When Einstein, Podolsky and Rosen considered reality in physics, the term "certainty" was the crucial one. According to them, every description of reality that is bound to be taken seriously has to have certainty of prediction of its characters.
On this ground they dismissed the notion of quantum mechanics being complete description of nature. Bohr argued that the problem lies in previously unscrutinized idea of independent reality of every particle.
There is no independence on measurements, because the particle and the apparatus exist in relation. If we conceive reality from the standpoint of Peirce's semiotic metaphysics we can argue that the proponents of said debate inferred different conceptions of reality from their differing criteria of representability, and that inherent uncertainty of quantum mechanics measurements is a part of physical reality, because everything that is given to us as reality is given to us as its representation.