Economic design problems are more successful in garnering support from practitioners when the axioms are relevant to the practical context. We use the well-known Dummy axiom as a concentrated example of several ways in which axioms can fail to be meaningful in practice. We then describe two channels through which characterization results using axioms that are not relevant to a specific context can undermine the axiomatic program, both from an internal (theoretical) standpoint and from its relationship with the practical world. Yet, a great deal of intellectual stimulation can be found in disciplining ourselves to be guided by context, despite the theorist’s traditional leaning towards universality.