Cantor Confusion
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From: David Marcus on 25 Oct 2006 00:39 Lester Zick wrote: > On Mon, 23 Oct 2006 22:01:25 -0400, David Marcus > <DavidMarcus(a)alumdotmit.edu> wrote: > > >Han de Bruijn wrote: > > [. . .] > > >> > >> There are many readers here who DO understand Mueckenheim's binary tree. > >> And no, binary trees will not be found in Halmos' "Naive Set Theory". > >> Because it's too naive, I suppose .. > > > >You mean all the cranks think they understand it. > > So this set of all cranks. Would that be those who disagree with you? That's not the definition of "crank". Wikipedia has a definition of crank. You can readily detect cranks because they never clearly state what their words mean, they keep repeating the same things rather than understanding and replying to what others say to them, and they seem to be unfamiliar with the standard literature/books on the topic they discuss. Since Mueckenheim claims his binary tree shows an inconsistency in standard mathematics (at least he sometimes claims that--at other times he claims to not be discussing standard mathematics), if anyone really understood what Mueckenheim was saying, they could translate it into standard mathematics and demonstrate the inconsistency. Some people claim they understand it, but fail to give their translation. These people either don't understand it, don't understand standard mathematics, or both. Everyone who has succeeded in translating it into standard mathematics has also shown that the translation does not show an inconsistency. So, these people either don't understand what Mueckenheim really means, what Meuckenheim is saying is wrong, or both. I tend to think it is "both" in both cases. -- David Marcus
From: David Marcus on 25 Oct 2006 00:44 Lester Zick wrote: > On Mon, 23 Oct 2006 22:06:05 -0400, David Marcus > <DavidMarcus(a)alumdotmit.edu> wrote: > >Han de Bruijn wrote: > >> And no, binary trees will not be found in Halmos' "Naive Set Theory". > >> Because it's too naive, I suppose .. > > > >I don't see how you would know it is not there since you said that while > >you own the book, you've never read it. Funny how books aren't much use > >if you don't actually read them. > > > >Anyway, I didn't say binary trees were in the book. I said that if > >Muckenheim wants to talk using the mathematical concepts of sets, > >functions, and relations, he should use standard terminology, where > >"standard" means the same as in some mathematics book. It is like saying > >that if he wants to speak in English he should use words according to > >the meanings as given in an English dictionary. > > So you're suggesting we should argue against a paradigm in terms set > by the paradigm? So perhaps I should argue my definition of "infinity" > in standard set analytic terms even though cast in Newtonian terms of > the calculus? Curious to say the least. You didn't actually read what I wrote, did you? Mueckenheim claims his example is part of standard mathematics. That's the whole point, since he claims it shows standard mathematics is inconsistent. If the example can't be given in standard mathematics, then it can't show that standard mathematics is inconsistent. If the example is part of standard mathematics, Mueckenheim should be able to state it using standard terminology. Of course, he is free to use any new terminology he wishes, as long as he identifies it as such and defines it. If Mueckenheim would merely admit that he was creating a new type of mathematics, most people would leave him to it. -- David Marcus
From: David Marcus on 25 Oct 2006 00:47 Lester Zick wrote: > On Mon, 23 Oct 2006 22:16:36 -0400, David Marcus > <DavidMarcus(a)alumdotmit.edu> wrote: > >Dik T. Winter wrote: > >> In article <1161377915.999210.39660(a)m7g2000cwm.googlegroups.com> "MoeBlee" <jazzmobe(a)hotmail.com> writes: > >> > mueck...