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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). ||||
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367:, 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? --
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Having taken a look at that article, I kind of think it's misnamed. It's not really just about the axiom. Logistics aside, much of that content (especially the "doctrine" section) should live in a philosophical article without "axiom" in the name, and there should be a small technical article about
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Maybe the easiest would be to merge this into the current "axiom" article, then move the "axiom" article to the "limitation of size" name over the redirect — this would require admin help. Then the intro of the combined article could be edited to somewhat de-emphasize the formal axiom and talk more
383:
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?
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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 can only be recognized, never known, not even approximately...The absolutely infinite sequence of numbers
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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. ||||
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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. ---
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I don't agree. Limitation of size as a philosophical concept seems quite different from any formal axiom. If anything the axiom article should be merged to the philosophical one. --
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on
Knowledge. If you would like to support the project, please visit the project page, where you can get more details on how you can help, and where you can join the
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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:
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the axiom specifically, which should have the "axiom" name. I don't have an immediate proposal for how to get there. --
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Does someone have a reference for his meaning for that phrase? --
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