Cantor Confusion
in [Math]
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From: Virgil on 16 Feb 2007 22:23 In article <rubrum-2C1A89.18112316022007(a)newsclstr02.news.prodigy.com>, Michael Press <rubrum(a)pacbell.net> wrote: > In article > <virgil-E37A5B.15421415022007(a)comcast.dca.giganews.com>, > Virgil <virgil(a)comcast.net> wrote: > > In article <1171576194.042084.91330(a)a34g2000cwb.googlegroups.com>, > > mueckenh(a)rz.fh-augsburg.de wrote: > > [...] > > > > It seems you are in a very deep confusion. > > > > It is called transference. > > Technically, it is called projection. > Transference is when A treats B as if > B were someone else from A's life. > Transference could be in play, > but this exchange is not evidence. Whatever WM's misbehavior may be called in fields other than mathematics, in the field of mathematics it is called silly.
From: cbrown on 16 Feb 2007 22:32 On Feb 16, 12:38 am, mueck...(a)rz.fh-augsburg.de wrote: > On 15 Feb., 14:05, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: > <snip> > Let's get on with the actual > > representation of 3: {{{{}}}}. > > This is not a representation of 3 other than in a perverted system, > which calls 0 the first number, 1 the second and so on. Of course > {{{{}}}}, or better and easier {{{{, denotes the fourth number which > is 4 and not 3. So, if I have no bananas, what number of bananas do I have? Suppose we agree that we will put both of our collections of bananas in a basket. I have no bananas, you have {{{{. How many bananas are your bananas + my bananas? How many bananas remain when we remove your contribution? Cheers - Chas
From: Michael Press on 17 Feb 2007 02:05 In article <a0bat2ph8kof1gjb1qfrb06vjhmlmkpbke(a)4ax.com>, G. Frege <nomail(a)invalid> wrote: > On Fri, 16 Feb 2007 03:39:36 GMT, "Dik T. Winter" <Dik.Winter(a)cwi.nl> > wrote: > > > > > Actually it has already been used in Alice in Wonderland, published when > > Frege was 17 years old ... > > > Actually I was referring to (1) the insight that there really a > problem is lurking and (2) the idea of using quotation marks to > prevent such confusion. :-) > > See: > http://plato.stanford.edu/entries/quotation/ A good read. With no claim of originality I advance the glove box theory of quotation. Quotation marks isolated a progression of tokens from the remainder of the sentence. The quotation may be grammatically correct natural language prose with semantic content; or not, to any degree whatever. The quotation need not grammatically fit into the sentence that it is imbedded in. The reader and author examine, probe, and experiment upon the quotation; while the quotation may not escape the confines of the quotation marks; as it would in a science fiction movie, wreaking a well-deserved and grisly comeuppance on the author. The quotation is presented for the reader to study and to make of it what he will. The reader then soldiers on to hear what the author makes of the quotation. -- Michael Press
From: Michael Press on 17 Feb 2007 02:12 In article <MPG.203ef87d4dd2aa7989cd0(a)news.rcn.com>, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > Dik T. Winter wrote: > > In article <gn2at2565gmfg5kjlbpr2jn10l6mfuiht3(a)4ax.com> G. Frege <nomail(a)invalid> writes: > > > On Thu, 15 Feb 2007 20:29:22 -0500, David Marcus > > > <DavidMarcus(a)alumdotmit.edu> wrote: > > ... > > > >>> For one thing, WM is missing the knowledge that a name is not the object > > > >>> named. > > > >>> > > > >> Is this valid for names too? > > > >> > > > > I think so. My name is "David". ""David"" is a name for my name. Another > > > > name for my name would be "my name". > > > > > > Actually, again one of the many insights of Gottlob Frege [the real > > > one]. > > > > Actually it has already been used in Alice in Wonderland, published when > > Frege was 17 years old: > > Knight: The name of the song is called Haddocks' Eyes. > > Alice : Oh, that's the name of the song, is it? > > Knight: No, you don't understand, that is what the name is called, the > > name really is The Aged Aged Man. > > Alice : Then I ought to have said that's what the song is called? > > Knight: No, you oughtn't: that's quite another thing! The song is > > called Ways And Means, but that's only what it's called. > > Alice : Well, what is the song then? > > Knight: I was coming to that, the song really is A-sitting On A Gate. > > Lewis Carroll was not entirely stupid... > > As Martin Gardner pointed out, the Knight should have just started to > sing the song after saying "... the song really is". "A-sitting On A > Gate" is another name, not the song itself. Exactly what I thought. Very entertaining, and an object lesson in knowing exactly what words someone is using. I wish Carroll had finished strongly. Perhaps if he had read Korzybski ... -- Michael Press
From: mueckenh on 17 Feb 2007 03:52
On 16 Feb., 15:58, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: > In article <1171615110.930410.270...(a)s48g2000cws.googlegroups.com> mueck....(a)rz.fh-augsburg.de writes: > > > On 15 Feb., 14:05, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: > ... > > > Indeed, my error. So your comment: > > > > When seen as a set of curly brackets it has 3 at the left sinde and 3 > > > > at the right. > > > was actually completely irrelevant. Let's get on with the actual > > > representation of 3: {{{{}}}}. =20 > > This is not a representation of 3 other than in a perverted system, > > which calls 0 the first number, 1 the second and so on. Of course > > {{{{}}}}, or better and easier {{{{, denotes the fourth number which > > is 4 and not 3. > > Can you tell me a form of set theory where 0 is *not* the first ordinal > or cardinal number? If so, how many elements does the empty set have > in such a system? 0 may be the first (or better the zeroest) ordinal or cardinal number (if you wish to have the empty set in the theory). Nevertheless it is not the first natural number and not a natural number at all. > > > > > Only set theory needs this absurd definition of nought to be the > > "first" number, because 3 counting the numbers up to 2 but not 3 > > itself fits well with omega counting all the natural numbers but being > > not a natural number. No, this is sham does not help: The number of > > all natural numbers=B4, if existing, is a natural number, because the > > natural numbers count themselves (so they were designed). > > So how many natural numbers precede the first natural numbers? We are > counting natural numbers, so it should be a natural number? Natural numbers are counting the elements of natural sets, i.e., of sets which exist in reality (in nature, as Cantor woud have said). > > > |{1}| = 1 > > |{1,2}| = 2 > > |{1,2,3}| = 3 > > ... > > |{1,2,3,...}| = ... i.e. potentially infinite, not fixed, capable of > > growing without bound, denoted by oo but not by a fixed number omega. > > And |{}| = ? A set which "also streng genommen als solche gar nicht vorhanden ist" (Cantor) A set which "ist also vermöge der Definition von S. 4 gar keine Menge" (Fraenkel) An unnatural set cannot have a natural number of elements. Regards, WM |