Talk:Ultrafinitism

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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)Reply

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)Reply

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)Reply

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)Reply

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)Reply

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)Reply

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)Reply

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)Reply

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)Reply

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)Reply

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)Reply

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)Reply

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

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)Reply

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)Reply

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)Reply

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)Reply

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)Reply

It is not reasonable to include Norman Wildberger in the list of people who "worked on ultrafinitism". I can personally vouch for mathematicians like Ed Nelson and Doron Zeilberger, who have both done valuable contributions to actual mathematics. I am aware of their work, though I cannot say that I have come across any of it that happens to elucidate any aspects of ultrafinitism in particular. But for Wildberger, I see it as problematic that he is now currently in the business of monitizing youtube videos that feature unsubstantiated attacks on mainstream mathematics by a wide range of obvious deception mechanisms such as straw man tactics as well as a variety of the strategies described on the Wikipedia page on Equivocation. It is not reasonable to include the name of a recognizable crackpot among names of recognized mathematicians, as it is bound to tarnish their well-owned reputations. — Preceding unsigned comment added by 90.185.105.208 (talk) 19:58, 16 July 2018 (UTC)Reply

I haven't looked deeply into Wildberger, but he seems to have a position at a legit university. He holds unusual views that I don't share, but then all ultrafinitists do; I'm not sure by what clear criterion we're going to separate Wildberger from the others here.

Zeilberger may be more problematic as an example of someone who has "worked in the topic". I'm not actually aware that he has, in any serious way. He expresses his opinions forcefully in the course of his other mathematical work, but he does not seem to publish serious papers in foundations, at least that I have seen in a cursory search from his webpage. Let me know if I've missed something.

Nelson, on the other hand, did seriously "work in the topic", in Predicative Arithmetic. Whether Wildberger's "rational trigonometry" is serious or not I haven't looked into enough to offer an opinion, but it does seem to be work on the topic. --Trovatore (talk) 05:29, 17 July 2018 (UTC)Reply

While one might accept that the expression

${\displaystyle x^{5}=x\cdot x\cdot x\cdot x\cdot x}$

is meaningful as an abbreviation, that does not mean that one must accept

${\displaystyle x^{n}}$

as meaningful when n is a variable. In the absence of the axiom of powerset, there may not be any way to prove the existence of an exponential function. JRSpriggs (talk) 18:59, 22 January 2026 (UTC)Reply

A popular mathematics youtuber recently uploaded a video that goes over this subject, and explains why it's regarded as.... not very smart by mathematicians, which may result in viewers coming to make humorous edits to this article like a previous edit today. It doesn't seem to be an issue worthy of article protection yet, but just something to watch out for. Rai1i1inbow (talk) 18:32, 16 June 2026 (UTC)Reply