 In the case of the second theorem, \(F\) must contain a little bit more arithmetic than in the case of the first theorem, which holds under very weak conditions. It is important to note that this result, like the first incompleteness theorem, is a theorem about formal provability, or derivability (which is always relative to some formal system; in this case, to \(F\) itself). It does not say anything about whether, for a particular theory \(T\) satisfying the conditions of the theorem, the statement “\(T\) is consistent” can be proved in the sense of being shown to be true by a conclusive argument, or by a proof generally acceptable for mathematicians. For many theories, this is perfectly possible.