Deeper than primes

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zooterkin said:
You said (1) and (6) meant different things.
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zooterkin said:
If you are wrong about something so straightforward, why should anyone give credence in your more 'advanced' proposals?
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I made a mistake by reply to jsfisher's argument, as if it is my argumnet.

Here is my argument:

[latex]$$$
\exists z \, \forall (x \ne x) \, (x \ne x) \rightarrow ((x \ne x) \in z)$$$[/latex]​

[latex]$$$
\exists z \, \forall (x = x) \, (x = x) \rightarrow ((x = x) \notin z)$$$[/latex]​

Here is jsfisher's argument:

[latex]$$$
\exists z \, \forall x \, (x \in z) \rightarrow (x \ne x) \equiv \\ \exists z \, \forall x \, (x = x) \rightarrow (x \notin z)
$$$[/latex]​

and it has nothing to do with my argument about (X=X) and (X≠X) as used in http://www.internationalskeptics.com/forums/showpost.php?p=6667634&postcount=13318 .


So, zooterkin try to get out of your loop and move on.
 
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doronshadmi said:
I made a mistake by reply to jsfisher's argument, as if it is my argumnet, which is:
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No. You repeatedly claimed the two are not equivalent. It was not a mistake. You argued for pages that the "strong" version is not equivalent to the "weak" version. Show some backbone and admit you were utterly wrong.

Also, the gibberish you are trying to pass now is not even well-formed, it does not compile under the syntax for the logic used. If you wish to use a different syntax, you have to define it formally. Of course, there is no reason why you would want to use a different syntax. This mainly shows you're lost like a puny wabbit in the design room for a nuclear reactor.
 
Can someone please get Doron to leave the goalposts where they were? This constant movement is tiresome.
 
jsfisher said:
Can someone please get Doron to leave the goalposts where they were? This constant movement is tiresome.
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Why jsfisher, do you have some problem to follow the corrections made in http://www.internationalskeptics.com/forums/showpost.php?p=6667634&postcount=13318 ?


Do you also can't follow the fact that your argument is not relevant anymore to the considered subject ( as shown in http://www.internationalskeptics.com/forums/showpost.php?p=6667691&postcount=13321 )?
 
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jsfisher said:
How can you say that? Doron has provided an elegant simplification heretofore undocumented in boolean algebra. Because of Doron's incredible insight, we now know that A OR B can be replaced by the much simpler form (A XOR B) OR (A AND B). Don't you get it? Are you really so thick?

Moreover, (A XOR B) OR (A AND B) in turn can be simplified even further. It becomes ((A XOR B) XOR (A AND B)) OR ((A XOR B) AND (A AND B)). And it does not stop there. These simplifications can continue without limit.
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Thank you jsfisher.

It is a nice demonstration of self referential system that has infinite complexity based of the same simple principles, exactly as found in the case of fractals' self similarity over scales.

In other words jsfisher, you can't comprehend the logic of complex objects like fractals, and the I/O feedback principle.

Whether you like it or not, the true results of OR connective are the same as XOR connective + AND connective true results.
 
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doronshadmi said:
Once again you demonstate your inability to get indivisible elements A and B, such that B is at AND not at A, where A is at XOR not at B.
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Once again you demonstrate your inability to understand that "B is at AND not at A" is simply and directly self-contradictory. As noted and explained before, your acceptance of such an obvious self-contradiction is most likely due to the fact that you are using some criteria for asserting that "B" is "not at A" that is something other than the negation of the criteria you use for asserting that "B" is "at" "A". Which is again just self-inconsistent. Also it is highly unlikely that you are using your same criteria for "at" in your "B is at" "A" as you are for your "A is at" "B", which would be a generally inconsistent use of your criteria for "at".


So Doron do you actually have a self-consistent and generally consistent criteria for your "at" such that your " B is at" "A" as well as your "A is at" "B" both use that same criteria and your "at AND not at" is that criteria AND its negation?



doronshadmi said:
A linkage among indevisible elements provides the existence of complex objects that are understood in terms of collections.

Sice you have no Meta view of the considered subject, you are missing the following:

I wish to share with you some Meta view of the Mathematical Science, which does not follow after some basic agreed notions. Let us start by using Gottlob Frege's notion about X≠X. He defined number 0 as the amount of the objects of the class of all X≠X ( ( http://plato.stanford.edu/entries/frege/ ) )

0 is not equivalent to Nothing, because 0 is, after all something, called a number. But it does not mean that Emptiness or Nothing can't directly be used in order to do some Math. Let us follow this notion by re-examine, for example, the notion of the empty set:

(X=X) means: "X exists" or "X is true"

(X≠X) means: "X does not exist" or "X is false"

According to this Meta view, there are different versions of the empty set as follows:

p case:
[latex]$$$
\exists z \, \forall (x \ne x) \, (x \ne x) \rightarrow ((x \ne x) \in z)$$$[/latex]​
By p case version, z exists as an empty set only if the non-existing (nothing) "belongs" to it, but then this version does not cover the case of the existing things that do not belong to z.


q case:
[latex]$$$
\exists z \, \forall (x = x) \, (x = x) \rightarrow ((x = x) \notin z)$$$[/latex]​
By q case version, z exists as an empty set only if the existing things (something) do not belong to it, but then z is one of the exiting things that are used to define the existence of z, which is a circular reasoning.

