resurgence. In those debates, positivists often used "postmodernism" as a code word for any social science approach that was not positivist and so, they claimed, could not be scientific. To remind us of the nature of positivism and the limits of the knowledge it enables, this paper reviews its assumptions and then returns to Lyotard's 1979 cogent critique, paralogy that describes postmodern knowledge that moves toward the unknown by engaging undecidables, paradox, incomplete information and catastrophes.