Obections to Cantor's Theory (Wikipedia article)
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From: Han de Bruijn on 29 Jul 2005 06:48 David Kastrup wrote: > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: > > >>David Kastrup wrote: >> >> >>>Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: >>> >>> >>>>Robert Kolker wrote: >>>> >>>> >>>> >>>>>Han de Bruijn wrote: >>>>> >>>>> >>>>>>Glad that we have such a bright spirit here that it challenges >>>>>>Newton's. >>>>> >>>>>Newton got time wrong too, as Einstein showed. >>>> >>>>Of course, Bob. Your car has been designed with the wrong mechanics. >>> >>>Newton was a car designer? >> >>No, he was a Mechanics designer. And a damned good one. > > > Well, Henri Ford was a good car maker, and you don't see us driving > around in Model T's nowadays, either. That comprises a difference, because we are still designing cars with Newtonian mechanics, not with GR. Han de Bruijn
From: Martin Shobe on 29 Jul 2005 07:35 On Fri, 29 Jul 2005 12:48:31 +0200, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: >David Kastrup wrote: >> Well, Henri Ford was a good car maker, and you don't see us driving >> around in Model T's nowadays, either. > >That comprises a difference, because we are still designing cars with >Newtonian mechanics, not with GR. Not entirely accurate. For one thing, a number of cars include GPS systems nowdays. And those don't work properly if designed with Newtonian mechanics. Martin
From: Martin Shobe on 29 Jul 2005 07:42 On Fri, 29 Jul 2005 11:14:56 +0200, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: >Martin Shobe wrote: > >> On Thu, 28 Jul 2005 15:56:32 +0200, Han de Bruijn >> <Han.deBruijn(a)DTO.TUDelft.NL> wrote: >> >>>But without the claim that it >>>is the one and only foundation possible. Why not have _several_ pillars >>>that provide a foundation, instead of just one? >> >> Actually, I don't have a problem with that. In a sense, we have that >> now with set theory and category theory (And lets not forget logic). >> But while physics will continue to provide inspirition to mathematics, >> it will not qualify as a foundation for methematics. > >And I don't want that either. Read my lips: > > A little bit of Physics would be NO Idleness in Mathematics > >See? Just that tiny pinch of salt in your otherwise tasteless soup. > >But nevertheless: *IN* your soup. A "tiny pinch of salt"? From the axioms I've seen you proposing that would be more like a ten pound bag of rock salt added to single serving. Martin
From: Martin Shobe on 29 Jul 2005 07:45 On Fri, 29 Jul 2005 11:07:23 +0200, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: >Martin Shobe wrote: > >> Maybe I should have said "Set theory does not have physics as it's >> immediate inspiration, so failing to satisfy some direct connection to >> physics is irrelevant." > >No. It's highly relevant. The fact that something IS such and so doesn't >mean that it SHOULD BE such and so. Ah, but it shouldn't be such and so. >(Maybe some shouting helps ...) Not really. Martin
From: Robert Low on 29 Jul 2005 07:56
Han de Bruijn wrote: > Robert Low wrote: >> OK, Han. Let's try your game. >> What are the axioms you use in place of ZF(C)? >> Once you've listed them, tell us what your >> standard model is (an equivalent for the >> cumulative hierarchy), and what the natural >> numbers are in that standard model. > Whoa! Not so fast! Even Einstein didn't finish GR in one day! Right. So you want to throw away something that works and replace it with something you haven't got yet. You understand our reluctance to quit our game and try to play one where the rules haven't even been given? |