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:
“Three elements go to make up an idea. The first is its intrinsic quality as a feeling. The second is the energy with which it affects other ideas, an energy which is infinite in the here-and-nowness of immediate sensation, finite and relative in the recency of the past. The third element is the tendency of an idea to bring along other ideas with it.”
—Charles Sanders Peirce (1839–1914)
“People who love only once in their lives are ... shallow people. What they call their loyalty, and their fidelity, I call either the lethargy of custom or their lack of imagination. Faithfulness is to the emotional life what consistency is to the life of the intellect—simply a confession of failures.”
—Oscar Wilde (1854–1900)