&gt;Consider two axiomatic systems with different starting axioms. They are both internally consistent but may differ widely. How do we choose which ones to teach? Is diversity and scope important to building an objective perspective?<p>If we want to evaluate the axioms, you better teach both.<p>Internal consistency is just that - internal to that system.  Metaphilosophy would want to judge both, but if you never teach both, how would you judge?