Boolean Logic cannot deal with infinitely many objects

[master_coda]

Providing pdfs with even more undefined terms makes it harder to understand what you are talking about.

 

[Organic]

Hi master_coda,

Please give me an example of an undefined term in this pdf:

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

and then we shall try together (if you want) to address it in a formal way.

Thank you.


Organic

 

[NateTG]

Here's a short list:

limits
potential infinity
actual infinity
emptiness
fullness
limited information model
symetric potential infinity
directed potential infinty
floating point
floating point system
extrapolation
interpolation
scales
information cells
notated information cells
specific direction
aleph0
{}
{__}

I assume that integers part and fractions part, you mean integer part and fractional part, otherwise those are also not well-defined.

Some of the terms have common mathematical definitions, but you do not use them in ways that make sense using those definitions. For example "- aleph0" does not make any sense if you mean the cardinal number \aleph_0

 

[moshek]

Hilbert problems

It is known that among the list
of the 23 problem of Hilbert ( 1900 Paris)
only 3 left unsolved : 6,8,16.

So I just want to ask Organic:

Does your study in matematics
is relate to any of them?

thank you
Moshek

 

[Organic]

Hi NateTG,

Thank you for your reply.

Please take this by the standard mathematical meaning:

limits
emptiness
floating point
{}
extrapolation
interpolation
scales

The other concepts can be understood from the examples in the last pdf file.

Please fill free to ask any question that you like about them.

Thank you,


Organic

 

[Organic]

Hi moshek,

My ideas are deeply connected to the 6th problem.

 

[moshek]

Thank you for sharing that.

Moshek

 

[master_coda]

Originally posted by Organic
Hi NateTG,

Thank you for your reply.

Please take this by the standard mathematical meaning:

limits
emptiness
floating point
{}
extrapolation
interpolation
scales

The other concepts can be understood from the examples in the last pdf file.

Please fill free to ask any question that you like about them.

Thank you,


Organic

Emptiness does not have a mathematical meaning.

 

[moshek]

On which mathematics emptiness have no meaning?

 

[Organic]

Hi master_coda,

Emptiness is the content of {}.

Without it Axiomatic set theory can't hold.

 

[moshek]

Hi Organic,

I did not understand until now,
That you wan't axiomatic set theory to hold as it is today?

Are you please with P.Choen forcing method
to solve Hilbert first problem CH ?

please explain that to me.

Moshek

 

[master_coda]

{} is the empty set. Emptiness is a word that has a great deal of philosophical baggage that adds confusion to the issue.

For example, you seem content to define fullness as the opposite of emptiness. After all, fullness is clearly the opposite of emptiness.

Except that it isn't rigorous at all. What is fullness? The set of all sets? The set of all things?

 

[Organic]

Hi moshek,

CH problem has some meaning if 2^aleph0 > aleph0, but in my first post in this thread i show that (2^aleph0 >= aleph0) = {}.

 

[Organic]

Master_coda

Fullness is the highest limit of any form of information.

Emptiness is the lowest limit of any form of information.

 

[master_coda]

Originally posted by Organic
Master_coda

Fullness is the highest limit of any form of information.

Emptiness is the lowest limit of any form of information.

This is exactly the problem with you saying emptiness is {}, and saying that axiomatic set theory depends on it. The mathematical definition of the empty set is the set A such that x\notin A is always true, regardless of what x is.

Your definition talks about "lowest limits of information" which is just something else you haven't defined.

Then you seem to apply your non-mathematical definition to the standard definition in set theory.

 

[Organic]

Master_coda,

At this point i need your help.


Zf set theory defines the empty set as:

the set A such that x not in A is always true, regardless of what x is.

If you look at this definition, then x must be some existing input form of information.

My idea go deeper then that, and start its research by including the limits of any form of information.


Can you help me to define this idea in a formal way?

Thank you.

Organic

 

[master_coda]

Originally posted by Organic

the set A such that x not in A is always true, regardless of what x is.

If you look at this definition, then x must be some existing form of information.

Why must x be an existing form of information?

 

[Organic]

And what if x is Emptiness?

 

[master_coda]

Originally posted by Organic
And what if x is Emptiness?

Then x is not in the empty set.

 

[Organic]

And what if x is Fullness?

 

[master_coda]

Originally posted by Organic
And what if x is Fullness?

Then x is not in the empty set.

No matter what x is, x is not in the empty set.

 

[Organic]

x is the input A is the set.

the set A such that x not in A is always true, regardless of what x is.

Whet is A if x is Emptiness?

What is A if x is Fullness?

What is A if x is not Epmtiness nor Fullness?

 

[master_coda]

Originally posted by Organic
x is the input A is the set.

the set A such that x not in A is always true, regardless of what x is.

Whet is A if x is Emptiness?

What is A if x is Fullness?

What is A if x is not Epmtiness nor Fullness?

A is the same thing in all three cases. A is the empty set. It doesn't matter what x is.

 

[Organic]

A is the same thing in all three cases. A is the empty set. It doesn't matter what x is.

Really ?

x=Eemptiness

the set A such that Emptiness not in A is always true.

 

[master_coda]

Originally posted by Organic
Really ?

x=Eemptiness

the set A such that Emptiness not in A is always true.

Of course, I'm still waiting for a mathematical definition of Emptiness from you. But however you define it, it isn't contained in the empty set.

 

[Hurkyl]

Your post is poorly written, my best guess is that this sentence is supposed to be a definition of A:

the set A such that x not in A is always true, regardless of what x is.

And if that is correct, then A has been defined; it doesn't become something different. master_coda would thus be correct.

 

[Organic]

No, you used a formal definition and learned through our last posts
that this formal definition has logical holes in it that you did not close.

Please show me why do i have to define intuiative concepts like 'Emptiness' and 'Fullness'?

 

[master_coda]

Originally posted by Organic
No, you used a formal definition and learned through our last posts
that this formal definition has logical holes in it that you did not close.

Please show me why do i have to define an intuiative concepts like 'Emptiness' and 'Fullness'?

Because in math, you have to define everything. Intuitive concepts have no mathematical value until they've been formally defined.


If you use the definition Emptiness=Empty Set then it is still true that \mathrm{Emptiness}\notin\mathrm{Empty Set}.

If you define Emptiness as "the thing that is contained in the empty set" than your formal system is inconsitent.

If you provide a non-mathematical definition than there's no point in even talking about what your definition has to do with math.

 

[Hurkyl]

Please show me why do i have to define intuiative concepts like 'Emptiness' and 'Fullness'?

You wanted help expressing your ideas in a formal way. That entails defining everything.

 

[Organic]

There is no such a thing like "Empty set".

All we have is the set concept, and its name is given by its content.

We cannot separate between a set's name and its content's property,
as you wrongly show in your example.