Deeper than primes

[laca]

Hate to rain on your parade, Doron, but you still got this hanging over your head:

[latex]$$$\begin{eqnarray}
\exists z \, \forall x \, (x \in z) \rightarrow (x \ne x) \equiv \\
\exists z \, \forall x \, (\lnot (x \in z)) \vee (x \ne x) \equiv \\
\exists z \, \forall x \, (\lnot (x \in z)) \vee \lnot (x = x) \equiv \\
\exists z \, \forall x \, (x \notin z) \vee \lnot (x = x) \equiv \\
\exists z \, \forall x \, (\lnot (x = x)) \vee (x \notin z) \equiv \\
\exists z \, \forall x \, (x = x) \rightarrow (x \notin z)
\end{eqnarray}
$$$[/latex]​

Care to address the issue?

 

[HatRack]

Hate to rain on your parade, Doron, but you still got this hanging over your head:

[latex]$$$\begin{eqnarray}
\exists z \, \forall x \, (x \in z) \rightarrow (x \ne x) \equiv \\
\exists z \, \forall x \, (\lnot (x \in z)) \vee (x \ne x) \equiv \\
\exists z \, \forall x \, (\lnot (x \in z)) \vee \lnot (x = x) \equiv \\
\exists z \, \forall x \, (x \notin z) \vee \lnot (x = x) \equiv \\
\exists z \, \forall x \, (\lnot (x = x)) \vee (x \notin z) \equiv \\
\exists z \, \forall x \, (x = x) \rightarrow (x \notin z)
\end{eqnarray}
$$$[/latex]​

Care to address the issue?

QFD

Doron is still stuck on trying to figure out what X = X means, he's a good 20 years away from being able to address the above.

 

[epix]

Hate to rain on your parade, Doron, but you still got this hanging over your head:

[latex]$$$\begin{eqnarray}
\exists z \, \forall x \, (x \in z) \rightarrow (x \ne x) \equiv \\
\exists z \, \forall x \, (\lnot (x \in z)) \vee (x \ne x) \equiv \\
\exists z \, \forall x \, (\lnot (x \in z)) \vee \lnot (x = x) \equiv \\
\exists z \, \forall x \, (x \notin z) \vee \lnot (x = x) \equiv \\
\exists z \, \forall x \, (\lnot (x = x)) \vee (x \notin z) \equiv \\
\exists z \, \forall x \, (x = x) \rightarrow (x \notin z)
\end{eqnarray}
$$$[/latex]​

Care to address the issue?

Why is there the swap between p and q in (4) and (5)? Did Doron dispute the exact conclusion in (6) beforehand?

 

[jsfisher]

Why is there the swap between p and q in (4) and (5)? Did Doron dispute the exact conclusion in (6) beforehand?

The commutation used from (4) to (5) is to get things in the right order for the final conversion ((5) to (6)) from OR back to IMPLY. The expression a -> b is equivalent to ~a V b; the commutation moved the negated term to the left position.

Since Doron has been known to quibble over the most inane things as a distraction from the main point, it seemed appropriate to include all the baby steps.

 

[HatRack]

The commutation used from (4) to (5) is to get things in the right order for the final conversion ((5) to (6)) from OR back to IMPLY. The expression a -> b is equivalent to ~a V b; the commutation moved the negated term to the left position.

Since Doron has been known to quibble over the most inane things as a distraction from the main point, it seemed appropriate to include all the baby steps.

You really can't appreciate this thread until you get completely hammered and read over some of Doron's arguments. The fact that he willfully misunderstands so many things, including the reflexivity of equality, is just astounding. It is truly amazing what some people will do in the name of ego defense. If it wasn't for the fact that he has posted this crap in so many forums over so many years, I could never believe that someone is truly this insane.

 

[epix]

The commutation used from (4) to (5) is to get things in the right order for the final conversion ((5) to (6)) from OR back to IMPLY. The expression a -> b is equivalent to ~a V b; the commutation moved the negated term to the left position.

Since Doron has been known to quibble over the most inane things as a distraction from the main point, it seemed appropriate to include all the baby steps.

