Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
fom

Posts: 1,969
Registered: 12/4/12
Re: Matheology §252
Posted: Apr 18, 2013 4:46 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 4/18/2013 3:38 AM, WM wrote:
> On 18 Apr., 09:15, fom <fomJ...@nyms.net> wrote:
>> On 4/18/2013 2:07 AM, WM wrote:
>>

>>> On 18 Apr., 08:52, fom <fomJ...@nyms.net> wrote:
>>
>>>> WM does not know what a mathematical
>>>> rule-governed process is.

>>
>>> Divide 1 by 9, then you have an example probably easy enough for you
>>> to understand.

>>
>> Yes. Something -- namely, an algorithm --
>> by which the rule-governed constructive
>> mathematics of Markov and Sanin developed
>> Brouwer's idea of rule-governed mathematics.
>>
>> WM DENIED THIS MATHEMATICS

>
> No.


YES. WM DID.

I SPENT A LOT OF TIME WHEN I
FIRST STARTED READING THESE
THREADS TRYING TO CORRELATE
WM'S STATEMENTS WITH STANDARD
MATHEMATICS.

WM IS BEING DISHONEST

WM IS EXACTLY WHAT THE ANALYSIS
CLAIMS


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
'contradictory' in his explanations

"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 statements and reasoning
as opposed to what he says with
rhetoric.






Date Subject Author
4/17/13
Read Matheology §252
mueckenh@rz.fh-augsburg.de
4/17/13
Read Re: Matheology §252
fom
4/17/13
Read Re: Matheology �252
Virgil
4/18/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/18/13
Read Re: Matheology §252
fom
4/18/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/18/13
Read Re: Matheology §252
fom
4/18/13
Read Re: Matheology §252
fom
4/18/13
Read Re: Matheology §252
fom
4/18/13
Read Re: Matheology §252
fom
4/18/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/18/13
Read Re: Matheology §252
fom
4/18/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/18/13
Read Re: Matheology §252
fom
4/18/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/18/13
Read Re: Matheology §252
fom
4/18/13
Read Re: Matheology �252
Virgil
4/18/13
Read Re: Matheology �252
Virgil
4/19/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/19/13
Read Re: Matheology §252
fom
4/19/13
Read Re: Matheology §252
fom
4/19/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/19/13
Read Re: Matheology §252
fom
4/19/13
Read Re: Matheology §252
fom
4/19/13
Read Re: Matheology §252
fom
4/19/13
Read Re: Matheology �252
Virgil
4/20/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/20/13
Read Re: Matheology §252
netzweltler
4/20/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/20/13
Read Re: Matheology §252
netzweltler
4/20/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/20/13
Read Re: Matheology §252
netzweltler
4/20/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/20/13
Read Re: Matheology §252
fom
4/20/13
Read Re: Matheology �252
Virgil
4/20/13
Read Re: Matheology §252
fom
4/20/13
Read Re: Matheology �252
Virgil
4/21/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/21/13
Read Re: Matheology §252
fom
4/21/13
Read Re: Matheology §252
Bergholt Stuttley Johnson
4/21/13
Read Re: Matheology §252
gus gassmann
4/21/13
Read Re: Matheology �252
Virgil
4/21/13
Read Re: Matheology §252
netzweltler
4/21/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/21/13
Read Re: Matheology §252
netzweltler
4/21/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/21/13
Read Re: Matheology §252
netzweltler
4/21/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/21/13
Read Re: Matheology §252
fom
4/21/13
Read Re: Matheology §252
netzweltler
4/21/13
Read Re: Matheology §252
netzweltler
4/22/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/22/13
Read Re: Matheology §252
netzweltler
4/22/13
Read Re: Matheology �252
Virgil
4/22/13
Read Re: Matheology §252
netzweltler
4/22/13
Read Re: Matheology �252
Virgil
4/23/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/23/13
Read Re: Matheology �252
Virgil
4/23/13
Read Re: Matheology §252
netzweltler
4/24/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/24/13
Read Re: Matheology �252
Virgil
4/24/13
Read Re: Matheology §252
netzweltler
4/24/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/24/13
Read Re: Matheology �252
Virgil
4/24/13
Read Re: Matheology §252
netzweltler
4/24/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/24/13
Read Re: WMytheology �252
Virgil
4/24/13
Read Re: Matheology §252
netzweltler
4/21/13
Read Re: Matheology §252
fom
4/21/13
Read Re: Matheology �252
Virgil
4/22/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/22/13
Read Re: Matheology �252
Virgil
4/23/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/23/13
Read Re: Matheology �252
Virgil
4/21/13
Read Re: Matheology §252
Bergholt Stuttley Johnson
4/21/13
Read Re: Matheology �252
Virgil
4/20/13
Read Re: Matheology §252
fom
4/20/13
Read Re: Matheology �252
Virgil
4/20/13
Read Re: Matheology §252
fom
4/20/13
Read Re: Matheology �252
Virgil
4/20/13
Read Re: Matheology §252
fom
4/20/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/20/13
Read Re: Matheology §252
fom
4/20/13
Read Re: Matheology �252
Virgil
4/20/13
Read Re: Matheology �252
Virgil
4/19/13
Read Re: Matheology �252
Virgil
4/20/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/20/13
Read Re: Matheology §252
fom
4/20/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/20/13
Read Re: Matheology §252
fom
4/20/13
Read Re: Matheology §252
fom
4/20/13
Read Re: Matheology §252
fom
4/20/13
Read Re: Matheology �252
Virgil
4/20/13
Read Re: Matheology �252
Virgil
4/18/13
Read Re: Matheology §252
fom
4/18/13
Read Re: Matheology §252
fom
4/18/13
Read Re: Matheology �252
Virgil
4/18/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/18/13
Read Re: Matheology �252
Virgil
4/18/13
Read Re: Matheology §252
Bergholt Stuttley Johnson
4/18/13
Read Re: Matheology §252
fom
4/18/13
Read Re: Matheology §252
fom
4/18/13
Read Re: Matheology �252
Virgil
4/18/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/18/13
Read Re: Matheology §252
fom
4/18/13
Read Re: Matheology �252
Virgil
4/18/13
Read Re: Matheology �252
Virgil
4/18/13
Read Re: Matheology §252
mueckenh@rz.fh-augsburg.de
4/18/13
Read Re: Matheology §252
fom
4/18/13
Read Re: Matheology �252
Virgil
4/18/13
Read Re: Matheology �252
Virgil

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.