What are some examples of paradoxes throughout history?

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Chapter Foundations of Mathematics

The oldest paradoxes may be from the Greek Epimenides the Cretan (lived sometime during the 6th century B.C.E.), who stated, “All Cretans are liars.” If this statement is true—and any other culture you would care to put in the Cretans’ place—then the implication is that the statement is a lie. This is also called the “Liar’s paradox.”

The number of paradoxes continued almost ad infinitum since then. Some of the more popular ones include those listed as Zeno’s paradoxes. They were named after Greek philosopher Zeno of Elea (c. 490 B.C.E.), a disciple of the philosopher Parmenides, who believed that reality was an absolute, unchanging whole—and, thus, many things we take for granted, such as motion, were simply illusions. In order to defend his master’s highly debated philosophy, Zeno developed his paradoxes. Most of Zeno’s paradoxes are still highly debated by modern mathematicians and philosophers, thus proving another paradox: Nothing truly changes throughout history—or does it?


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