Obections to Cantor's Theory (Wikipedia article)
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From: Alec McKenzie on 22 Jul 2005 04:21 "Poker Joker" <Poker(a)wi.rr.com> wrote: > Mathematicians would stop looking so foolish when they say > things like: > > "All natural numbers are finite but there are an infinite number > of them." Of course they look foolish. It should be: "All natural numbers are finite but there is an infinite number of them." -- Alec McKenzie mckenzie(a)despammed.com
From: Han de Bruijn on 22 Jul 2005 04:22 Robert Kolker wrote: > Han de Bruijn wrote: >> >> It's the standard definition of the "actual infinite", but it is not >> "perfectly good". Worse. It's not good at all. > > What is wrong with it? No one has shown it leads to a contradiction. No contradiction. That's perhaps the only good thing about it. If that is the only thing you care about, let me tell you that most of us care about other things, such as a physics that has a reliable mathematical machinery at its disposal. Han de Bruijn
From: Han de Bruijn on 22 Jul 2005 04:32 Robert Kolker wrote: > Han de Bruijn wrote: >> >> 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 ? > > You are beating a dead horse. Mathematics as such as no empirical > content, whatsoever. It is purely abstract. > > It may be the case that a mapping or correspondence can be established > between some mathematics systems and measurable quantities, but that is > purely happenstantial. So let's say to mathematicians who want to enter physics: access denied. Han de Bruijn
From: Martin Shobe on 22 Jul 2005 07:57 On Fri, 22 Jul 2005 10:22:58 +0200, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: >Robert Kolker wrote: > >> Han de Bruijn wrote: >>> >>> It's the standard definition of the "actual infinite", but it is not >>> "perfectly good". Worse. It's not good at all. >> >> What is wrong with it? No one has shown it leads to a contradiction. > >No contradiction. That's perhaps the only good thing about it. If that >is the only thing you care about, let me tell you that most of us care >about other things, such as a physics that has a reliable mathematical >machinery at its disposal. And physics does have reliable mathematical machinery at its disposal. You are blaming mathematics for the choices made by physicists. It's the physicist who are choosing to continue using the mathematics that involve infinity. Martin
From: Han de Bruijn on 22 Jul 2005 08:14
Martin Shobe wrote: > On Fri, 22 Jul 2005 10:22:58 +0200, Han de Bruijn > <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >>Robert Kolker wrote: >> >>>Han de Bruijn wrote: >>> >>>>It's the standard definition of the "actual infinite", but it is not >>>>"perfectly good". Worse. It's not good at all. >>> >>>What is wrong with it? No one has shown it leads to a contradiction. >> >>No contradiction. That's perhaps the only good thing about it. If that >>is the only thing you care about, let me tell you that most of us care >>about other things, such as a physics that has a reliable mathematical >>machinery at its disposal. > > And physics does have reliable mathematical machinery at its disposal. > You are blaming mathematics for the choices made by physicists. It's > the physicist who are choosing to continue using the mathematics that > involve infinity. I am not blaming mathematics. This is what I said somewhere else in this thread: Now I ... > don't say that mathematicians should be blamed for this, if it happens. > But the fact is that most physicists have a blind faith in mathematics > and can be easily deluded by the fact that infinities actually exists, > within mainstream mathematics, and think that they do exist in physics > as well. Han de Bruijn |