(a)rz.fh-augsburg.de wrote: > >> ... > >> > Okay, now that I asked for a definition of the relation you mentioned, > >> > you're not giving that definition, but instead giving a > >> > combinatorical/numerical argument with more terminology. What is a > >> > "load of edges"? What is the definition of "a path carries a load of > >> > edges"? If this is standard terminology in graph theory, then please > >> > forgive my ignorance and supply me with the standard definition. If it > >> > is not standard terminology, then please give me your own definition. > >> > >> By this time you ought to know that Mueckenheim *never* gives definitions. > >> Or actually states that he is not able to give a definition for a > >> particular term. Asking for definitions from Mueckenheim is as useful as > >> talking to an eel. > > > >This does seem to be true. I suspect he doesn't know what the word > >"definition" means in mathematics. > > "Definition" in mathematics would appear to mean pretty much whatever > people who claim to do mathematics say it means. Ex: Cardinality is > card(x)= least ordinal(x) equinumerous(x). In other words mathematical > definition is when definition(x) defines mathematical definition(x).Or > mathematics is when mathematician(x) and a mathematician is when > mathematics(x). I don't know whether M. gives mathematical definitions > or not.However I know a great many mathematikers who definitely don't. OK, so both Mueckenheim and you don't know what the word "definition" means in Mathematics. I suppose most of us already knew that. What we find somewhat puzzling is why you don't take the trouble to learn. Have you tried, but not been able to? What math courses have you taken? -- David Marcus
From: David Marcus on 25 Oct 2006 01:13 cbrown(a)cbrownsystems.com wrote: > David Marcus wrote: > > cbrown(a)cbrownsystems.com wrote: > > > David Marcus wrote: > > > > But, if one theory is vague or ill defined, then it can be hard to say > > > > whether an experiment really supports it. > > > > > > I donlt quite get what you are implying here. I assume you have some > > > particular physical experiment in mind where this is the case as > > > regards QM. Could you elaborate? > > > > Not a particular experiment, but the Copenhagen interpretation itself. > > See "What is the meaning of the wave function" by Jean Bricmont. Google > > turns up several copies on the Web. > > I appreciate your comments, and will look up the indicated references. > Thanks for your time. After you read Bell's explanation of Bertlmann's socks, you should read the section "The Story Distorted" in Chapter 12 of the book "The Quark and the Jaguar" by Murray Gell-Mann. This demonstrates that being able to think logically is not required in order to win the Nobel Prize in Physics. Jean Bricmont in "What is the meaning of the wave function?" refers to Gell-Mann's discussion of Bertlmann's socks as "a remarkable misunderstanding". -- David Marcus
From: stephen on 25 Oct 2006 07:45
David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > Lester Zick wrote: >> >> In article <1161377915.999210.39660(a)m7g2000cwm.googlegroups.com> "MoeBlee" <jazzmobe(a)hotmail.com> writes: >> >> > mueck...(a)rz.fh-augsburg.de wrote: >> >> ... >> >> > Okay, now that I asked for a definition of the relation you mentioned, >> >> > you're not giving that definition, but instead giving a >> >> > combinatorical/numerical argument with more terminology. What is a >> >> > "load of edges"? What is the definition of "a path carries a load of >> >> > edges"? If this is standard terminology in graph theory, then please >> >> > forgive my ignorance and supply me with the standard definition. If it >> >> > is not standard terminology, then please give me your own definition. >> >> >> >> By this time you ought to know that Mueckenheim *never* gives definitions. >> >> Or actually states that he is not able to give a definition for a >> >> particular term. Asking for definitions from Mueckenheim is as useful as >> >> talking to an eel. >> > >> >This does seem to be true. I suspect he doesn't know what the word >> >"definition" means in mathematics. >> >> "Definition" in mathematics would appear to mean pretty much whatever >> people who claim to do mathematics say it means. Ex: Cardinality is >> card(x)= least ordinal(x) equinumerous(x). In other words mathematical >> definition is when definition(x) defines mathematical definition(x).Or >> mathematics is when mathematician(x) and a mathematician is when >> mathematics(x). I don't know whether M. gives mathematical definitions >> or not.However I know a great many mathematikers who definitely don't. > OK, so both Mueckenheim and you don't know what the word "definition" > means in Mathematics. I suppose most of us already knew that. What we > find somewhat puzzling is why you don't take the trouble to learn. Have > you tried, but not been able to? What math courses have you taken? > -- > David Marcus You are talking to someone who thinks that dr/dt = r/t for circular motion, where r is the radius and t is time. Do not expect anything sensible. Stephen |