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Topic: Matheology § 258
Replies: 29   Last Post: Apr 27, 2013 7:43 PM

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Posts: 2,720
Registered: 2/15/09
Re: Matheology § 258
Posted: Apr 27, 2013 6:47 PM
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On Apr 27, 3:12 pm, Virgil <> wrote:
> In article
> <>,
>  WM <> wrote:

> > On 27 Apr., 21:51, Virgil <> wrote:
> > > No one ever works with actual numbers in mathematics,
> > > they only work with names or numerals for numbers.

> > Therefore no one can prove uncountability.
> If one had to get hold of actual numbers to do mathematics, there could
> be no mathematics at all.
> And it is the axiom system for the field of real numbers which implies
> uncountability, not the naming of numbers.

> > > So why is working only with names a problem?
> > That is not a problem in mathematics. It is a problem for
> > matheologians.

> A type that exists only in WM's imagination, though he applies the term
> broadly to the vast majority of those whom everyone else calls
> mathematicians.

> > > > Infinite strings do not exist in the internet
> > > They do as named objects, as do numbers.
> > Yes, but not more than countably many.
> The evidence for uncountability does not rely on being able to name
> uncountably many individuals.
> There are more things in heaven and earth, WM ,than are dreamt of in
> your philosophy.
> --

But, didn't you just dream of them in your philosophy? Or, is your
theory incomplete, or inconsistent?

Having just put a name on all of them, congratulations: there's
more. Basically Burali-Forti: Ord is irregular.

Well-order the reals, via Fefermann V = L, the universe as
constructible has for each element: that's its own name. Are the
reals a set?

The evidence for uncountability relies largely on constructive
proofs. And, the arguments for uncountability of the reals don't
apply to EF the natural/unit equivalency function.

Arguments for uncountability of the reals don't apply to EF: putting
the elements of the unit interval in a row, while satisfying notions
such as continuity, has range R_[0,1].

Bring forth applications of transfinite cardinals. EF has application
as the unit line segment.


Ross Finlayson

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