Foundations of Mathematics

Axiomatic System

What is a paradox?

In logic, paradoxes are statements that seem to be self-contradictory or contrary to one’s expectations. These arguments imply both a proposition and its opposite. One of the most famous paradoxes was stated by English logician Bertrand Russell (1872–1970) in 1901 dealing with sets: “If sets that are not members of themselves are normal, is the set of normal sets itself normal?” (For more information about Russell’s paradoxes in set theory, see below.)


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