So the whole steps were undertaken to convince Doron that

(p → ~q) ↔ (q → ~p)

is tautology. Sometimes he pastes the truth tables, but this time he forgot to look and compare. Maybe he didn't want to; perhaps he feels depressed when there is nothing around to shoot at. LOL.

 

[HatRack]

So the whole steps were undertaken to convince Doron that

(p → ~q) ↔ (q → ~p)

is tautology. Sometimes he pastes the truth tables, but this time he forgot to look and compare. Maybe he didn't want to; perhaps he feels depressed when there is nothing around to shoot at. LOL.

Yes, that is exactly why those steps were undertaken. As seen here http://www.internationalskeptics.com/forums/showthread.php?postid=6611705, Doron does not believe these two statements are logically equivalent. This all stems from his argument that the empty set is based on circular reasoning.

I got him to agree that one version of the Axiom of the Empty Set was valid, but when it was pointed out that it was logically equivalent to all the other versions which he thought were invalid, he began insisting that the laws of logic themselves were invalid. The man just cannot admit to being wrong.

 

[doronshadmi]

Says the man who can't even understand what X=X means...

Let us check it.

Please tell us zooterkin, what is the meaning of X=X?

 

[doronshadmi]

Doron is still stuck on trying to figure out what X = X means

HatRack, please tell us what is the meaning of X=X?

 

[doronshadmi]

It is truly amazing what some people will do in the name of ego defense.

EDIT:

Indeed your Ego prevents the understanding of the following:

p case:

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

In p case z exists as empty set only if the non-existing belongs to it, but then p case 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]​

In q case z exists as empty set only if the existing things 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 can be seen p case ≠ q case, so this discussion is closed because

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

has nothing to do with my argument about (X=X) and (X≠X).

The fact that he willfully misunderstands so many things, including the reflexivity of equality, is just astounding.

I wonder if your Ego will give himself the chance to realize that he is running after his own tail in this case, and also in http://www.internationalskeptics.com/forums/showpost.php?p=6655853&postcount=13285 case

 

[zooterkin]

Which step has the error, Doron?

[latex]$$$\begin{eqnarray}
\exists z \, \forall x \, (x \in z) \rightarrow (x \ne x) \equiv \\
\exists z \, \forall x \, (\lnot (x \in z)) \vee (x \ne x) \equiv \\
\exists z \, \forall x \, (\lnot (x \in z)) \vee \lnot (x = x) \equiv \\
\exists z \, \forall x \, (x \notin z) \vee \lnot (x = x) \equiv \\
\exists z \, \forall x \, (\lnot (x = x)) \vee (x \notin z) \equiv \\
\exists z \, \forall x \, (x = x) \rightarrow (x \notin z)
\end{eqnarray}
$$$[/latex]​

 

[The Man]

EDIT:

This is the beauty of OR connective, it is used to demonstrate XOR+AND connectives under a one framework, where the XOR aspect of OR is used for locality, such that a given object is understood by (partial (in the case of a line)) OR (complete (in the case of line or point)) membership w.r.t a given domain.

No Doron it is simply your very ugly, deliberate, obvious, extraneous and self-contradictory manipulation of "OR", by modifying it to "XOR" then trying to 'add' an "AND" in an attempt to simply reverse that extraneous and self-imposed modification.

Pay attention that p="partial" OR q="complete" are used here, such that p≠q and therefore there is no contradiction exactly because p≠q.

Pay attention that " p="partial" OR q="complete"" is just more of your usual nonsensical gibberish.

The AND aspect of OR is a novel notion if the OR T T inputs are related to an indivisible object that is simultaneously at AND not at a given domain.

No, TRUE OR TRUE = TRUE is not a "novel notion". While "at AND not at" is still a direct contradiction.

If it is comprehended as an indivisible object > a given domain , then its size (the property of length>0) w.r.t a given domain (being simultaneously at AND not at a given domain) provides its consistent non-local existence.

Lines or line segments (if not understood in terms of collections) have the ability of being simultaneously at AND not at a given domain, where a point can't be simultaneously at AND not at a given domain.

Nope, once again " as an indivisible object" it is not "at" any " given domain" less then itself. Yet can be a union of segments, rays or points "at" any number of given domains.

