Acta Mathematica

, Volume 124, Issue 1, pp 65–107 | Cite as

An unpublished paper by Georg Cantor: Principien einer Theorie der Ordnungstypen Erste Mittheilung

  • I. Grattan-Guinness
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  1. (1).
    No manuscript survives of the lecture, but a set of notes made by Stäckel was seen by Fraenkel when preparing his biography of Cantor [see [30], 265–266]. In his bookAbstract set theory, Fraenkel cited these notes to remark thatActa Mathematica had rejectedthe survey paper of 1895–97 at some earlier time for being “100 years too early” [see [31], 1–2, 249; and also [30], 213]. But Cantor must have been referring to the manuscript of 1884: thus there was either a misunderstanding of Cantor's lectures by Stäckel, or of Stäckel's notes (which we have not yet traced) by Fraenkel. In his review of the correspondence, Schönflies thought that the manuscript on ordered sets—which of course he did not find—appeared as part of a later publication [that is [23], §§I, VIII; see [39], 15].Google Scholar
  2. (1).
    [Scheffer died a few months later, in his 27th year. For Cantor's obituary notice, see [21].]Google Scholar
  3. (1).
    [Cantors reference is toTannery's review of the whole of the first two volumes ofActa Mathematica.]Google Scholar
  4. (1).
    [The reference is to Charles Frédéric Gerhardt (1816–1856). On his theory of chemical types, see [37], 456–460.]Google Scholar
  5. (1).
    [On p. 14 of the letter-book, Cantor added the following sentence to the draft, but omitted it from the final version: “Es hat also hier das Wort „abbilden” einen andern Sinn (und ich darf hinzufügen, einem dem Sprachgebrauch entsprechenderen Sinn), als es seit Gauss und Riemann in der Funct.theorie und Geometrie gewonnen hat, wo man jetzt sogar jede functionelle Zuordnung zweier Gebilde für eine „Abbildung” ausgiebt, was m. e. sich durch aus nicht rechtfertigen lässt. Wenn ich nicht irre, so ist dieser maaslose Gebrauch des Wortes auf Herrn A. Clebsch zurückzuführen”.]Google Scholar
  6. (1).
    [This is the end of the proof-pages. We now read on from p. 9 of the manuscript.]Google Scholar
  7. (1).
    [In a postcard of the 23rd November, 1884, Cantor summarised and then changed the original text at this point as follows: “Am Schlusse des § 4 [sic] meiner Arbeit hat sich folgendes Versehen eingeschlichen. Ich sage: Wenn α, β, γ, … Zahlen sind, so sei: ... + α + *β + γ + *δ + ... einTypus, der sich selbst nur aufeine Weise ähnlich ist.Es soll aber heissen: Sind α, β, zwei finite oder transfinite Zahlen, so ist den Typus: α + *β sich selbst nur auf eine Weise ähnlich. Dagegen gilt diesnicht vom Typus *β + α, wie man leicht sieht. Bitte die Stelle in diesem Sinne zu ändern!” But in his letter of the 30th November, Cantor changed the passage again to the text that now follows.]Google Scholar
  8. (1).
    [On p. 16 of the letter-book Cantor noted that the text that had been written so far was sent off to Mittag-Leffler on the 18th November, 1884. But the parcel seems to have contained also the section beginning two paragraphs below: “Ist π…” and ending “… beschäftigen soll”, for it was drafted on p. 17 of the letter-book and written out on both sides of a small slip of paper attached to p. 11 of the manuscript. Later Cantor drafted a version of the intermediate paragraphs in the margin of p. 16 of the letter-book and sent the final version to Mittag-Leffler, who wrote them out in his own hand on a separate sheet of paper, dated it “5th February, 1885” and indicated to the printer that they should be inserted at the present place. In view of this situation, we indicate by our sign // three extra unnumbered paginations: the sheet written out by Mittag-Leffler, and the two sides of Cantor's slip of paper attached to p. 11 of the manuscript.]Google Scholar
  9. (1).
    [This was the original end of the paper: on p. 30 of the letter-book Cantor noted that he sent this latter half of the manuscript to Mittag-Leffler on the 25th February, 1885. There now follows the addendum, drafted on the rest of p. 30 of the letter-book (where the numbering §9 was put and then deleted), and written out on a separate sheet.]Google Scholar
  10. (1).
    [To the change of date (written on page 20 of the manuscript) Cantor added the remark: “N. B. Bitte dieses Datum zu behalten, es ist das Datum, unter welchem die ersten 6 Paragraphen an Herrn Mittag-Leffler geschickt worden sind.” But we know that that was the date of thecommencement of the paper: the first six paragraphs were sent to Mittag-Leffler only on the 18th November, and the rest on the 25th of February.]Google Scholar

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Copyright information

© Almqvist & Wiksells Boktryckeri AB 1970

Authors and Affiliations

  • I. Grattan-Guinness
    • 1
  1. 1.Enfield College of TechnologyEnfieldEngland

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