Does There Exist a LaTeX/Word Rewrite of Georg Cantor's Works?

Question

I've got a reprint version of Georg Cantor's Contributions to the Foundings of the Theory of Transfinite Numbers (see http://www.maths.ed.ac.uk/~aar/papers/cantor1.pdf), but the print quality is quite poor (lots of missing dots and commas). Additionally, there's a lot of outdated terminology and notation, such as using the words "aggregate" and "part" instead of set and subset, and using $A = (M, N)$ instead of $A = M \cup N$.

Does anyone know if there exists a modern $\mathrm{\LaTeX}$ or Word rewrite of any of Cantor's Set Theory works, whether they be a single paper, several works, or a complete bibliography?

If not, I was considering doing it myself but I'm stuck as to whether I should update the terminology and notation or keep it. Furthermore, say I do make it myself, where should I publish it free of charge?

EDIT: Just to be clear, I'm not just looking for an entire collection of all of Cantor's works, just what currently exists in modern formats (e.g. $\mathrm{\LaTeX}$) and what there is left to rewrite.

Answer 1

Besides Philip E. B. Jourdain's 1915 translation of Cantor's two long 1890s papers and the translation of one of Cantor's papers in Edgar's Classics on Factrals, the following are the only English translations of Cantor's papers that I know about. I also have a personally procured translation of Cantor's review of Hermann Hankel's 1870 memoir Untersuchungen über die unendlich oft oszillierenden und unstetigen funktionen (see reference [3] here for publication details about Hankel's memoir), but this translation is not deposited anywhere on the internet.

There are several French translations of Cantor's work that were published in the 1880s, but these are fairly well known. For example, see the bibliography of Dauben's biography of Cantor. In fact, I cited a few of these French translations about 3 weeks ago in a Mathematics Stack Exchange answer.

Since the translation by Bingley [3] seems to not be very well known, I've included all of Bingley's introductory comments.

[1] William Bragg Ewald, From Kant to Hilbert: A Source Book in the Foundations of Mathematics, two volumes, Clarendon Press, 1996, xviii + 1340 pages (both volumes). reprinted in 2005

Volume II contains English translations of the following items: Cantor’s 1874 paper Ueber eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen (pp. 840-843); 1872-1882 correspondence between Cantor and Dedekind (pp. 843-878); Cantor’s 1883 booklet Grundlagen einer allgemeinen Mannigfaltigkeitslehre: Ein mathematisch-philosophischer Versuch in der Lehre des Unendlichen (pp. 881-920); Cantor’s 1892 paper Ueber eine elementare Frage der Mannigfaltigkeitslehre (pp. 920-922); 1897-1899 correspondence between Cantor and Dedekind & Hilbert (pp. 926-940).

[2] Shaughan M. Lavine, Understanding the Infinite, Harvard University Press, 1994, xii + 372 pages.

An English translation of Cantor’s 1892 paper Ueber eine elementare Frage der Mannigfaltigkeitslehre is given in Chapter IV, Appendix B, pp. 99-102.

[3] Transfinite Numbers. Three Papers on Transfinite Numbers from the Mathematische Annalen, translated by George Althoff Bingley (1888-1966), The Classics of the St. Johns Program, 1941, ii + 150 pages.

On pp. 92-150 Bingley has translated Cantor’s paper Ueber unendliche, lineare punktmannichfaltigkeiten 5 [On infinite, linear point sets 5], Mathematische Annalen 21 #4 (1883), 545-591. In Cantor’s original paper, pages 587-591 are Cantor’s “Endnotes”, which are longer footnotes put at the end of the paper. These five pages are sometimes omitted in the paging information for this paper in bibliographies. French translation (omitting the philosophical comments that make up the first half of the Mathematische Annalen version): Fondements d'une théorie générale des ensembles, Acta Mathematica 2 (December 1883), 381-408. Reprinted in Cantor’s 1932 “Collected Works” [4] (pp. 165-204 + Zermelo’s notes on pp. 204-209), and published separately as Grundlagen einer allgemeinen Mannigfaltigkeitslehre: Ein mathematisch-philosophischer Versuch in der Lehre des Unendlichen [Foundations of a General Theory of Manifolds: A Mathematical-Philosophical Essay in the Theory of the Infinite], B. G. Teubner (Leipzig), 1883, 47 pages. This 47-page separately published booklet (what Ewald translates on pp. 881-920) includes a half-page preface and 4 newly added footnotes, in addition to all the original endnotes of the Mathematische Annalen version.

