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, also called the Principle of Non-Contradiction]. In Aristotle’s phrase: ‘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’.
In short, this is a pretty important principle.
Aristotle’s defense of this pivotal principle is the oldest documented application of the Self-Eating Expression in the Western Tradition [at least that I am aware of].