Re: On Ultrafinitism


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

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar

.

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