Well, I'm thinking of something like: What's an a charged particle? Something that responds to an electric field. What's an electric field? Something that makes a charged particle move.It's not nearly as bad as an inconsistency, but it's certainly undesirable. I think we can define "inconsistent" as "it's possible to derive the negation of one of the axioms from the others". This would obviously be disaster, but I think it's also pretty bad to have a situation where "it's possible to derive one of the axioms from the others". Then we have an axiom that adds nothing to the theory, and I would certainly prefer to remove it. To include it would give people the impression that we either believe that it adds something significant, or don't understand that it doesn't.
I like this MTW claim: Here and elsewhere in science, as stressed not least by Henri Poincare, that view is out of date which used to say, "Define your terms before you proceed." All the laws of physics, including the Lorentz force law, have this deep and subtle character, that they both define the concepyts they use and make statements about these concepts. Contrariwise, the absence of some body of theory, law and principle deprives one of the means properly to define or even to use concepts. Any forward step in human knowledge is truly creative in this sense: that theory, concept, law, and method of measurement - forever inseparable - are born into the world in union.