A Transfinite Shave

July 11, 2015

A version of this post has been accepted into the Journal of the Association for Information Science and Technology as a letter-to-editor. Congratulations Alex DeCastro!

Tambo University

barberpoleRussell’s Barber: paradox or (else) pseudoparadox?

Some axioms can be “unprovable truths” of Godel’s incompleteness theorem. Today, we show that Godel’s theorem can be easy to understand in general terms, but hard to understand beyond a typical contradiction, as per Russell’s barber (pseudo) paradox.

Consider the classical Russell’s gedankenexperiment wherein, all the men that live in a village are cleanly shaven. They either shave themselves or they do not. If they do not shave themselves, the village’s only barber must shave them.

Hence there exist two sets: the set of all men who shave themselves and the set of all men who have the barber do it for them.

But, who shaves the barber?

Let us analyze this problem based on Zermelo-Fraenkel’s set theory and Cantor’s set theory.

Zermelo-Fraenkel’s set theory

Take a male barber that lives in the village. He is clean-shaven. Then, either he shaves himself or else he…

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2 Responses to “A Transfinite Shave”

  1. Joseph Nebus Says:

    Oh, congratulations!

    Liked by 1 person

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