Boxing Pythagoras

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Archive for the tag “Banach-Tarski”

Wildberger says that Banach-Tarski is Nonsense

Dr. N.J. Wildberger has added a new video to his “Sociology and Mathematics” series in which he discusses the Banach-Tarski Paradox. If you are unfamiliar with this particular concept, it suffices to say that Banach-Tarski illustrates some very peculiar and counterintuitive properties of infinite sets. Fairly unsurprisingly for anyone familiar with Dr. Wildberger’s work, he considers the entire discussion undertaken by Banach-Tarski to be nothing but nonsense. In the video, Dr. Wildberger explicitly notes that he rejects the Axiom of Choice (one of the major axioms upon which Banach-Tarski relies) and I have discussed previously that he also rejects the Axiom of Infinity (which is similarly necessary for Banach-Tarski). Thus, Dr. Wildberger’s video (and his original blog post which inspired the video) seemed fairly curious to me.

Yes, of course the Banach-Tarski Paradox is nonsense if you reject the axioms upon which it depends. Any and every mathematical theorem in existence would be nonsensical to a person who rejected the axioms underlying that theorem.

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