  For Aristotle, the status of LNC as a first, indemonstrable principle is obvious. Those who mulishly demand a proof of LNC clearly “lack education”: since “a demonstration of everything is impossible”, resulting in infinite regress. At least some principles must be taken as primitive axiomata rather than derived from other propositions—and what principle more merits this status than LNC? (1006a6–12). In first philosophy, as in mathematics, an axiom is both indemonstrable and indispensable; without LNC, Aristotle argues, “a is F” and “a is not F” are indistinguishable and no argumentation is possible. While Sophists and “even many physicists” may claim that it is possible for the same thing to be and not to be at the same time and in the same respect, such a position self-destructs “if only our opponent says something”, since as soon as he opens his mouth to make an assertion, any assertion, he must accept LNC. But what if he does not open his mouth? Against such an individual “it is ridiculous to seek an argument” for he is no more than a vegetable (1006a1–15).