Cont: Deeper than primes - Continuation 2

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Happy Easter, doronshadmi.

You honor this day of Christian celebration of the resurrection of their Messiah by resurrecting old posts. Many are grateful for your act of respect and kindness.
 
jsfisher said:
Happy Easter, doronshadmi.

You honor this day of Christian celebration of the resurrection of their Messiah by resurrecting old posts. Many are grateful for your act of respect and kindness.
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Happy Easter, jsfisher.

Can you kindly reply to http://www.internationalskeptics.com/forums/showpost.php?p=12239821&postcount=2960 even if it is not a religious text?

If only membership 1 is your mathematical universe, you actually can't do that, kindly or not.

Many of your students are unaware of the artificial restriction of membership 1 as taught by traditional mathematics, which unfortunately became some kind of a religious dogma.
 
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One of the deep notions of modern mathematics is the idea of inaccessibility, such that X is inaccessible from below.

For example, the cardinality of all natural numbers is inaccessible to any given natural number since any natural number is a finite value, where, according to modern mathematics, the cardinality of all natural numbers is the first non-finite value (named as ℵ0).

By expanding the notion of inaccessibility, such that no given object is accessible to NOthing from above (contradiction) or YESthing from below (tautology), any given mathematical object is logically closed under the relativity of the concept of collection, where the concept of set is the particular case of collections of distinct objects.

By being closed under the notion of set, one is actually artificially closed under a particular relative notion, which can't deal with the totality of NOthing (contradiction) or YESthing (tautology), nor with thing in itself, which is the real foundation of all there is that is naturally not restricted by its relative or total expressions.

So real mathematics is not less than the awareness of thing as the actual foundation of logic itself, and from this foundation the logic of collection of distinct objects is easily known as a very particular case of mathematics.

For the past 10 years jsfisher struggles to define the notion of set in terms membership 1 as the one and only one possibility to do what he calls "real mathematics".

But the notion of set (no matter of what membership's degree is used) is actually no more than a relative and some particular case of thing's expression, which is naturally inaccessible to thing since no thing's expression is thing in itself.

The only way to know thing in itself is done by directly being aware of the simplest state of awareness, which is preliminary to all of its expressions, subjective, objective, relative or absolute (total).

Real mathematics is the most accurate method to actually act right from the simplest state of awareness, without being lost within its expressions.
 
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Let's see how quickly doronshamdi can mangle established mathematical terms, ideas, understands, and/or makes up his own definitions.

doronshadmi said:
One of the deep notions of modern mathematics is the idea of inaccessibility, such that X is inaccessible from below.
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Aaaaaaaaaaaaaand here we go. Define "idea of inaccessibility". Define "inaccessible". Define "inaccessible from below".

And that's only the first sentence.

The rest of the post is mishmash of things that make no sense.

"Membership 1"? Still never defined "membership".

Let's see if doronshadmi can take the time to define things or if he'll start rambling on about other stuff.

I also like that doronshadmi takes over a month to respond to a message 90 posts ago.
 
Little 10 Toes said:
Let's see how quickly doronshamdi can mangle established mathematical terms, ideas, understands, and/or makes up his own definitions.

Aaaaaaaaaaaaaand here we go. Define "idea of inaccessibility". Define "inaccessible". Define "inaccessible from below".

And that's only the first sentence.

The rest of the post is mishmash of things that make no sense.

"Membership 1"? Still never defined "membership".

Let's see if doronshadmi can take the time to define things or if he'll start rambling on about other stuff.

I also like that doronshadmi takes over a month to respond to a message 90 posts ago.
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Start from http://www.internationalskeptics.com/forums/showpost.php?p=12167886&postcount=2957 and this time please carefully follow my posts, all you are asking is already there only if you really care to follow and understand them (which is something that you didn't, yet).
 
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Please look at post http://www.internationalskeptics.com/forums/showpost.php?p=11847070&postcount=2704 and the reply of jsfisher to this post.

In terms of Fuzzy Logic, membership is a spectrum between 0 and 1, such that membership 0 is total isolation among objects if it is compared to NOthing (logical contradiction), where membership 1 is total connection among objects if it is compared to YESthing (logical tautology).

By this notion, no collection of objects is reducible (it is inaccessible) into NOthing (logical contradiction) AND it is not extensible (it is inaccessible) into YESthing (logical tautology).

Extreme individuality or extreme connectivity among objects, prevents self awareness that enables both individuality and connection among objects, in terms of local (individual) AND global (connected) awareness among objects.

