Saturday, June 4, 2011

Georg Cantor's 1883 "Grundlagen" article

Several years ago in Halifax, I found this translation of Cantor's 1883 article "On Infinite Linear Point Manifolds". The text comes from a set of mimeographed typewritten translations of three of Cantor's foundational papers on set theory and transfinite numbers, typewritten and mimeographed, it seems, in Nova Scotia's Annapolis Valley in 1941. The translator we have to thank for this is named George Bingley, though I haven't been able to find out any more information about him.

Of the three texts included in the manuscript, two are already available in English in the decently priced Dover volume. The third, as far as I know, is not [[CORRECTION: as far as I knew it was not available in English. It turns out that it is, in another translationin the 2nd volume of the mammoth and fantastically useful anthology entitled From Kant to Hilbert).]] Milner's French translation of the text appeared in Vol. 10 of the Cahiers pour l'analyse and can be found here.

Cantor - Grundlagen


  1. Just thought i'd let you know that there is also a more recent english translation of the grundlagen in "From Kant to Hilbert: a source book in the foundations of mathematics, Vol 2" edited by William Ewald.

  2. Thanks! It seemed strange that there wouldn't be an English translation of the text out there somewhere.

  3. I suspect that the text was translated rather in Annapolis MD, at St. John's College, where reading the original texts of Cantor's work has long been a part of Junior or Senior math. Next time I'm down there, I'll try to find out if there's institutional memory of a tutor named Mr. Bingley. (I presume there will be, if only for the sake of the Jane Austen jokes?) Note that Jacob Klein came to St. John's in 1937, and it seems likely that he may have had a hand in suggesting that Cantor be translated there.