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. Philosophy has no axioms since it is simply what reason knows by means of concepts. The axioms of intuition in the Table of Principles are not axioms in the mathematical sense, they are the principles that specify the possibility of axioms in general. No empirical grounds of proof can ever amount to apodeictic proof.