Complex creatures like us are concrete examples of local AND global awareness, where the following diagram (support by the following diagram) is a nice analogy of the linkage between complex expressions and local_global linkage.

By following this diagram visually AND verbally, there is no problem to understand the development of the spectrum of awareness between isolation (unaware isolated objects) and connectivity (awareness without objects), and how developed complexity is the result of the balance between 0 and 1 memberships, which are all emerge from thing (illustrated by the straight line at the bottom of the diagram) that is not limited to any of its expressions (NOthing, YESthing or anything between them).
 
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doronshadmi said:
Start from http://www.internationalskeptics.com/forums/showpost.php?p=12167886&postcount=2957 and this time please carefully follow my posts, all you are asking is already there only if you really care to follow and understand them (which is something that you didn't, yet).
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You say nothing about accessibility in that post, and your posts aren't easy to follow or understand. Part of the reason for that is that you seem to make up new, undefined terms as you go. Could you please try to define some of the terms regarding accessibility, in one post?
 
Hevneren said:
You say nothing about accessibility in that post, and your posts aren't easy to follow or understand. Part of the reason for that is that you seem to make up new, undefined terms as you go. Could you please try to define some of the terms regarding accessibility, in one post?
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Take, for example, this:
doronshadmi said:
For example, the cardinality of all natural numbers is inaccessible to any given natural number since any natural number is a finite value, where, according to modern mathematics, the cardinality of all natural numbers is the first non-finite value (named as ℵ0).
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This is an example of an inaccessibility from below.

Please tell me what is not understood to you here?
 
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doronshadmi said:
Take, for example, this:

This is an example of an inaccessibility from below.

Please tell me what is not understood to you here?
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Do you expect us to search through all your posts to find an example of inaccessibility, instead of you defining it?

An example isn't a definition. You obviously can't define your terms.
 
Hevneren said:
You obviously can't define your terms.
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You obviously ignore the example, which is actually used by traditional mathematics in order to define the smallest transfinite cardinal as the limit cardinal of any finite cardinal:
This means that one cannot "reach" λ from another cardinal by repeated successor operations.
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or in other words, λ is inaccessible from below (where in my example here, λ is ℵ0).

Hevneren, if "An example isn't a definition. You obviously can't define your terms." is your fundamental approach, don't expect to understand non-traditional mathematical notions, as done, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=12244994&postcount=2968.
 
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And reaching understanding, in the considered subject, is logically understand that no collection of objects is logically accessible into logical contradiction (represented by no symbol between the outer "{" and "}"), and logically inaccessible into logical tautology (represented by the outer "{" and "}").

So, by understanding { } both spatially AND symbolically, one immediately understands that logically there is no such thing like a complete collection of infinitely many objects (which means that transfinite cardinality that tries to define a fixed size like |N|, is logically wrong).
 
If the notion of collection is logically understood as inaccessible to NOthing (logical contradiction, which is represented by the space between, for example, "{" and "}") or inaccessible to YESthing (logical tautology, which is represented, for example, by the outer "{" and "}"), then the very notion of collection can't be used in order to logically define fixed sizes like |N|, in the first place.

In other words, by this view, the very notion of collection is too strong ("above" contradiction) or too weak ("below" tautology), in order to logically deal with the absolute logical borders of Mathematics (according to this notion, contradiction is the "lowest" border of Mathematics, where tautology is the "highest" border of Mathematics).
 
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doronshadmi said:
If the notion of collection is logically understood as inaccessible to NOthing (logical contradiction, which is represented by the space between, for example, "{" and "}") or inaccessible to YESthing (logical tautology, which is represented, for example, by the outer "{" and "}"), then the very notion of collection can't be used in order to logically define fixed sizes like |N|, in the first place.

In other words, by this view, the very notion of collection is too strong ("above" contradiction) or too weak ("below" tautology), in order to logically deal with the absolute logical borders of Mathematics (according to this notion, contradiction is the "lowest" border of Mathematics, where tautology is the "highest" border of Mathematics).
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You said “if”. Many people in this thread have observed that the premise stated is not supported by evidence beyond your personal dislike of the mathematical status quo and arbitrary use of undefined and non mathematical terms.

Upthread you introduced fuzzy logic, so I went looking for the relevance and linkage. I could find none beyond insertion of some fuzzy logic terms in your argument.

But let’s cut to the chase: so what? Why does your argument even matter? What are we missing out on due to this alleged mathematical mischief? What disadvantage is the human race suffering?
 
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