Relative Consistency
Beyond consistency, relative consistency is also the mark of a worthwhile axiom system. This is when the undefined terms of a first axiom system are provided definitions from a second such that the axioms of the first are theorems of the second.
A good example is the relative consistency of neutral geometry or absolute geometry with respect to the theory of the real number system. Lines and points are undefined terms in absolute geometry, but assigned meanings in the theory of real numbers in a way that is consistent with both axiom systems.
Read more about this topic: Axiomatic System
Famous quotes containing the words relative and/or consistency:
“Are not all finite beings better pleased with motions relative than absolute?”
—Henry David Thoreau (1817–1862)
“All religions have honored the beggar. For he proves that in a matter at the same time as prosaic and holy, banal and regenerative as the giving of alms, intellect and morality, consistency and principles are miserably inadequate.”
—Walter Benjamin (1892–1940)