 The quantum probability space that predicts the EPR correlations does not contain common causes for these correlations because this quantum probability space is defined on a finite dimensional Hilbert space and such a quantum probability space is not purely non-atomic hence not common cause complete. The question of whether “hidden” common causes for such correlations can in principle exist has been extensively discussed in a large literature. The first informal discussion seems to be von Neumann’s letter to Schrödinger in 1935 (Von Neumann 2005: 211–213). In this letter von Neumann takes the position that no correlation, including EPR-type quantum correlations, is problematic as long as one can find a common cause for it—although von Neumann does not use the term “common cause”, nor does he define any notion of common cause explicitly (Rédei 2006). The first technically explicit no-go theorem on common causes of EPR correlations is due to van Fraassen (1982). In this paper it is assumed however that a single common cause explains different correlations—i.e., that common causes are common common causes. It turns out however that, given a set \((A_i,B_i)\) (\(i=1,2,\ldots\)) of pairs of correlated events in a classical probability measure space, requiring the existence of a common cause \(C_i\) for each correlated pair \((A_i,B_i)\) is a much weaker assumption than requiring the existence of a single C that is the common cause of all correlated pairs \((A_i,B_i)\) (\(i=1,2,\ldots\)): one can give examples of different correlations in a classical probability measure space that cannot have the same common cause (Hofer-Szabó, Rédei, &amp; Szabó 2002). Thus if one aims at deriving no-go propositions on the existence of common causes of EPR correlations then one has to either argue that the different correlations in the EPR-situation should have the same common cause or one should impose further conditions on the common causes in addition to those in  Reichenbach’s definition (2)–(5).