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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.
> 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.
Eckard Blumschein
>
> -+-+-+-+-
>
> i have not seen this done in "fuzzifying" the truth characteristic
> (by
> for instance
> making it a more general subobject classifier)
> but you could possibly develop such a theory
>
>
> if you study the formalisation of ultrafinitsm
> and follow the debates on appropriate model constraints
> papers like
> "characterising finite kripke structures
> in propositional temporal logic"
> by browne, clarke, and grumberg
> start standing out
>
> !! Christian rationality:
> !! A god killing himself to save his own creation from his own wrath.
>
> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
> galathaea: prankster, fablist, magician, liar
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