Obections to Cantor's Theory (Wikipedia article)
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From: stephen on 21 Jul 2005 10:29 In sci.math Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: > Virgil wrote: >> One issue here is that TO keeps ignoring standard mathematical >> definitions, however often presented, and then declaring that that the >> defined words and phrases must have other meanings than the ones >> mathematicians have agreed on. > Meanings ? Agreed on ? Yes. When communicating with others you have to use the agreed upon meanings of words. Is that really such a hard concept? Otherwise, banana coaster throat warbling yachtsman. > Look at Daryl McCullough's arguments, where he asks Tony to think about > "fluffy pink flying elephants". So what meanings have you mathematicians > agreed on ? There is agreed upon definition for "infinite set", "countably infinite", "bijection", "cardinality", etc. They are all fairly simply definitions. Stephen
From: stephen on 21 Jul 2005 10:37 In sci.math Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: > stephen(a)nomail.com wrote: >> These seems to be another common misconception among >> the anti-Cantorians that words cannot have specific >> meanings in specific contexts. Somehow they >> think an all-encompassing definition of 'infinite' must >> be provided before someone can say what an infinite set is. >> I am not sure what they mental hangup is. I wonder >> how any of them would ever learn a foreign language. > Ha, ha, ha. _This_ anti-Cantorian has learned six languages: Dutch, > German, French, English, Latin and Greek. We in the Netherlands are > privileged with our knowledge of foreign languages. Yet I find that > an "all-encompassing definition of 'infinite' must be provided". That seems silly. > For the simple reason that 'infinity' is not a concept that is limited > to mathematics alone. The word 'infinity' is not limited to mathematics alone, but 'infinite set' is limited to mathematics. 'infinite set' has a precise definition, and the definition does not have to include all possible uses of the word 'infinity' or 'infinite' in other areas. > It spreads out i.e. into physics, and gives rise > there to singularities that exist but one can never perceive them, due > to a Cosmic Censorship that prevents us to take a look into the inside > of a Black Hole. Thanks to Roger Penrose. Does somebody believe this ? Why are you bringing physics into this? Whether black holes exist or not has nothing to do with set theory. Stephen
From: David Kastrup on 21 Jul 2005 10:46 stephen(a)nomail.com writes: > In sci.math Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: > >> It spreads out i.e. into physics, and gives rise >> there to singularities that exist but one can never perceive them, due >> to a Cosmic Censorship that prevents us to take a look into the inside >> of a Black Hole. Thanks to Roger Penrose. Does somebody believe this ? > > Why are you bringing physics into this? Whether black > holes exist or not has nothing to do with set theory. Something that is so dense that everything you throw at it does not leave an impact apart from even more denseness? I am not sure this can be called irrelevant to this thread. -- David Kastrup, Kriemhildstr. 15, 44793 Bochum
From: Han de Bruijn on 21 Jul 2005 10:48 stephen(a)nomail.com wrote: > Why are you bringing physics into this? Whether black > holes exist or not has nothing to do with set theory. Theoretically: no. In practice: yes. Because some consequences of set theory have invaded into physics by the fact that mathematics becomes somewhat _applied_ there, huh ! Geez ... Han de Bruijn
From: David Kastrup on 21 Jul 2005 10:56
Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: > stephen(a)nomail.com wrote: > >> Why are you bringing physics into this? Whether black >> holes exist or not has nothing to do with set theory. > > Theoretically: no. In practice: yes. Because some consequences of > set theory have invaded into physics by the fact that mathematics > becomes somewhat _applied_ there, huh ! Geez ... Physics can influence where mathematics is heading, but not what it is finding there. Its verdict on mathematics can't be "true"/"false", but just "interesting"/"irrelevant". -- David Kastrup, Kriemhildstr. 15, 44793 Bochum |