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Foundations of Mathematics

Axiomatic System

What is a fallacy?

A fallacy is an incorrect result—in this case, one arrived at through misleading reasoning when examining a logical argument. One of the more common fallacies in logic is thinking incorrectly that if “p implies q” is true, “then q implies p” is also true. The idea of such invalid arguments was well-known in the past: With Greek mathematician Aristotle’s syllogisms, an argument was valid if it adhered to all the laws; to be false, it only needed to break one law. Euclid, another Greek mathematician, was known to have written an entire book on fallacies in geometry, but the book has since been lost.

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English logician, philosopher, and mathematician Bertrand Russell came up with a puzzling paradox involving sets.



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