Complementary Set Theory

[Guest Doron Shadmi]

Complementary Set Theory Axioms, exmples and explanations can be found in:

 

http://www.geocities.com/complementarytheory/My-first-axioms.pdf

 

I'll be glad to get your remarks and insights, thank you,

 

 

Doron

[e(ho0n3]

You paper is too unorganized for me to follow (without getting a headache). What are you trying to accomplish with this set theory anyways?

[Guest Doron Shadmi]

Dear e(ho0n3,

 

 

In my opinion, the most important concept of the Language of Mathmatics is Symmetry.

 

Symmetry is the invariant common source that stands in the basis of infinitely many variations of it.

 

From this point of view, to understand something is first of all to discover the connection between, so called, different things through their common source.

 

For example:

 

A ball is the invariant symmetry of a closed cube, closed cylinder, closed cone, closed pyramid, .... , and so on.

 

The ball (which is the most symmetric closed 3-D form) is the "gateway" to make a transformation from one closed 3-D shape to another, and by this ability we have a better and deeper understanding of any of the above closed shapes.

 

In general, if we find "gateways" between simpler levels and more complex levels of some system, we increase our abilities understand and act in better ways.

 

If you ask me, than I think that the most important research is:

 

To find the relations between the Symmetry concept and the Information concept, where our cognition’s abilities to search these possible relations, has to be included as a part of the research.

 

For example, please look at my papers, where I try to develop a new framework for the Language of Mathematics, which is based on the above attitude:

 

http://www.geocities.com/complementarytheory/ONN1.pdf

 

http://www.geocities.com/complementarytheory/ONN2.pdf

 

http://www.geocities.com/complementarytheory/ONN3.pdf

 

and if you find these link interesting, then please read also

 

http://www.geocities.com/complementarytheory/My-first-axioms.pdf

 

http://www.geocities.com/complementarytheory/No-Naive-Math.pdf

 

I hope that some of my work can be useful for you.

[jordan]

The ball (which is the most symmetric closed 3-D form) is the "gateway" to make a transformation from one closed 3-D shape to another

What do you mean?

[Guest Doron Shadmi]

The ball is the most symmetric closed shape of all other 3-D closed shapes.

 

It means that it looks the same from any direction.

 

On the contrary a closed cube, a closed cylinder, a closed cone or a closed pyramid are looks different from different points of view.

 

Therefore the ball, which is the simplest symmetry, is the basic closed 3-D form, that standing in the basis of any transformation between the other closed 3-D shapes.

[e(ho0n3]

I try to develop a new framework for the Language of Mathematics

Can you expound on this matter? Are you just developing your own little set theory or are you trying to do what Russell and Whitehead did with the Principia Matematica?

[Guest Doron Shadmi]

My goal is to fulfill the dream of the great mathematician Gottfried Wilhelm Leibniz ( http://www.andrews.edu/~calkins/math/biograph/bioleib.htm )

 

Actually my number system ( which some arithmetic of it can be found in http://www.scienceforums.net/forums/showpost.php?p=76489&postcount=20 ) is the fulfillment of Leibniz's Monads ( http://www.angelfire.com/md2/timewarp/leibniz.html ), and beyond it.

[haggy]

Doron, don't you get tired proclaiming your ideas to those who don't care?

 

You always point out others not understanding your methods of reasoning. Could it not be that you haven't expressed them in a concise and clear manner? I personally doubt that "professional mathematicians" don't understand your work due to their own limitations. You'd be surprised at their capabilities to consider complicated ideas.

 

Don't come with that tripe about them not understanding included middle reasoning. In its purest state Set Theory comes very close to different types of philosophy, so those mathematicians that "don't understand" are likely to have seen errors in your work rather than been inadequate in their reasoning ability.

 

How long are you going to harrass all and sundry with your ideas? Will it be until you get your own little following of people? Should we call them the "Doronians" as a fallback to the days of the Pythagoreans who couldn't accept that irrational numbers existed?

[MandrakeRoot]

Yeah can't you write down for exemple the two pages of your first axioms clearly ?

On the second page of this PDF you start talking of directions without defining it, i somewhere have the idea you try to define stuff that you assume already exists using properties of the stuff you try to define in order to define it. Some clarity is needed please

 

Mandrake

[Guest Doron Shadmi]

Doron' date=' don't you get tired proclaiming your ideas to those who don't care?

