Cantor's Diagonal?
in [Math]
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From: Herman Jurjus on 10 Feb 2010 06:34 Transfer Principle wrote: > On the other hand, the following WM quote appears in the > thread to which I linked above: > >> "Axiom Of Potential Infinity: For every natural number there is a set >> that contains this number together with all smaller natural numbers, >> and for every set of natural numbers there is a natural number that >> is larger than every number of the set." > > In this post, WM has expressed that he wants potentially > infinite sets to exist, but for no _actually_ infinite > sets to exist. It matters little to "cranks" like WM > that without actually infinite sets, calculus is most > likely impossible. On the contrary. For all practical purposes, all of it can still be done, be it in a more clumsy way. (After all, before 1908, all mathematics had to be done without relying on infinite sets.) -- Cheers, Herman Jurjus
From: Carsten Schultz on 10 Feb 2010 07:11 Am 10.02.10 10:30, schrieb Herman Jurjus: > Transfer Principle wrote: >> >> The main point here is not to attack ultrafinitism, but merely >> to point out that if I hold Y-V and WM to my same standards, >> then either both are "cranks," or neither are. > > So much for your standards, then. > > The problem with WM is not so much that he's 'wrong', but that he's a ^^ ^^^^ > lousy mathematician. ^^^^^^^^^^^^^^ I have marked a mistake that you made, but apart from that I totally agree with you. > He's confused about lots of things: > He confuses rejection of actual infinity with ultra-finitism. > He claims to have proved ZFC inconsistent with a proof that's not > formalizable in ZFC (and doesn't show any signs of being aware of the > latter). > He claims he agrees with Robinson where he doesn't. > Etc, etc. > > But worst of all: he doesn't even attempt a formalization or precise > elucidation of what is and is not allowed in his mathematics. > > A rather big contrast with Yessenin-Volpin, wouldn't you say? -- Carsten Schultz (2:38, 33:47) http://carsten.codimi.de/ PGP/GPG key on the pgp.net key servers, fingerprint on my home page.
From: Franz Fritsche on 10 Feb 2010 07:26 On Wed, 10 Feb 2010 10:30:54 +0100, Herman Jurjus wrote: > Transfer Principle wrote: >> >> The main point here is not to attack ultrafinitism, but merely >> to point out that if I hold Y-V and WM to my same standards, >> then either both are "cranks," or neither are. >> > So much for your standards, then. Right. Another funny thing: This bull (WM) explicitly _rejects_ to be considered a (representative of) ultrafinitism! :-) FF P.S. Note that he's _not_ a mathematician, but a physicist by profession.
From: FredJeffries on 10 Feb 2010 07:40 On Feb 9, 2:01 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > On Feb 9, 8:14 am, FredJeffries <fredjeffr...(a)gmail.com> wrote: > > > On Feb 7, 10:55 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > > Therefore, _ultra_finitists such as WM and > > > Yessenin-Volpin will now be considered cranks (and that's > > > _without_ the scare quotes, since the label is deserved). > > That you consider Alexander Yessenin-Volpin a crank does not say much > > for your method of classification. <snip /> > strongly implying that in Jeffries's own method of classification > Y-V isn't a "crank," even though WM is. Bzzzzzzzzzzzzzzztttttttttttt. You just failed Logic 101.
From: FredJeffries on 10 Feb 2010 07:56
On Feb 9, 2:01 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > On Feb 9, 8:14 am, FredJeffries <fredjeffr...(a)gmail.com> wrote: > > > On Feb 7, 10:55 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > > Therefore, _ultra_finitists such as WM and > > > Yessenin-Volpin will now be considered cranks (and that's > > > _without_ the scare quotes, since the label is deserved). > > That you consider Alexander Yessenin-Volpin a crank does not say much > > for your method of classification. <snip /> > the standard theorist Jeffries That you consider Fred Jeffries a standard theorist does not say much for your method of classification. |