Contradiction, from the Latin: Contra Dicere, ‘to speak at-odds, against’.
Any attempt at the resolution of the Self-Eating Expression requires extended unflinching intimacy with this unpleasant beast. So let’s get started.
Anytime we use the word ‘Consistency’ [‘Of Course! That makes sense!’] in Mathematics or Language, we are drawing on the Non-Contradiction Principle. Much of what is called ‘Proof’, a word that makes every kid wet his pants in high-school, is a demonstration of the Internal Consistency of a set of Logico-Mathematical assertions.
‘Once one accepts a Logical Contradiction’ observes an eminent and anxious contemporary Physicist ‘one can prove anything one likes. It is the end of Rational-Thought’.
‘The Higgs Boson [a.k.a: ‘God-Particle’] is certain to be found’ assures a high scientist working with CERN in Geneva. ‘It is required to be there by the laws of [theoretical] consistency‘.
The Principle of Non-Contradiction is burdened with not only keeping all Rational-Thought alive but also providing a proper ‘God-Particle’ for the denied scientists. [God-Sighting was indeed confirmed this year, but annoyingly a smaller new techno-particle also showed-up. But the Scientists are on the chase.]