The Banach-Tarski Paradox

Logique Et Analyse 261:41–53 (2023)
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Abstract

Emile Borel regards the Banach-Tarski Paradox as a reductio ad absurdum of the Axiom of Choice. Peter Forrest instead blames the assumption that physical space has a similar structure as the real numbers. This paper argues that Banach and Tarski's result is not paradoxical and that it merely illustrates a surprising feature of the continuum: dividing a spatial region into disjoint pieces need not preserve volume.

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Ulrich Meyer
Colgate University

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References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
The Axiom of Choice.Thomas J. Jech - 1973 - Amsterdam, Netherlands: North-Holland.
Zeno’s paradox of measure.Brian Skyrms - 1983 - In Robert S. Cohen & Larry Laudan (eds.), Physics, Philosophy and Psychoanalysis: Essays in Honor of Adolf Grünbaum. D. Reidel. pp. 223--254.
Grit or Gunk.Peter Forrest - 2004 - The Monist 87 (3):351-370.
Les paradoxes de l'infini.Emile Borel - 1946 - [Paris]: Gallimard.

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