 for integers \(m\) and \(n\), then (in essence) \((*)\) is provable in the system; and if \((*)\) is false, then it is not provable in the system, then \(f\) is recursive. See  supplement A.2  for a more detailed discussion of this controversial argument—controversial because Church simply assumes that the set of axioms and rules of a symbolic logic must be recursive, and this has seemed to some to beg the question of the truth of  CT1  and thus to constitute a “stumbling block” to the acceptance of Church’s argument (Sieg 1997).