An uncountable countable set
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From: Virgil on 27 Oct 2006 20:43 In article <4542a3b2(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > > If TO were to support someone reasonably in touch with mathematical > > reality, I should not have regarded it as a "last straw" situation. > > Like Boole? Boole does not need, or want, TO's support.
From: Virgil on 27 Oct 2006 20:45 In article <4542a431(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <4542164c(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> Virgil wrote: > >>> TO seems to swallow camels and strain at gnats. > >>> > >> There's nothing difficult about that. I agreed that, without removing > >> balls, one gets an uncountable rate of increase at t=0. The problem is > >> that there is no time when it can become empty in the original > >> experiment, and there is no way it can become empty. > > > > Except by having all balls removed by noon. > > I'm sorry, Virgil. This is just so full of nonsense I can't even find > anything worth responding to. The only relevant question is "According to the rules set up in the gedankenexperiment, is each ball which is inserted into the vase before noon also removed from the vase before noon?" An affirmative answer, as is required by the gedankenexperiment itself, confirms that the vase is empty at noon.
From: Virgil on 27 Oct 2006 20:47 In article <4542a581(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <45421735(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> Virgil wrote: > > > >>> In order to have emptiness at noon, all removals must take place no > >>> later than noon, which they are forced to do by the rules of the problem. > >> That means either before noon, or at noon. No balls are removed at noon. > >> Balls remain at every time before noon. You're busted. > > > > Except that every ball inserted before noon has been removed before > > noon according to the specifications of the gedankenexperiment. > > > > So it is TO who is busted for violating the rules of the > > gedankenexperiment. > > > Chuckles with blood splatters, Is TO trying to bring Halloween into this? It doesn't fly. The only relevant question is "According to the rules set up in the problem, is each ball which is inserted into the vase before noon also removed from the vase before noon?" An affirmative answer confirms that the vase is empty at noon. A negative answer directly violates the conditions of the problem. How does TO answer?
From: Virgil on 27 Oct 2006 20:50 In article <4542a60d(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <45421a34(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> David Marcus wrote: > > > >>> So, "noon exists" in this case, even though nothing happens at noon. > >> Not really > > > > Yes really. > > Nope. > (see? I can be an imbecile too) How can there be times before noon without a noon? What time is some undefined time minus one minute? TO claims to know.
From: Tony Orlow on 27 Oct 2006 20:43
Virgil wrote: > In article <4542201a(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> cbrown(a)cbrownsystems.com wrote: > >>> When you say "noon doesn't occur"; I think "he doesn't accept (1): by a >>> time t, we mean a real number t" >> That doesn't mean t has to be able to assume ALL real numbers. The times >> in [-1,0) are all real numbers. > > By what mechanism does TO propose to stop time? By the mechanism of unfinishablility. >>> When you say "if we always add more balls than we remove, the number of >>> balls in the vase at time 0 is not 0", I think "he doesn't accept (8): >>> if the numbers of balls in the vase is not 0, then there is a ball in >>> the vase." >> No, I accept that. There is no time after t=-1 where there is no ball in >> the vase. > > That is not the same thing at all, as it requires that some ball remain > in the vase after it has been removed. No it requires that some ball e=remain after some other ball is removed. > >> I didn't say that exactly. If 0 occurs, then all finite balls are gone, > > As those are the only balls that the gedankenexperiment allows, that > means the vase is then empty. > And so, nothing can happen at noon. >> but infinite balls have been inserted > > Where in the original gedankenexperiment is there any provision made for > those alleged "infinite" balls? At noon. > > What TO does is decide what result he wants and then tries to bend the > facts to fit. Does anything happen at noon? > > But it does not work. Does the vase empty before, or at, noon? > > The only relevant question is "According to the rules of the > gedankenexperiment , is each ball which is inserted into the vase before > noon also removed from the vase before noon?" > > An affirmative answer confirms that the vase is empty at noon. > A negative answer directly violates the conditions of the > gedankenexperiment. > > So TO keeps violating the conditions of the gedankenexperiment. Nope. I keep obeying them. |