 When a set of sentences provides an implicit definition of a relation, one can ask whether that relation (and, by extension, the set of sentences itself) is satisfiable. That is, one can ask whether there is an n-tuple which, when serving as the interpretation of the relevant terms in the sentences, will make each sentence true. Each of Hilbert’s consistency-demonstrations in FG provides an n-tuple that satisfies the relevant defined relation, and hence provides a proof of the satisfiability of that relation. Satisfiability in this sense is sufficient for consistency, via the reasoning given  above.[6] 