 The philosophical significance of common cause completability and common cause extendability of (classical and quantum) probability spaces is that they show that it is always possible in principle to explain any correlation, hence also any correlation between causally independent events, in terms of (possibly hidden) common causes—hidden in the sense that the common causes need not be in the probability space that contains the correlation: the common causes can be “hiding” in a larger probability space. Thus these common cause completability and common cause extendability results constrain the possible ways of attempts to falsify the Common Cause Principle: Any attempt at falsification should impose some further conditions on the common causes in addition to the four defining  conditions (2)–(5),  otherwise falsification can be evaded by referring to hidden common causes. Formulated differently: The Common Cause Principle, as formulated exclusively in terms of the notion of a Reichenbachian common cause, either in a classical or in a quantum probability theory, is not falsifiable. This does not mean that the common cause extendability results can be regarded as proof that the Common Cause Principle is true: Even the weaker question of whether a common cause extendability result can be taken as confirming evidence for the Common Cause Principle depends on whether the extended probability measure space, existence of which is warranted by the mathematical common cause extendability results, is (part of) an empirically confirmed scientific theory.