As demonstrated, if Non-existence (Nothing or Emptiness) is taken directly as "a legitimate participator" of some mathematical framework, then even an intuitive concept like The empty set, is shown by a now light, because by the meaning of (X≠X) we are able to understand the meaning of (X=X), as shown above.

----------

Let us do a further step and look at the Mathematical Science by using a Meta view about Deduction. From this Meta view, some mathematical theory is (hopefully) a consistent framework of unproved context-dependent collection of decelerations, known as axioms.

Since the development of Non-Euclidian geometries and Gödel's Incompleteness theorems, most of the mathematicians are actually reinforce the deductive and context-dependent nature of their mathematical work, such that no systematic research is done in order to understand better the cross-contexts linkages that are invented\discovered from time to time among, so called, "mathematical branches".

Actually a phrase like "mathematical branches" (if related to context-dependent frameworks) is misleading, because there is no Mata view of Cross-contexts research of these Context-dependent frameworks, which rigorously and systematically demonstrates the linkage between them, such that they can be considered as "branches of a one tree" or as "organs of a one organism".

Gelfand wonders about the weak effectiveness of the mathematical science on disciplines like Biology ( http://en.wikipedia.org/wiki/Unreasonable_ineffectiveness_of_mathematics ), which is characterized by its organic nature.

Organic Mathematics (which is a non-standard view of Math) is an attempt to develop a Meta view of the Mathematical Science, which its aim is to discover\invent the paradigm of the organic notion of the Mathematical Science.

By the current paradigm, which is generally based on Deduction, any given mathematician (or group of mathematicians) is asked to invent\discover his\their Context-dependent framework by avoiding any "mutations" of already agreed terms. I believe that one of the possible answers to Gelfand's remark is the impossibility of "mutations" among deductive frameworks.

The deductive-only paradigm of the Mathematical science for the past 3,500 years can't agree with "mutations" of already accepted terms.

It has to be stressed that mutations are changes of basic terms that may fundamentally change a given organism (where the term "organism" is generalized to any abstract or non-abstract framework).

Furthermore, these "mutations" are not destructive-only exactly because of the cross-context and non-local nature of the organism as a whole with respect to its organs, which uses the mutations for further development of itsef as a complex phenomanon.

The notion of Non-locality is essential to Cross-contexts frameworks like organic systems, and it is essentially forbidden by the deductive-only paradigm.

By using Cross-contexts framework of the mathematical science, concepts like (Non-existence=Fallacy) or (Existence=Truthfulness) is used, as previously shown.

Let us draw a preliminary view of a Cross-contexts' axiomatic framework.

According to it, total notions like Emptiness and Fullness are defined, such that Emptiness is weaker than the notion of Collection and Fullness is stronger than the notion of Collection. It has to be stressed that the notion of Collection is a fundamental term of deductive-only frameworks, and the use of a notion like Fullness (which is the opposite of Emptiness) enables to define the non-local property of Cross-contexts' axiomatic framework.

The first version of the development of the axioms of the the paradigm of Cross-contexts framework is (the remarks are allowed at this preliminary development's state and are use to help the reader to move from the Context-dependent framework to the Cross-contexts framework. After the paradigm-shift is done, these remarks are not needed anymore):

(Predecessor is what is less than a considered thing.

Successor is what is more than a considered thing.)

The axiom of minima:
Emptiness is that has no predecessor.

The axiom of maxima:
Fullness is that has no successor.

(Only Emptiness does not have a predecessor in the absolute sense.

Only Fullness does not have a successor in the absolute sense.

The next axioms are at the level of the existence of collections, which is > Emptiness AND < Fullness, where > or < are the order of existence w.r.t Emptiness or Fullness.)

The axiom of existence:
Any existing thing has a predecessor.

(y and x are place holders for an intermediate state of existence between Emptiness and Fullness.)

The axiom of infinite collection:
If x exists then y>x exists.

The axiom of Locality:
There exist y and x, such that x is at the context of y.

The axiom of Non-Locality:
There exist y and x, such that y is at AND not at the context of x.
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I didn't miss any of it Doron and my response is the same as it was before. You evidently think your "Meta view of the considered subject" just means you can spout whatever self-contradictory and generally contradictory nonsense that suits you.
 
doronshadmi said:
EDIT:

I made a mistake by reply to jsfisher's argument, as if it is my argumnet.

Here is my argument:

[latex]$$$
\exists z \, \forall (x \ne x) \, (x \ne x) \rightarrow ((x \ne x) \in z)$$$[/latex]​

[latex]$$$
\exists z \, \forall (x = x) \, (x = x) \rightarrow ((x = x) \notin z)$$$[/latex]​

Here is jsfisher's argument:

[latex]$$$
\exists z \, \forall x \, (x \in z) \rightarrow (x \ne x) \equiv \\ \exists z \, \forall x \, (x = x) \rightarrow (x \notin z)
$$$[/latex]​

and it has nothing to do with my argument about (X=X) and (X≠X) as used in http://www.internationalskeptics.com/forums/showpost.php?p=6667634&postcount=13318 .
Click to expand...