[/quote']

Eech time when I get detailed remarks about my work (which is not the case of your last post to me) there ia a good chance that I will learn a new thing.

 

Therefore I am not getting tired.

[Guest Doron Shadmi]

On the second page of this PDF you start talking of directions without defining it

My last version of 'Complementary Set Theory' axiomatic system is clear if and only if you first can do a paradigm-shift in your mind about the definition concept, which is not based on a the standard 'if, then' proposition tautology.

 

After you make this paradigm shift, then there is no problem to understand exactly the meaning of direction in my framework, and how I use it as a very powerful and fruitful fundamental concept of my framework.

 

You have to understand that my reasoning is first of all a paradigm-shift of the reasoning concept itself, and this is why professional Mathematicians have very hard time to understand that they first need to re-define the reasoning concept itself, in order to understand my framework.

[MandrakeRoot]

The entire power of MAth is this concept. Once somethign is defined everybody knows what you mean when you use it !

e.g. Once i defined what is a continuous functino there is no doubt for anyone what i mean when i say a function is continuous !

How could you possibly want to do something other then that ? The whole goal of science is to make results/things insightfull !

Science has to be reproductable and understandable to other people then yourself !

people should be able to verify your results !

If your stuff doesnt submit to these criteria then it is not science !

I will actually try to read some of your stuff to see if i can make some sense of it.

 

Mandrake

[Guest Doron Shadmi]

The entire power of MAth is this concept.

I totally agree with you that definition is a fundamental must have tool that can connect between different points of view in order to establish a common framework between people.

 

But 'if, then' proposition is only one of many possibilities to achieve the goal of common work between people.

 

My way to define things is based on Leibniz Monadology, where the existence of a thing does not depend on 'if,then' proposition, but on the self and unique similarity of a thing to itself (which is circular only from the 'if, then' point of view).

 

In the case of a point {.} and a segment {._.}, from their own self and unique identities, it is obvious that {.} can related to itself only by '=', where {._.} goes beyond '=' and also have '<' and/or '>' which are the most fundamental notations that breaking the only '=' symmetry, and give us the existence of a direction, which is a fundamental broken symmetry of any segment {._.}, when it is compared to a point {.}.

 

Also, only segments can be '<' or '>' when they are compared with each other, and no point {.} is effected by '<' or '>', and I clearly and simply demonstrate and explain it in http://www.geocities.com/complementarytheory/My-first-axioms.pdf and its related links.

[MandrakeRoot]

I have tried to read your first stuff (the part on Non-Naive math) on your page, but it is rather confusing. You should really write it down more clearly because it is written down rather chaotically. Cant you write like :

introduction

=>definition

=>Theorems (or whatever the equivalent in this new logic, it should have statements anyway no ?)

 

So in this logic of yours (True and False) is a meaningfull statement ?

And (True and False) and (True and False) is another statement not necessarily the same outcome.

 

When you say that each interval has the same cardinal as the real line you are using old set theory results that do not yet exist when you are creating new set theory !

Moreover in no way that means that the real line is this interval, one can not exist without the other, i mean the interval has the same cardinality only because the real line exists !

The same is true for scaling. Yeah ofcourse the real line can be obtained by arbitrarely rescaling pi, but well the real line has to exists forthat, since you need these scalars to obtain it.

 

Why in your system are the set of odds numbers not equally sized as the set of natural numbers ?

 

Mandrake

[Guest Doron Shadmi]

Why in your system are the set of odds numbers not equally sized as the set of natural numbers ?

Dear MandrakeRoot,

 

First you have to understand my axiomatic system ( http://www.geocities.com/complementarytheory/My-first-axioms.pdf ) in order to undetstand the rest of my work.

 

In my system, which is based on Leibniz's Monads idea, there are 4 independent types of Monads: {}, {.}, {._.}, {__} .

 

In standard Math there are only 2 types of Monads: {}, {.} .

 

Please first reply if you understand my 4 Monads axiomatic system (which in it there are 2 types of cardinals and 2 types of ordinals) that some examples of its basic arithmetics can be found in pages 7 - 10 of http://www.geocities.com/complementarytheory/MyGoal.pdf .