Foreward [sic] (pp. i-ii): The translator offers in a single volume three papers of Georg Cantor on transfinite numbers all of which appeared in issues of the Mathematische Annalen. The first two, of volumes 46 and 49, form together a kind of text-book on transfinite numbers and were written after Cantor’s ideas had reached full maturity and had been generally accepted by mathematicians and logicians, and were no longer on the defensive. The earlier paper, of volume 21, usually called the “Grundlagen”, is an a̲p̲o̲l̲o̲g̲i̲a̲ and is indispensable if one is to know something of the genesis and development of Cantorian theory. Some of Cantor’s arguments in his own defence may now seem superfluous in a world which generally accepts them. The recent attack on Cantor by Brouwer and the intuitionalist school, however, calls for a new and thorough reassessment of the theory of point-sets. The beautiful superstructure of Cantor’s edifice cannot give us genuine pleasure if there linger doubts as to the soundness of the foundation. Cantor has been frequently defended by emiment [sic] mathematicians and logicians but in accordance with the St. John’s plan, we prefer that Cantor should speak for himself. This the “Grundlagen” in its labored and involved style, does. Also some will find in Cantor a modern phase of the age-old Platonic-Aristotelian controversy which runs through the entire list of the Great Books. The first two papers have already appeared in an English translation by Philip E. B. Jourdain. So far as the translator is aware no English translation of the “Grundlagen” has been published, although a French translation appeared some time ago in Acta Mathematica. These papers do not cover the entire range of Cantor’s ideas but are limited to that important field which best exemplifies the Cantorian point of view, that of transfinite numbers. In translating a work in a technical field it is quite impossible to please everyone in the matter of terminology. The translator in his own defence can merely say that he adopted the present terminology only after considerable thought and discussion. “Set” rather than “aggregate” seemed obviously preferable for “Menge”, for example. The difference between German rhetorical expression and English − a difference which superficially at least seems greater than that between ancient Greek and English − has made the translation of the “Grundlagen” no light task. The translation may be found to be too literal for comfortable reading but any attempt to improve Cantor’s style is attended with the danger of altering the meaning. The translator is greatly indebted to Mrs. Edward Flint Lathrop who has patiently and cheerfully cooperated in an earnest effort to keep the text reasonably free from typographical errors.

(ADDED NEXT DAY) Because many of those who study Cantor's original works rely almost entirely on the versions that appear in his 1932 collected works [4] (although in the last couple of decades this reliance is probably a lot less, since it's easy to find digitized versions of the original published versions), I thought it would be of interest to point out that there are many slight variations and even omissions between the original versions of Cantor's papers and those that appear in [4].

[4] Georg Ferdinand Ludwig Philip Cantor, Gesammelte Abhandlungen Mathematischen und Philosophischen Inhalts [Collected Papers of Mathematical and Philosophical Content], edited by Ernst Friedrich Ferdinand Zermelo, Springer, 1932, viii + 486 pages.

Some of Cantor’s papers in this 1932 collection are not reproduced in their exact original form, as noted by: Dauben (1979) [see: p. 44 (after equation 2.18) and p. 335 (note 1)]; Ferreirós (1999) [see: p. 160 (footnote 2) and p. 203 (footnote 2)]; Grattan-Guinness (1980) [see: p. 65, footnote 12]; Hallett (1984) [see: p. 5 (near bottom)]; Purkert (1989) [see: p. 52 (middle, beginning with Unfortunately, this footnote $\ldots)].$

Answer 2

All of Cantor's works? I doubt it.

plug
There in one Cantor paper (translated into English) here:

Edgar, Gerald A. (ed.), Classics on fractals, Reading, MA: Addison-Wesley Publishing Company. x, 366 p. (1993). ZBL0795.28007.

It is Cantor's paper “On the power of perfect sets of points” where the "Cantor set" can be found. It does have explanations about outdated notations and terminologies.