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Topic: some amateurish opinions on CH
Replies: 57   Last Post: Apr 16, 2013 8:12 PM

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fom

Posts: 1,968
Registered: 12/4/12
Re: some amateurish opinions on CH
Posted: Apr 9, 2013 11:24 PM
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On 4/9/2013 4:12 PM, Dan wrote:
>> So, although I had to start out by thinking
>> that CH would decide something, what I have
>> learned is that pluralism on these matters
>> is far more valuable.

>
> Heisenberg's matrix mechanics and Schrodinger wave mechanics were a
> 'pluralistic interpretation' in the development of quantum mechanics.
> Nonetheless, they ultimately proved to be identical . Pluralism has
> its value, but pluralism for pluralism's sake is unacceptable in
> mathematics . We should always seek out to understand where and why
> pluralism arises, and thus construct a 'unified theory' , a higher
> vantage point from which all the 'pluralistic interpretations' would
> appear as facets, if they cannot be reconciled in themselves.


I take it that is why you suggested looking
at the Weaver article. It began, of course,
speaking of a larger conceptual framework.

I will look at it again, more closely. I needed
to look at New Foundations in order to reply
to William Elliot today.

> If we don't understand how to look at a cube, one may see a square,
> another , a hexagon .
> Practitioners of intuitionist and classical logic can understand one
> another and 'translate between languages' even if they do not speak a
> common language . So it is with standard and non-standard analysis .
> My fear is that we'll never manage to find a clear unambiguous
> interpretation for the concept of set, let alone several.
>


My path has been very hard.

First, what any mathematical use of a word
means outside of any pattern of grammatical
usage (thus covering formal and informal)
is a strange question. So, everything I
look at has been relative to a 'system'.

ZFC is the general system of set theory
claimed implicitly by virtue of celebrity,
if you understand what I mean by that. So,
all of my set theoretic focus has been with
that system. That does not mean I have
"chosen" it as a "correct" representation.

But, because my sense of what is at issue
concerns the use of the sign of equality,
my "research" has driven beyond set theory
although I would never have expected that
it had to.

I will not try to state what I have done
beyond an example to give you a sense.

In the link

http://plato.stanford.edu/entries/logical-constants/#ProPse

you will find a discussion of "demarcaters",
"debunkers", "deflaters" and "relativists". The
article itself discusses the problems of
demarcation.

As a "demarcater" in my attempts to understand
the foundational questions I pursued, I came
to demarcate logical constants on the basis
of a projective geometry as described in

news://news.giganews.com:119/Jr2dnbdYvtfPdlrNnZ2dnUVZ_t-dnZ2d@giganews.com

The system described is just a schema in the sense
that a system of quantifiers would involve a
an amalgam of ortholattices based on the lines
forming the affine geometry.

So, I suppose I am "Brouwerian" in the sense of
grounding the classical logical negation in a construct
of mathematical origin. But, returning to your
final remark, I think that this illustrates just
how difficult these questions of foundations can
become. At least, having put in the time to decide
some things for myself, it is easier to consider
how other systems interrelate.

That is a good thing.






Date Subject Author
4/7/13
Read some amateurish opinions on CH
fom
4/7/13
Read Re: some amateurish opinions on CH
mueckenh@rz.fh-augsburg.de
4/7/13
Read Re: some amateurish opinions on CH
Bergholt Stuttley Johnson
4/7/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/7/13
Read Re: some amateurish opinions on CH
mueckenh@rz.fh-augsburg.de
4/7/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/7/13
Read Re: some amateurish opinions on CH
mueckenh@rz.fh-augsburg.de
4/7/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/7/13
Read Re: some amateurish opinions on CH
mueckenh@rz.fh-augsburg.de
4/7/13
Read Re: some amateurish opinions on CH
Virgil
4/8/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/8/13
Read Re: some amateurish opinions on CH
mueckenh@rz.fh-augsburg.de
4/8/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/8/13
Read Re: some amateurish opinions on CH
mueckenh@rz.fh-augsburg.de
4/8/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/8/13
Read Re: some amateurish opinions on CH
mueckenh@rz.fh-augsburg.de
4/8/13
Read Re: some amateurish opinions by WM
Virgil
4/8/13
Read Re: some amateurish opinions on CH
Virgil
4/9/13
Read Re: some amateurish opinions on CH
apoorv
4/8/13
Read Re: some amateurish opinions on CH
Virgil
4/7/13
Read Re: some amateurish opinions on CH
Virgil
4/9/13
Read Re: some amateurish opinions on CH
Guest
4/9/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/9/13
Read Re: some amateurish opinions on CH
fom
4/10/13
Read Re: some amateurish opinions on CH
Guest
4/10/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/10/13
Read Re: some amateurish opinions on CH
fom
4/10/13
Read Re: some amateurish opinions on CH
JT
4/11/13
Read Re: some amateurish opinions on CH
apoorv
4/11/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/11/13
Read Re: some amateurish opinions on CH
apoorv
4/11/13
Read Re: some amateurish opinions on CH
fom
4/15/13
Read Re: some amateurish opinions on CH
apoorv
4/15/13
Read Re: some amateurish opinions on CH
fom
4/16/13
Read Re: some amateurish opinions on CH
Shmuel (Seymour J.) Metz
4/16/13
Read Re: some amateurish opinions on CH
fom
4/7/13
Read Re: some amateurish opinions on CH
Virgil
4/7/13
Read Re: some amateurish opinions on CH
William Elliot
4/7/13
Read Re: some amateurish opinions on CH
fom
4/7/13
Read Re: some amateurish opinions on CH
fom
4/8/13
Read Re: some amateurish opinions on CH
William Elliot
4/8/13
Read Re: some amateurish opinions on CH
fom
4/9/13
Read Re: some amateurish opinions on CH
William Elliot
4/9/13
Read Re: some amateurish opinions on CH
fom
4/9/13
Read Re: some amateurish opinions on CH
William Elliot
4/9/13
Read Re: some amateurish opinions on CH
fom
4/9/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/9/13
Read Re: some amateurish opinions on CH
fom
4/9/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/9/13
Read Re: some amateurish opinions on CH
fom
4/9/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/9/13
Read Re: some amateurish opinions on CH
fom
4/10/13
Read Re: some amateurish opinions on CH
fom
4/11/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/11/13
Read Re: some amateurish opinions on CH
fom
4/11/13
Read Re: some amateurish opinions on CH
dan.ms.chaos@gmail.com
4/11/13
Read Re: some amateurish opinions on CH
fom
4/9/13
Read Re: some amateurish opinions on CH
fom

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