Cantor Confusion
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From: William Hughes on 6 Oct 2006 07:44 mueckenh(a)rz.fh-augsburg.de wrote: > William Hughes schrieb: > > > Note the question was very carefully posed so it was not > > "Can X write about all his days?", but "Can X write about > > every single day?". > > There is the answer 1) There is no day which will not be written. > There is the answer 2) There is a day which will not be written namely > the present day. I have decided to agree with answer 2 every second day. So I agree with answer 2 yesterday and tomorrow but never today. - William Hughes
From: Tonico on 6 Oct 2006 07:47 mueckenh(a)rz.fh-augsburg.de ha escrito: > William Hughes schrieb: > > > Note the question was very carefully posed so it was not > > "Can X write about all his days?", but "Can X write about > > every single day?". > > There is the answer 1) There is no day which will not be written. > There is the answer 2) There is a day which will not be written namely > the present day. > > Both answers contradict each other. > > Regards, WM ******************************************************* Answer (2) is incorrect, as can easily be proved: the present (this) day will be written down in 50,000 years more. Q.E.D. Tonio
From: William Hughes on 6 Oct 2006 08:12 Tonico wrote: > mueckenh(a)rz.fh-augsburg.de ha escrito: > > > William Hughes schrieb: > > > > > Note the question was very carefully posed so it was not > > > "Can X write about all his days?", but "Can X write about > > > every single day?". > > > > There is the answer 1) There is no day which will not be written. > > There is the answer 2) There is a day which will not be written namely > > the present day. > > > > Both answers contradict each other. > > > > Regards, WM > ******************************************************* > Answer (2) is incorrect, as can easily be proved: the present (this) > day will be written down in 50,000 years more. Q.E.D. > Tonio And 50,000 years from now, the present day will be different. Remember "The rule is, jam tomorrow and jam yesterday - but never jam today." If you want to indulge in discussions like this you have to be up on your looking-glass logic. For every possible present day. -The present day will not have been written about yet. -The present day will eventually be written about. -William Hughes
From: William Hughes on 6 Oct 2006 09:24 Albrecht wrote: > William Hughes schrieb: > > > Albrecht wrote: > > > > <...> > > > > > I don't controvert the axiomatic methode anymore. But I claim that it > > > isn't the only and the important one in math. In teaching and in the > > > mind of the people the axiomatic method appears to be the only right > > > way to do math. That's not correct. > > > The nondenumerable infinity of the reals is not the only one truth. > > > Nobody is wrong who claims only one kind of infinity, the one we only > > > can know: the endless infinity. > > > > > > > > > The problem is not that someone who believes > > in your intuitive "endless infinity" (intuitive because it cannot > > be put on a mathematical footing) is wrong. > > Oh yes, it is the problem. I came to these subject by reading a bunch > of popular books about math. When I read the diagonal argument the > third or fourth time I started to wonder. The textes were of differnt > quality but all of them had a special sort of feeling. And all stated, > that this proof is so elementary, easy and absolute right that nobody > had anything to reflect or critizise about it. > But I found in shortest time a lot of questions about the issue. > Later I read professional works about set theorie and I found a similar > feeling in the textes about the diagonal argument. And then I started > to learn about the role of ZF in the teaching on universities and I had > a lot of disputes about the matter in newsgroups. Don't you find it interesting that of all the places you looked, the only place where anyone disagreed with the diagonal argument was the newsgroups? > And I learnd that > there are a lot of people who react irrational if someone questions > about the issue. > > In my opinion, the problem is that many people belief, they understand > the diagonal proof - but they don't. But since you cannot back up this opinion it is worth as much as your intuitive understanding of infinity. > And that a lot of people belief, > that the axiomatic method is the top of math, as Hilbert had declared. > And that a lot of people belief that math without ZF is dubious. And > that a lot of people seem to have a religious feeling if they rant > about transfinite numbers and unreachable cardinal numbers and all this > stuff. > Possibly, but I have seen no evidence of this, and you have presented none (true, you accuse anyone who disagrees with you of doing so because of religious grounds, but your bald statement is not evidence). > ZF introduces a nonsientific element in math which is not beneficial > for the science, I'm really sure. And I'm really sure it does not. End of discussion. It does not help for you to be sure, you need convincing arguments. > Good brains waste their time with transfinite numbers and all of this > stuff and with fixing the problems which appear by using ZF. Math is > much more. > That's the way I see the problem. > Well in terms of utility. most of mathematics fails (given that most theorems about how accurate an integral approximation is are useless in practice, where does that leave the more esoteric parts of mathematics (almost all of it)). I do not find the study of transfinites to be any more or less a waste of time than any branch of mathematics. - William Hughes
