It seems that, over many centuries, no philosopher or mathematician ever seriously questioned Aristotle’s law of the excluded third: for every proposition p, either p or not p, symbolically p V ¬p. In retrospect, it appears that Aristotle himself had some doubts about applying this law when talking about events in time, e.g., when p was the proposition: there will be a sea battle tomorrow. But in mathematics, which deals with unchanging entities, the law of the excluded third was accepted as gospel truth, as was the equivalent assertion: for every proposition p, ¬¬p ⇒ p; two negations make an affirmation.