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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 Knowledge 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.
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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
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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
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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
534:
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
495:
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?
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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.
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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
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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 ?
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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.
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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.
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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
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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
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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
774:. 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. --
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Hi, does anyone know further references about the subject, expecially from a mathematical point of view? I could not find the word
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The link to
Completed infinity is bogus. It redirects to Infinity and there is no clear explanation of the term there.
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Ultra-finitism is more commonly used as far as I know. I think we should redirect the other names to ultra-finitism.
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Since I've filled this out with information from
Troelstra, who says "ultra-finitism", I've made the switch. --
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Indeed. I've added it to the article as an external link; we could also expand/rewrite the article based on it.
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http://www.maa.org/sites/default/files/images/upload_library/46/HOMSIGMAA/Shell_1st-Maloney-constructivists.pdf
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It was added by an IP editor at the beginning of March; I undid that edit. Thanks for pointing it out. — Carl
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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.
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the sense of being an extension of finitist principles. Rather than being extreme finitism, it is merely
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He has a book on philosophy of mathematics. I think this is mainly related to what he says in the book.
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http://math.stackexchange.com/questions/531/what-is-ultrafinitism-and-why-do-people-believe-it
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Good idea. There are also a considerable number of discussions on the FOM mailing list:
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The Lavine section needs help, sounds contradictory
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