But your argument involves expressions that are not used by mathematicians -- expressions that you haven't bothered to define or explain in such a way they would be accepted as legitimate means. That amounts to a punishment without disclosing the reason for it. Are you sure that you have landed in the right century?
 
doronshadmi said:
The axiom of existence:
Any existing thing has a predecessor.

The axiom of infinite collection:
If x exists then y>x exists.
Click to expand...

The axiom of infinite collection states that if 'x' exists, then there is 'y' such as 'x<y'. From this, we can conclude that 'y' must have a natural predecessor, which is 'x', and we therefore proved The axiom of existence. But axioms are statements that must be independent of each other -- they are statements that cannot be proven with the usage of other axioms. (See the attempts to prove Euclid's Fifth Postulate.)

What kind of minaret are you building, Doron?
 
doronshadmi said:
Whether you like it or not, the true results of OR connective are the same as XOR connective + AND connective true results.
Click to expand...


Only if by this addition symbol you really mean OR....and in that case, your observation is trivial. If not, then it is just another instance of you being wrong.

So, Doron, which is it? Are you belaboring the trivial again or just wrong again?
 
epix said:
The axiom of infinite collection states that if 'x' exists, then there is 'y' such as 'x<y'. From this, we can conclude that 'y' must have a natural predecessor, which is 'x', and we therefore proved The axiom of existence.
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Actually, no, not quite. The second axiom can not be used to establish that X has a predecessor.

The axioms are poorly expressed and poorly named, but they are separate. Also, both axioms establish the existence of an infinite collection given one existing thing.

The first axiom would be better named the axiom of predecessor and the second, the axiom of successor.

The better expression of each would be (1) for all X, there exists a Y, Y < X, and (2) for all X, there exists a Y, Y > X.

As would be expected, these axioms contradict other axioms of doronetics.
 
The Man said:
Once again you demonstrate your inability to understand that "B is at AND not at A" is simply and directly self-contradictory. As noted and explained before, your acceptance of such an obvious self-contradiction is most likely due to the fact that you are using some criteria for asserting that "B" is "not at A" that is something other than the negation of the criteria you use for asserting that "B" is "at" "A". Which is again just self-inconsistent. Also it is highly unlikely that you are using your same criteria for "at" in your "B is at" "A" as you are for your "A is at" "B", which would be a generally inconsistent use of your criteria for "at".


So Doron do you actually have a self-consistent and generally consistent criteria for your "at" such that your " B is at" "A" as well as your "A is at" "B" both use that same criteria and your "at AND not at" is that criteria AND its negation?





I didn't miss any of it Doron and my response is the same as it was before. You evidently think your "Meta view of the considered subject" just means you can spout whatever self-contradictory and generally contradictory nonsense that suits you.
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The Man, as long as your reasoning can't get a simple notion like an atom (an indivisible element) with size > 0, all you get from Organic Mathematics is contradiction and self-inconsistency.
 
jsfisher said:
Actually, no, not quite. The second axiom can not be used to establish that X has a predecessor.

The axioms are poorly expressed and poorly named, but they are separate. Also, both axioms establish the existence of an infinite collection given one existing thing.

The first axiom would be better named the axiom of predecessor and the second, the axiom of successor.

The better expression of each would be (1) for all X, there exists a Y, Y < X, and (2) for all X, there exists a Y, Y > X.

As would be expected, these axioms contradict other axioms of doronetics.
Click to expand...

jsfisher, since you don't get Emptiness and Fullness, you do not get the use of predecessor and successor in terms of existence.

Without this understanding you have no way to get OM.
 
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jsfisher said:
Only if by this addition symbol you really mean OR....and in that case, your observation is trivial. If not, then it is just another instance of you being wrong.

So, Doron, which is it? Are you belaboring the trivial again or just wrong again?
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Trivial? You have no ability to get the logic of an atom (an indivisible element) with size > 0, which is at AND not at a given context, so you are actually talking about your trivial logic that can't comprehend such elements.

Try just try to get out of your :boxedin: because there is a universe beyond it, that is blocked by your deductive-only view.
 
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doronshadmi said:
jsfisher, since you don't get Emptiness and Fullness, you do not get the use of predecessor and successor in terms of existence.

Without this understanding you have no way to get OM.
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In order to "get" Doronetics, one must completely suspend reason and consistency. We all get that.

That aside, though, are you asserting that predecessor means something different from what I wrote in the post you quoted?
 
jsfisher said:
In order to "get" Doronetics, one must completely suspend reason and consistency. We all get that.

That aside, though, are you asserting that predecessor means something different from what I wrote in the post you quoted?
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EDIT:

jsfisher, all you have to do is to get the way I use predecessor and successor in terms of existence.

If you do that maybe, just maybe, you will be able to get out of your :boxedin: and get things like atoms with size > 0.

You still try to get OM as a deductive-only framework.
 
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