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Topic: Matheology §252
Replies: 110   Last Post: Apr 24, 2013 5:58 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology �252
Posted: Apr 20, 2013 8:25 PM

In article <KdGdnfqxb_A8gu7MnZ2dnUVZ_rqdnZ2d@giganews.com>,
fom <fomJUNK@nyms.net> wrote:

> On 4/20/2013 12:03 PM, WM wrote:
> >
> > All atoms of the accessible universe and all positions they can take
> > belong to a finite set.
> >

>
> Well, that is a strange statement given
> that they are forming Bose-Einstein
> condensates with atoms now.

Not to mention:
"As far as the laws of mathematics refer to
reality, they are not certain; and as
far as they are certain, they do not refer
to reality.

Albert Einstein
>
> Anyway, what scientifically falsifiable
> natural number does WM assert to be the
> number of positions available to the
> atoms of the accessible universe?
>
>
> WM is an unabashed ultrafinitist who refuses to fix
> a largest finite number. Each "n" in his description
> depends on the subsequence of triangular numbers.
>

> > F(n)=Sum_i(1..n)(i)
> >
> > 1 :=> 1
> > 2 :=> 3
> > 3 :=> 6
> > 4 :=> 10
> >
> > and so on

>
> According to Brouwerian intuitionistic reasoning,
> when WM's construction reaches the point where
> the sequence of triangular numbers exceeds the
> ultrafinitist limit, the contradiction nullifies
> the construction.
>
> This is WM's model of mathematics:
>
> http://en.wikipedia.org/wiki/Finite_model_property
>
> until he reaches his contradiction and
> it vanishes.
>
> =====================================
>
> The triangular numbers correspond with
> the number of 'marks' representing numerals
> or significant denotations occurring in any
> of WM' representations of the form:
>
> 1
> 2, 1
> 3, 2, 1
> ...
> n, ..., 3, 2, 1
> ...
>
> -------------------------------------
>
> This number of 'marks' satisfies a structural
> feature of the natural numbers called a
> directed set:
>
> Defintion
>
> A binary relation >= in a set D is said
> to direct D if and only if D is nonempty
> and the following three conditions are
> satisfied:
>
> DS1)
>
> If a is an element of D, then a>=a
>
> DS2)
>
> If a, b, c are elements of D such
> that a>=b and b>=c, then a>=c
>
> DS3)
>
> If a and b are elements of D, then there
> exists an element c of D such that c>=a
> and c>=b
>
>
> So, WM's geometric reasoning for any given
> n obtains a finite model domain with its
> cardinality given by the associated
> triangular number. The triangular number
> is the "element c" of condition DS3 from
> the definition.
>
> -------------------------------------
>
> Finally, Brouwer's explanation for finitary
> reasoning is used because WM refuses to
> commit to any mathematical statement with
> coherent consistent usage.
>
> Brouwer distinguishes between results with
> regard to 'endless', 'halted' and
>
> "A set is a law on the basis of
> which, if repeated choices of
> arbitrary natural numbers are made,
> each of these choices either
> generates a definite sign series,
> with or without termination of the
> process, or brings about the
> inhibition of the process together
> with the definitive annihilation
> of its result."
>
> WM cannot be an ultrafinitist and
> expect others to not hold him to
> task for it. In constrast to
> Brouwer, he repeatedly states
> that there is absolutely no
> completed infinity. Therefore,
> there must be a maximal natural
> number for his model of
> mathematics. Beyond that
> number, there is no mathematics.
>
> That is WM's belief as surmised
> from his statements and reasonings
> as opposed to what he says with
> rhetoric.

--

Date Subject Author
4/17/13 mueckenh@rz.fh-augsburg.de
4/17/13 fom
4/17/13 Virgil
4/18/13 mueckenh@rz.fh-augsburg.de
4/18/13 fom
4/18/13 mueckenh@rz.fh-augsburg.de
4/18/13 fom
4/18/13 fom
4/18/13 fom
4/18/13 fom
4/18/13 mueckenh@rz.fh-augsburg.de
4/18/13 fom
4/18/13 mueckenh@rz.fh-augsburg.de
4/18/13 fom
4/18/13 mueckenh@rz.fh-augsburg.de
4/18/13 fom
4/18/13 Virgil
4/18/13 Virgil
4/19/13 mueckenh@rz.fh-augsburg.de
4/19/13 fom
4/19/13 fom
4/19/13 mueckenh@rz.fh-augsburg.de
4/19/13 fom
4/19/13 fom
4/19/13 fom
4/19/13 Virgil
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 netzweltler
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 netzweltler
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 netzweltler
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 Virgil
4/20/13 fom
4/20/13 Virgil
4/21/13 mueckenh@rz.fh-augsburg.de
4/21/13 fom
4/21/13 Bergholt Stuttley Johnson
4/21/13 gus gassmann
4/21/13 Virgil
4/21/13 netzweltler
4/21/13 mueckenh@rz.fh-augsburg.de
4/21/13 netzweltler
4/21/13 mueckenh@rz.fh-augsburg.de
4/21/13 netzweltler
4/21/13 mueckenh@rz.fh-augsburg.de
4/21/13 fom
4/21/13 netzweltler
4/21/13 netzweltler
4/22/13 mueckenh@rz.fh-augsburg.de
4/22/13 netzweltler
4/22/13 Virgil
4/22/13 netzweltler
4/22/13 Virgil
4/23/13 mueckenh@rz.fh-augsburg.de
4/23/13 Virgil
4/23/13 netzweltler
4/24/13 mueckenh@rz.fh-augsburg.de
4/24/13 Virgil
4/24/13 netzweltler
4/24/13 mueckenh@rz.fh-augsburg.de
4/24/13 Virgil
4/24/13 netzweltler
4/24/13 mueckenh@rz.fh-augsburg.de
4/24/13 Virgil
4/24/13 netzweltler
4/21/13 fom
4/21/13 Virgil
4/22/13 mueckenh@rz.fh-augsburg.de
4/22/13 Virgil
4/23/13 mueckenh@rz.fh-augsburg.de
4/23/13 Virgil
4/21/13 Bergholt Stuttley Johnson
4/21/13 Virgil
4/20/13 fom
4/20/13 Virgil
4/20/13 fom
4/20/13 Virgil
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 Virgil
4/20/13 Virgil
4/19/13 Virgil
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 fom
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4/20/13 Virgil
4/20/13 Virgil
4/18/13 fom
4/18/13 fom
4/18/13 Virgil
4/18/13 mueckenh@rz.fh-augsburg.de
4/18/13 Virgil
4/18/13 Bergholt Stuttley Johnson
4/18/13 fom
4/18/13 fom
4/18/13 Virgil
4/18/13 mueckenh@rz.fh-augsburg.de
4/18/13 fom
4/18/13 Virgil
4/18/13 Virgil
4/18/13 mueckenh@rz.fh-augsburg.de
4/18/13 fom
4/18/13 Virgil
4/18/13 Virgil