Obections to Cantor's Theory (Wikipedia article)
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From: Han de Bruijn on 21 Jul 2005 05:52 Daryl McCullough wrote: > No, give a definition that *doesn't* use the words > "infinite", "finite", "limitless", "limit", "boundless", > etc. Give a *mathematical* definition. What he means is a *Hilbertian*, formalists definition. That's the way they suck you into their camp. Han de Bruijn
From: Han de Bruijn on 21 Jul 2005 06:03 Daryl McCullough wrote: > Tony Orlow (aeo6) <aeo6(a)cornell.edu> writes: > >>I asked for a definition of infinite, and no one could give me a >>definition of that word. The best I could get was that an infinite >>set can have a bijection with a proper subset, which is hardly a >>definition of the word "infinite". > > On the contrary, that's a perfectly good definition of the concept > "infinite set". It's the standard definition of the "actual infinite", but it is not "perfectly good". Worse. It's not good at all. Han de Bruijn
From: Han de Bruijn on 21 Jul 2005 06:21 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". For the simple reason that 'infinity' is not a concept that is limited to mathematics alone. 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 ? Han de Bruijn
From: Han de Bruijn on 21 Jul 2005 06:48 Chris Menzel wrote: > Guess what? That means you reject the continuum hypothesis! Isn't that > exciting? Don't you just want to go out and learn all about it rather > than just spouting vague, uninformed, and often silly nonsense? Really, do you mean that _accepting_ the Continuum Hypothesis somehow represents no-nonsense behaviour ? Han de Bruijn
From: Han de Bruijn on 21 Jul 2005 07:06
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 ? 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 ? Han de Bruijn |