Hi arildno:
If you do not want to understand that
x_AND_not_
x is beyond (cannot be well-defined, and it means that the "paradox" cannot be defined) the domain of
x_XOR_not_
x (which is the basis of an excluded-middle reasoning), then your basic attitude, in my opinion, is to be no more then a full time job bodyguard of The language of Math, and (as I see it) you do not give yourself any chance to see fundamental things from a different point of view.
CrankFan said:
Maybe you missed the part in the text you linked which said that:
"In Cantor's system, M is a well-defined set."
So what if Cantor thought that M is well-defined in his system.
The Langauge of Mathematics is not based on gurus, but on fundamental concepts that are never beyond re-examination.
I look at this "paradox" from an included-middle reasoning, and the affect is similar as if I look on 2-D system from n>2-D system.
Someone who looks on some system from a
first-order higher level of reasoning system (where 2-D reasoning system is only a proper sub-system of it, and I clearly show it in my papers) can easily show new interpretations to fundamental concepts of the Langauge of Mathematics.
If you stick to the standard 2-D reasoning, you will never understand my work.
I made my move to new points of view that re-examine the most fundamental concepts of this beautiful language.
Take for example persons like Matt Grime, which in my opinion make here a very good job as the bodyguard of Math.
It took me some time (almost 2 years) to understand that I am talking to a full time job bodyguard, so now I take what I take and I do not care anymore that full time job bodyguards do not want to or can’t understand my work.
You, Matt Grime, CrankFan, Master Coda, Hurkyl, kaiser soze, Ahrkron , and more full time job bodyguards of Math, did not show even a little step to see things from new points of view on the most fundamental concepts of the language of Math.
Form my side, I clearly an simply show why Standard-Math approach does not hold in these most fundamental concept.
I learn my mistakes, and I am trying to improve the basis of the reasoning of my work, but because all you do is to be full time job bodyguards, you do not distinguish that.
For example, please look at the attitude of Ahrkron to my work:
https://www.physicsforums.com/showpost.php?p=243538&postcount=37
In my opinion this is nothing but a poor, non-detailed and limited approach to someone's ideas.
More examples:
Please look at the attitude of Matt Grime to my work:
I wrote to him:
https://www.physicsforums.com/showpost.php?p=242567&postcount=28
As an answer I got:
https://www.physicsforums.com/showpost.php?p=242639&postcount=29
Another example of Matt Grime's attitude:
https://www.physicsforums.com/showpost.php?p=250748&postcount=41
And my non-friendly reply to him:
https://www.physicsforums.com/showpost.php?p=250819&postcount=42
that he chose to ignore.
Also be aware to the name 'CrankFan' that can say a lot about his limited attitude to the possibility if new interpretations of fundamental concepts of the Langauge of Math.
All I asked in 'Theory development forum' is a little more flexible approach that can examine "well-defined" terms from (time to time) a new point of view.
What I have found is a community of hard minds that do not want anyone to change the fundamentals of their religion.
In short, I do not accept Cantor's M definition, and I clearly and rigorously show why I do not accept it.
No full time job bodyguard can understand it.