WikiProject Philosophy  (Rated Startclass, Lowimportance)  


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I'm not at all happy with this page. I don't know a lot about transfinites but there are things here that worry me. Limit? Not in the normal sense. This needs expansion at least.
You can't just give something a name and hope that it won't introduce inconsistency to do so. Often it does. Going to have a think about this. Andrewa 10:50 16 Jul 2003 (UTC)
This is a proper noun. I have moved the page back to "Absolute Infinite" (with "absolute infinite" redirecting here).  The Anome 08:55, 18 Sep 2003 (UTC)
In the see also section, what does "The Absolute" refer to?? Jaberwocky6669 02:28, Mar 30, 2005 (UTC)
 Allow me to redo my question, what is the "absolute" at the top of the article? Jaberwocky6669 02:30, Mar 30, 2005 (UTC)
The sentence " Indeed, naive set theory might be said to be based on this notion. " in BuraliForti is vague and seems incorrect to me. For example, in ^{[1]} the treatment is fully consistent with ZFC. I suggest removing this sentence altogether as it does not add anything useful and confuses the inexpert reader. cerniagigante (talk) 16:34, 24 January 2017 (UTC)
References
 ^ Halmos, Paul (1974). Naive Set Theory. Springer. ISBN 9780486814872.
Did he seriously think this?
Is this serious? Did Cantor actually believe that "that every property of the Absolute Infinite is also held by some smaller object"? I mean, he was clearly an incredibly smart guy, but on the face of it, that's an idiotic opinion.
For example, it implies that there is some smaller object that is also larger than all objects besides itself. Rwv37 04:25, Jun 27, 2005 (UTC)
 Isn't the universe such an object? 24.174.45.155 21:33, 16 July 2006 (UTC)
 No. The universe is an object that is larger than all objects besides itself. But that property is *not* shared with some smaller object. Rwv37 00:41, 22 July 2006 (UTC)
 I am using this exchange as justifying this article as "unclear." Cantor's quote "that every property..." is almost certainly a reference to the Reflection Theorem of set theorybut I can't be sure without a citation. See Reflection principle for more information. Cobaltnova 22:14, 10 November 2007 (UTC)
 No. The universe is an object that is larger than all objects besides itself. But that property is *not* shared with some smaller object. Rwv37 00:41, 22 July 2006 (UTC)
 Isn't the universe such an object? 24.174.45.155 21:33, 16 July 2006 (UTC)
The notion of multiplicity Cantor describes here can't possibly be the same as on multiplicity A multiplicity is called wellordered if it fulfills the condition that every submultiplicity has a first element; such a multiplicity I call for short a sequence. 24.174.45.155 21:33, 16 July 2006 (UTC)
 I think he means what we now call a cardinal number. I just piped the wikilink which I hope is ok. 75.62.4.229 (talk) 04:37, 24 November 2007 (UTC)
 Close. I am virtually certain he just means a set. Because the definition of a wellordered set is one in which each subset has a least member. Hccrle (talk) 21:36, 29 August 2009 (UTC)
Absolute Absolute Infinite, Absolute Absolute Absolute Infinite, etc.
The way that leads from Infinite to Absolute Infinite could lead also from Absolute Infinite to Absolute Absolute Infinite, from Absolute Absolute Infinite to Absolute Absolute Absolute Infinite and beyond. So, where is the limit? 89.1.112.168 07:25, 13 September 2007 (UTC)
The limit is at the beginning of your diatribe: the Absolute Infinite is the order of proper classes, which are not sets. Therefore we are not allowed to form bigger sets. So there is nothing larger than the Absolute Infinite. That's what is absolute about it. There is no Absolute Absolute Infinite. Hccrle (talk) 22:00, 29 August 2009 (UTC)
Proper Classes and Philosophical Qualms
I am removing "mysterious" from the description of proper classes. These ideas are mathematically welldefined (see Kunen, Kenneth "Set Theory: An Introduction to Independence Proofs").
von Neumann universe
I think the corresponding idea in axiomatic set theory is the von Neumann universe also known as the cumulative hierarchy. 75.62.4.229 (talk) 04:39, 24 November 2007 (UTC)
You're on the right track. Assuming the Axiom of Choice, the transfinite cardinal numbers are ordinal numbers that form the backbone, so to speak, of the von Neumann universe. Every stage of construction of that universe has a rank, which is an ordinal number and is a member of that stage. The class of all the ordinal numbers is a proper class, and is the Absolute Infinite. Hccrle (talk) 08:19, 30 August 2009 (UTC)
What is bigger than Absolute Infinite?
I shall call him XIBTAI  acronym of Xibtai Is Bigger Than Absolute Infinite! —Preceding unsigned comment added by 89.0.54.122 (talk) 08:27, 11 September 2008 (UTC)
See the above section Absolute Absolute Infinite ... Hccrle (talk) 22:05, 29 August 2009 (UTC)
Nothing is larger than The Absolute infinite
So, what is larger than Nothing? 217.132.68.201 (talk) 11:18, 16 February 2010 (UTC)
Variants of the quote
Currently the article uses this translation:
The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type.
Jané however has this translation in "The role of the absolute infinite in Cantor's conception of set":
The actual infinite can be divided according to three aspects: first, as it is realized in the supreme perfection, in the completely independent, extrawordly being, in God, where I call it absolute infinite or simply absolute; second as it is represented in the dependent world of things created; third as conceived in abstracto as a mathematical quantity, number or ordertype. (Cantor 188788, p. 378)
And from the original quote (https://www.unisiegen.de/fb6/phima/lehre/phima10/quellentexte/handoutphimateil4b.pdf) it seems to be:
The actual infinite was distinguished by three relations: first, as it is realized in the supreme perfection, in the completely independent, extrawordly existence, in Deo, where I call it absolute infinite or simply absolute; second to the extent that it is represented in the dependent, creatural world; third as it can be conceived in abstracto in thought as a mathematical magnitude, number or ordertype. In the latter two relations, where it obviously reveals itself as limited and capable for further proliferation and hence familiar to the finite, I call it Transfinitum and strongly contrast it with the absolute.
Fixuture (talk) 23:45, 4 July 2015 (UTC)
 That is a major difference. The first two translations suggest that Cantor was naive; the last seems suggests that Cantor's thinking was quite modern and uptodate (viz a premonition of 20th century transfinite work). 67.198.37.16 (talk) 04:27, 8 July 2016 (UTC)