In our theoretical and conceptual article, we propose that the application of Niklas Luhmann's sociological systems theory as a difference-theoretical approach to the opening of science unveils an openness paradox. We describe and discuss the general concept of open science as currently proposed by UNESCO and posit that only by accepting the scientific method as truly and inherently open, can higher education institutions and science at large indeed be considered open. The paradox arises by analyzing and discovering through systems theory how the relevant systems function and the various structures within science (e.g., publishing and funding) are seemingly destined to be and ultimately stay closed. Finally, we propose a desideratum for open science that could dissipate the openness paradox in the future and once and for all answer the question "Are we close(d)?".