From: Albrecht on 6 Oct 2006 10:31
William Hughes schrieb: > Albrecht wrote: > > William Hughes schrieb: > > > > > Albrecht wrote: > > > > > > <...> > > > > > > > I don't controvert the axiomatic methode anymore. But I claim that it > > > > isn't the only and the important one in math. In teaching and in the > > > > mind of the people the axiomatic method appears to be the only right > > > > way to do math. That's not correct. > > > > The nondenumerable infinity of the reals is not the only one truth. > > > > Nobody is wrong who claims only one kind of infinity, the one we only > > > > can know: the endless infinity. > > > > > > > > > > > > > The problem is not that someone who believes > > > in your intuitive "endless infinity" (intuitive because it cannot > > > be put on a mathematical footing) is wrong. > > > > Oh yes, it is the problem. I came to these subject by reading a bunch > > of popular books about math. When I read the diagonal argument the > > third or fourth time I started to wonder. The textes were of differnt > > quality but all of them had a special sort of feeling. And all stated, > > that this proof is so elementary, easy and absolute right that nobody > > had anything to reflect or critizise about it. > > But I found in shortest time a lot of questions about the issue. > > Later I read professional works about set theorie and I found a similar > > feeling in the textes about the diagonal argument. And then I started > > to learn about the role of ZF in the teaching on universities and I had > > a lot of disputes about the matter in newsgroups. > > Don't you find it interesting that of all the places you looked, > the only place where anyone disagreed with the diagonal > argument was the newsgroups? That's really untrue. I had read several books and papers of academics (who do not post in this or the german math newsgroups) in which they formulate (very cautious) criticism about ZF, axiomatic set theory or especially the axiom of infinity. I understand, why they are cautious. They fear the defamation they must be aware of if they would be very concrete in criticism. I have experienced this defamation (not for me but other persons). There are a lot of people who do not abhor from defamation and denuncation. This people react about criticism as their sanity or life is threatened. It's really not understandable. If you want I try to find some of this books and papers again and give you the information about authors and titels. Some may only be available in German language. Best regards Albrecht S. Storz > > > And I learnd that > > there are a lot of people who react irrational if someone questions > > about the issue. > > > > In my opinion, the problem is that many people belief, they understand > > the diagonal proof - but they don't. > > But since you cannot back up this opinion it is worth > as much as your intuitive understanding of infinity. > > > And that a lot of people belief, > > that the axiomatic method is the top of math, as Hilbert had declared. > > And that a lot of people belief that math without ZF is dubious. And > > that a lot of people seem to have a religious feeling if they rant > > about transfinite numbers and unreachable cardinal numbers and all this > > stuff. > > > > Possibly, but I have seen no evidence of this, and you have > presented none (true, you accuse anyone who disagrees with > you of doing so because of religious grounds, but your > bald statement is not evidence). > > > > ZF introduces a nonsientific element in math which is not beneficial > > for the science, I'm really sure. > > And I'm really sure it does not. End of discussion. It does > not help for you to be sure, you need convincing arguments. > > > Good brains waste their time with transfinite numbers and all of this > > stuff and with fixing the problems which appear by using ZF. Math is > > much more. > > That's the way I see the problem. > > > > Well in terms of utility. most of mathematics fails (given that most > theorems about how accurate an integral approximation is are > useless in practice, where does that leave the more esoteric > parts of mathematics (almost all of it)). I do not find the study > of transfinites to be any more or less a waste of time than > any branch of mathematics. > > - William Hughes |