Loop quantum gravity predicts that spatial geometry is fundamentally discrete. Whether this discreteness entails a departure from exact Lorentz symmetry is a matter of dispute that has generated an interesting methodological dilemma. On one hand one would like the theory to agree with current experiments, but, so far, tests in the highest energies we can manage show no such sign of departure. On the other hand one would like the theory to yield testable predictions, and deformations of exact Lorentz symmetry (...) in certain yet– to–be–tested regimes may have phenomenological consequences. Exposing their shortcomings, here I discuss two arguments that exemplify this dilemma, and compare them to other cases from the history of physics that share their symptoms. (shrink)