Talk:Limitation of size

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Mathematics rating:	Stub Class	Mid Priority	Field: Foundations, logic, and set theory
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Geometry guy 19:15, 21 May 2007 (UTC)

[edit] expert template

My hand was a little bit forced in writing this article; I had put it on requested articles, and someone fulfilled the request with a redirect to Von Neumann-Bernays-Gödel set theory, which was not what I was interested in. Since the existence of the redirect would have resulted in removal of the request from requested articles, I had to write a stub.

Unfortunately I'm not all that sure of my facts here. I don't have Hallett's book, for one thing. So if anyone can help out with this question, it'd be appreciated:

I said Cantor developed the notion in response to Cantor's paradox, but the article there says the paradox was not formulated until 1899, and I would have thought "inconsistent multiplicities" was an earlier concept than that. On the other hand I don't know what else would have led him to call such multiplicities "inconsistent". Can anyone straighten out the historical order? --Trovatore 23:44, 25 February 2006 (UTC)

Many experts believe--though it is controversial--that Cantor was aware of the set-theoretic paradoxes as early as 1883-4. There is a footnote (n.2) in his Grundlagen that says "The Absolute [i.e. the mind of God] can only be recognized, never known, not even approximately...The absolutely infinite sequence of numbers therefore seems to me in a certain sense a suitable symbol of the Absolute" (translated in Hallett 1984, p.42). With some heavy interpretation one can read into this quote the idea that the sequence of all ordinals cannot itself be a set with an ordinal number. This would then be a version of what we know as the Burali-Forti paradox (the ordinal version of Cantor's Paradox). ||||[user: anewstead, 14 Feb 2007]

Actually I also need someone to check the originator of the idea. I don't have Hallett's book, but from what I could find by browsing it at amazon, it looks like the idea, or at least the phrase, may have come from Jourdain. But "inconsistent multiplicities" is still Cantor's terminology, isn't it? Does someone have a reference for his meaning for that phrase? --Trovatore 06:32, 26 February 2006 (UTC)

Hmm. I don't really know anything about this, past having heard the term used. It sued to strike me as a silly way of talking about inconsistency, until I started to grasp what was going on with the large cardinal hierarchy. --- Charles Stewart(talk) 20:56, 28 February 2006 (UTC)

OK, thanks for taking a look. --Trovatore 21:01, 28 February 2006 (UTC)

Cantor uses the term 'inconsistent multiplicity' in his letter to David Hilbert discussing the paradoxes (1895). An inconsistent multiplicity is, according to Cantor, any many that cannot be conceived of as a unity or set without leading to contradictions. ||||[user:anewstead, 14 Feb 2007]

To Anewstead (talk · contribs): Please do not remove the comments of other users unless they are: vandalism, obscenity, libel, copyright violations, etc.. JRSpriggs 06:27, 15 February 2007 (UTC)