Some logicians-such as G. Kreisel-have stated that the Continuum Hypothesis is decided in ZFC2 ("Second-Order ZFC") although we do not know which way it is decided. This is rather confusing, since it is not usually made clear just what the collection of axioms (both logical and non-logical) of ZFC2-as a formalized theory-is to include. ZFC2 is presumably formalized in the Classical Second-Order Predicate Calculus which is not recursively axiomatizable. Is (at least) the following weaker alternative to Kreisel"s statement correct? "If T is any consistent and recursively axiomatizable sub-theory of ZFC2, then neither the Continuum Hypothesis nor its Negation is provable in T."