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.]
[I’ve always chuckled at this line from the writer F. Scott Fitzgerald: ‘The test of a first-rate intelligence is the ability to hold two opposed ideas in mind at the same time and still retain the ability to function…’.]
The Principal Principle of Logico-Mathematical model [in fact of all ‘Analytical Cognition’, to use Immanuel Kant’s expansive phrase] is the Principle of Contradiction.
In delightful irony, it is also called the Principle of Non-Contradiction.
When your high-school teacher asked you to ‘prove’ something in math-class, he was asking you to show that it all held together nicely. In other words, that you were not contradicting yourself somewhere in the fine-print.
Aristotle’s defense of this pivotal principle is the first formalized application of the Self-Eating Expression in the Western Tradition that I am aware of.
He called it: ‘The First Principle of Rational Knowledge’. It is ‘Aristotle’s Principle’; for it was he who had the courage of conviction to place it on center stage.
This dominant Principle [Virodha in Sanskrit, literally: ‘conflicted, to be countered’] had been known for centuries before Aristotle. But no philosopher before him made as brilliant, forceful and convincing a case for what, in his words: ‘one must have to understand anything whatsoever.’
Two thousand later, Immanuel Kant, who defined the domain of Academic Philosophy for two hundred years, in his Critique of Pure Reason called it the: ‘Principle Sine Qua Non-the universal and fully sufficient principle of all analytic cognition’.
Aristotle’s Principle is the pillar behind the most celebrated claims of High Intellection, of Rationality itself. If you question it you question everything.
Aristotle’s founding of Classical Logic began as an extension of its truth. And Philosophy and Logic, Language and Mathematics, indeed every subject claiming to be rational has had to make peace with its diktats.
In short, this is a pretty important principle.