Talk:Ultrafinitism

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Inexistifyable[edit]

What does this word means? If you google it the only hit is this page and a couple of copies of this page. PuercoPop (talk) 20:51, 30 March 2013 (UTC)

It was added by an IP editor at the beginning of March; I undid that edit. Thanks for pointing it out. — Carl (CBM · talk) 02:16, 31 March 2013 (UTC)

References[edit]

Hi, does anyone know further references about the subject, expecially from a mathematical point of view? I could not find the word ultrafinitism on MathSciNet, nor searching the American Mathematical Society site! I remember Penelope Maddy somewhere referring to ultrafinitism, but with no reference. Thanks.Popopp 16:04, 2 March 2007 (UTC)

This is informative: http://mathoverflow.net/questions/44208/is-there-any-formal-foundation-to-ultrafinitism

71.141.88.54 (talk) 22:52, 16 February 2011 (UTC)

Indeed. I've added it to the article as an external link; we could also expand/rewrite the article based on it. Shreevatsa (talk) 06:52, 17 February 2011 (UTC)
http://math.stackexchange.com/questions/531/what-is-ultrafinitism-and-why-do-people-believe-it
Good idea. There are also a considerable number of discussions on the FOM mailing list: http://www.google.com/search?q=site:cs.nyu.edu+ultrafinitism rdt (talk) 02:22, 10 June 2011 (UTC)
Another discussion on ultrafinitim is here: http://golem.ph.utexas.edu/category/2011/09/the_inconsistency_of_arithmeti.html rdt (talk) 15:28, 23 October 2011 (UTC)

Wittgenstein?[edit]

Under the section about notable personalities associated with ultrafinism Wittgenstein is listed. I'm curious, and this is certainly relevant to the article in my opinion: was this "early," "middle," or "late" Wittgenstein as the Stanford Encyclopedia of Philosophy might definite it? 108.218.2.235 (talk) 02:29, 12 December 2011 (UTC)

He has a book on philosophy of mathematics. I think this is mainly related to what he says in the book. 24.52.220.88 (talk) 07:04, 9 June 2012 (UTC)


Strict Finitism[edit]

It appears, after a quick search on Google, that this concept is much more commonly referred to as "ultrafinitism", but that the two terms are synonymous. I could be wrong, not being terribly familiar with either of the terms, but it seems that the article should probably be renamed in favor of the more popular term. -Chinju

Since I've filled this out with information from Troelstra, who says "ultra-finitism", I've made the switch. -- Toby Bartels 23:15, 15 Oct 2003 (UTC)

I believe that Strict Finitism is more standard terminology than Ultrafinitism. I suggest either renaming this article to "Strict Finitism" or, if the name "Ultrafinitism" is left, then redirecting Strict Finitism here.

Dagme (talk) 22:46, 17 April 2011 (UTC)

Ultra-finitism is more commonly used as far as I know. I think we should redirect the other names to ultra-finitism. rdt (talk) 02:19, 10 June 2011 (UTC)


Completed infinity[edit]

The link to Completed infinity is bogus. It redirects to Infinity and there is no clear explanation of the term there. Yecril 07:52, 30 March 2007 (UTC)

I removed it.--Patrick 11:23, 10 June 2007 (UTC)


Extremism[edit]

I'd be cautious using a word like "extreme" to describe a philosophy. It may be a minority opinion, but saying that it is an extreme form of finitism may be misleading, as it may suggest to the reader that it is held in some kind of disrepute by mainstream philosophers. Also, it is not extreme in the sense of being an extension of finitist principles. Rather than being extreme finitism, it is merely more constrained than finitism. Twelvethirteen 01:17, 28 September 2005 (UTC)

Skewes' Number[edit]

I think that the claim "it may not even be physically possible to do so" needs clarification. I suggest comparing it to a number such as the believed number of particles in the universe, which I think is significantly less? Someone who knows more should clarify. --Philip Ross 05:24, 1 May 2006 (UTC)

Dark Integers[edit]

Greg Egan's short stories "Luminous" and "Dark Integers" are wonderful science-fictional takes on ultrafinitism. I can't quite bring myself to add a "Ultrafinitism in fiction" section to this article, though. -- The Anome (talk) 13:13, 7 June 2015 (UTC)

Further reading[edit]

This looks like it might be relevant: http://www.maa.org/sites/default/files/images/upload_library/46/HOMSIGMAA/Shell_1st-Maloney-constructivists.pdf -- The Anome (talk) 13:56, 7 June 2015 (UTC)

The Lavine section needs help, sounds contradictory[edit]

The current page has this text: Lavine has shown that the basic principles of arithmetic such as "there is no largest natural number" can be upheld, as Lavine allows for the inclusion of "indefinitely large" numbers.

There's a citation on the sentence, that's fine. What's troubling to me is that this summary is incomplete. I do not understand Lavine's work, but I don't think it is acceptable to summarize the work like this. What you've essentially said is "this guy, who works only on numbers that can actually be written, has created a system that allows for no largest integer by allowing it to not be written." That makes no sense. Can someone who is familiar with Lavine's work please clean up this sentence and give it some more explanation ? AristosM (talk) —Preceding undated comment added 04:07, 2 July 2017 (UTC)