The completeness of the concept is always in doubt. Instead of definition, the term 'exposition' applies. The only kind of concept that allows of definition are arbitrarily invented concepts. If I invented it, I can always define it. Therefore, mathematics is the only science that has definitions.
Philosophical definitions are never more that expositions.
The definition ought to come at the end of our enquiries. In mathematics we have no concept prior to the definition. Mathematical definitions can never be in error. These, in so far as they are immediately certain, are synthetic a priori principles. Mathematics can have axioms since by means of the construction of concepts in the intuition of the object it can combine predicates of the object both a priori and immediately.