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Eckard Blumschein wrote:
> On 10/29/2006 3:04 AM, galathaea wrote:
>
> > ultrafinitsm takes a conceptual step beyond finitism
> > by stressing that
> > not only is mathematics a finite process
> > but there exist hard limits
> >
> > there is no potential infinity
>
> Mueckenheim was blamed an ultrafinitist. However, he denies the actual
> infinity while the potential infinity seems to be obvious to anybody.
plutarch was caught writing
"as the indifferent
is the mean between good and evil
so there is some mean
between finite and infinite"
> > or legitimate means to assume
> > a process can be continued indefinitely
> >
> > in any derivation
> >
> > it is necessary to question
> > for any process specification
> > whether that process can complete
> > "within the limits of resources"
> > available to mathematics
> >
> > because
> > they insist
> > mathematics is a physical process
> > and one day too may suffer the entropic decay
>
> Mueckenheim obviously shares this view. I do not understand why he
> cannot accept mathematics like dealing with the two abstract ideas
> number and continuum.
>
> One alternative after the other failed to unmask Cantors paradise as
> what I consider the Dedekind-Cantor Utopia. Kronecker even called the
> natural numbers given by the Lord. Brouwer even intended to improve set
> theory. Weyl suggested an atomist continuum.
>
> Even Cantor and Hilbert started at some sound finitist views. Now
> ultrafinitism is rumored to be the most silly counterpoint to formalism.
>
> Tell me please whether or not there is a drawer you may put me in?
> I consider the world of (countable) numbers quite different from the
> complementing world of (uncountable) continuum. In principle Cantor was
> conjecturing almost the same when he believed that there is nothing
> between aleph_0 and aleph_1.
at some point
we all must return to democrites
and the dilemma of the cone
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galathaea: prankster, fablist, magician, liar
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