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Michael Fox

Paradoxical Truth - NYTimes.com - 1 views

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    "Professor Greene is lecturing. Down the hall, her arch-rival, Professor Browne, is also lecturing. Professor Greene is holding forth at length about how absurd Professor Browne's ideas are. She believes Professor Browne to be lecturing in Room 33. So to emphasize her point, she writes on the blackboard the single sentence:

    Everything written on the board in Room 33 is false.

    But Professor Greene has made a mistake. She, herself, is in Room 33. So is what she has written on the board true or false? If it's true, then since it itself is written on the board, it's false. If it's false, then since it is the only thing written on the board, it's true. Either way, it's both true and false.

    Philosophers and logicians love paradoxes, and this is one - one of the many versions of what is usually called the Liar Paradox, discovered by the ancient Greek philosopher Eubulides (4th century B.C.).

    Paradoxes are apparently good arguments that lead to conclusions that are beyond belief (Greek: "para" = beyond, "doxa" = belief). And when you meet a paradox, you've got only two choices. One is to accept that the conclusion, implausible as it may seem, is actually true; the other is to reject the conclusion, and explain what has gone wrong in the argument."
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