Something can be both right and wrong

philosophy: Is there more than just true or false?

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The year is 340 before our time, maybe a decade or two sooner or later. Aristotle (384–322 BC) wrote a text in ancient Greece that later philosophers considered his metaphysics should denote. In her fourth book, he takes a look at some of his predecessors and argues for the principle of excluded third and for the principle of excluded contradiction.

What is meant by each is best understood with a little symbolism. If A. is any statement, then is ~ A its negation. Stands A. So for "The sun is shining", then stands ~ A for "It is not the case that the sun is shining". And if you are for A. "Brutus killed Caesar" then means ~ A "It is not the case that Brutus killed Caesar". We can also put it in a more natural way: "The sun is not shining" and "Brutus did not kill Caesar".

The principle of the excluded third party states that for everyone Declarative sentence A. either A. or ~ A true is. The sun is either shining or not; either Brutus killed Caesar or he didn't. A statement is either true or false. There is no third option.

Graham priest

The logician Graham Priest, born in London in 1948, was a professor of philosophy in Melbourne, Australia, and now teaches at the Graduate Center of City University in New York.

And the principle of excluded contradiction says that for everyone Declarative sentence A. applies: A. and ~ A cannot be true at the same time. The sun cannot shine and not shine at the same time; it cannot be the case that Brutus both killed and did not kill Caesar. A statement cannot be both true and false. That would be a contradiction; and contradictions cannot be true.

For Aristotle, some of his predecessors violated these principles. Modern scholars are divided on whether they really did. But there is no question that he believed this.

There are doubts as to whether the principle of the excluded third party was absolutely valid for Aristotle. Because in the rather famous chapter nine of one of his other writings, De interpretations (as the Romans called them) he seems to be claiming that contingent statements about the future are neither true nor false. The view of the Aegean shows us the fleets of Athens and Sparta. Will they go into battle tomorrow or not? There is still no decisive issue in this question. The future is open. Tomorrow either of these two statements will be true; at the moment it is neither.

Aristotle's stance on the principle of excluded contradiction, however, was unequivocal. He calls it the firmest of all principles and says (oddly enough, given his own account of its predecessors) that no one can really believe a contradiction.

From a modern perspective, Aristotle's arguments for the proposition of the excluded third party and the proposition of the excluded contradiction do not seem particularly compelling. In particular, what he cites for the latter is confused, unclear and often misses the point. In some places he claims that it could not be the case that all Contradictions are true - which is compatible with the fact that some are true.

Be that as it may, Aristotle's text elevated the propositions of the excluded third party and excluded contradiction in Western logic to orthodoxy - so much so that after him there were hardly any further attempts to justify the principles. They are simply assumed. Especially people who claim contradictions are accused of showing the highest degree of irrationality.