 What is the relevance of the failure of axiomatizability of \(\mathbf{IFL}\)? Discussing finite partially ordered quantifiers, Quine (1970: 89–91) suggests that we should refuse to give the status of logic to any generalization of \(\mathbf{FO}\) which does not have a sound and complete proof procedure both for validity and for inconsistency. For Quine, any such generalization belongs to mathematics rather than logic. Since \(\mathbf{FPO}\) is not axiomatizable, it falls outside the realm of logic, thus  delineated.[48]