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The Burali-Forti Paradox

Published online by Cambridge University Press:  14 March 2022

Irving M. Copi
Irving M. Copi*
Affiliation:
University of Michigan
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Extract

The year 1897 saw the publication of the first of the modern logical paradoxes. It was published by Cesare Burali-Forti, the Italian mathematician whose name it has come to bear. Burali-Forti's own formulation of the paradox was not altogether satisfactory, as he had confused well-ordered sets as defined by Cantor with what he himself called “perfectly ordered sets” (“Classe parfettamente ordinata”). However, he soon realized his mistake, and published a note admitting the error and making the correction. He concluded the note with the observation that his result could be established on the basis of the correct definition of well-ordered set as easily as for the “perfectly ordered sets” for which it had first been obtained. We shall reproduce his results in their corrected form.

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Type
Research Article
Information
Philosophy of Science , Volume 25 , Issue 4 , October 1958, pp. 281 - 286
Copyright
Copyright © 1958, The Williams & Wilkins Company

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Footnotes

1

From a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan.

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