  Although PNC is not subject to demonstration, it is subject to “elenctic refutation” according to Aristotle. The “elenchus” refers to the Socratic method of argument. When Socrates uses the elenchus, he gets his opponent to refute himself out of his own mouth. The opponent makes a proposal that is shown to conflict with other claims to which he agrees. To be consistent, the opponent must give up one of these claims, and he usually abandons the original proposal. This is the method of reductio ad absurdum familiar to ancient Greek geometers and modern formal logicians and mathematicians.