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Ideas for 'How the Laws of Physics Lie', 'U.S. Declaration of Independence' and 'Mathematical logic and theory of types'

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5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox

6407	The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling]
	Full Idea: The class of teaspoons isn't a teaspoon, so isn't a member of itself; but the class of non-teaspoons is a member of itself. The class of all classes which are not members of themselves is a member of itself if it isn't a member of itself! Paradox.
	From: report of Bertrand Russell (Mathematical logic and theory of types [1908]) by A.C. Grayling - Russell Ch.2
	A reaction: A very compressed version of Russell's famous paradox, often known as the 'barber' paradox. Russell developed his Theory of Types in an attempt to counter the paradox. Frege's response was to despair of his own theory.