Does rhythmic neural activity merely echo the rhythmic features of the environment, or does it reflect a fundamental computational mechanism of the brain? This debate has generated a series of clever experimental studies attempting to find an answer. Here, we argue that the field has been obstructed by predictions of oscillators that are based more on intuition rather than biophysical models compatible with the observed phenomena. What follows is a series of cautionary examples that serve as reminders to ground our hypotheses in well-developed theories of oscillatory behavior put forth by theoretical study of dynamical systems. Ultimately, our hope is that this exercise will push the field to concern itself less with the vague question of "oscillation or not" and more with specific biophysical models that can be readily tested.