We introduce a formal statistical definition for the problem of backdoor detection in machine learning systems and use it analyze the feasibility of such problem, providing evidence for the utility and applicability of our definition. The main contributions of this work are an impossibility result and an achievability results for backdoor detection. We show a no-free-lunch theorem, proving that universal backdoor detection is impossible, except for very small alphabet sizes. Furthermore, we link our definition to the probably approximately correct (PAC) learnability of the out-of-distribution detection problem, establishing a formal connections between backdoor and out-of-distribution detection.