As long as a line or a line segment is understood only in terms of collection, the simultaneity of the AND aspect of OR is understood as a contradiction,

No Doron it is understood as a contradiction simply because it simply and directly, well, contradicts itself.

because OR is understood only of terms of p≠q (it is not understood in therms of the same existing thing that its size > a given domain) in order to be considered as a consistent result.

"OR is understood only of terms of p≠q"? Well I guess that is part of your problem and as such it remains simply, well, your problem. There is no requirement or inference from "OR" such that "p" can not equal "q".

Being simultaneously at AND not at a given domain is possible only if the considered object has size > 0 and it is not partitioned (it is a non-local atom).

No Doron it is only possible if you are using a criteria to establish "not at" that is something other than the negation of the criteria you used to establish "at". That is just being self-inconsistent.

If you get it in terms of partitioning, then its non-locality is not considered anymore and you get things only in terms of collections.

At this very moment there is an unresolved dis-communication between us.

Once again Doron that "unresolved dis-communication" is still just between you and yourself. That is until you start to try to make at least some semblance of an effort for any kind of self-consistency in your assertions.

 

[The Man]

The man just cannot admit to being wrong.

What?!! If I were wrong I'd admit to it. It's just that I never am and by the way it's 'The Man' not 'The man'.




Oh wait..

...sorry, my mistake.

 

[jsfisher]

No Doron it is simply your very ugly, deliberate, obvious, extraneous and self-contradictory manipulation of "OR", by modifying it to "XOR" then trying to 'add' an "AND" in an attempt to simply reverse that extraneous and self-imposed modification.

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.

 

[epix]

What?!! If I were wrong I'd admit to it. It's just that I never am and by the way it's 'The Man' not 'The man'.




Oh wait..

...sorry, my mistake.

Everything is so confusing in this thread: "I never am." On the other hand, if The man isn't The Man... I better formalize it.

(The Man ≠ The man) → (first name = last name) => ( male XORAND female)

I don't think that it helped that much.

 

[epix]

No Doron it is simply your very ugly, deliberate, obvious, extraneous and self-contradictory manipulation of "OR", by modifying it to "XOR" then trying to 'add' an "AND" in an attempt to simply reverse that extraneous and self-imposed modification.

I think Doron is trying to self-exorcise the hell out of the demon that has found its abode inside Doron's neural network.

Doron => d OR on

So if he makes a one-letter change and renames himself to DORAN, then he can anagram his new name into OR and AND, which are two logical connectives that can be used to substitute for XOR -- a logical connective according to which demons are reasoned with:

e XOR cism.

But DORAN as AND & OR also anagrams into implicit RANDO... that concludes as RANDOM. That causes Doron to come up with expressions, such as "(x=x)(x=x)," and with other random choices, which he perceives as analytic due to the influence of the resident demon.

 

[doronshadmi]

Which step has the error, Doron?

[latex]$$$\begin{eqnarray}
\exists z \, \forall x \, (x \in z) \rightarrow (x \ne x) \equiv \\
\exists z \, \forall x \, (\lnot (x \in z)) \vee (x \ne x) \equiv \\
\exists z \, \forall x \, (\lnot (x \in z)) \vee \lnot (x = x) \equiv \\
\exists z \, \forall x \, (x \notin z) \vee \lnot (x = x) \equiv \\
\exists z \, \forall x \, (\lnot (x = x)) \vee (x \notin z) \equiv \\
\exists z \, \forall x \, (x = x) \rightarrow (x \notin z)
\end{eqnarray}
$$$[/latex]​

It is not about any step, but about being irrelevnt to the right interpretation of the considered subject, which is:

p case:

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

In p case z exists as empty set only if the non-existing belongs to it, but then p case 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]​

In q case z exists as empty set only if the existing things 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.

 

[doronshadmi]

Nope, once again " as an indivisible object" it is not "at" any " given domain" less then itself. Yet can be a union of segments, rays or points "at" any number of given domains.

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.

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 (

Frege defined the number 0 as the number of the concept not being self-identical,

( 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.

 

[zooterkin]

It is not about any step,

You said (1) and (6) meant different things. The intermediate steps show they mean the same. Please show which step is wrong, if you wish any credibility (hah!) to be attached to your comments about matters mathematical.

If you are wrong about something so straightforward, why should anyone give credence in your more 'advanced' proposals?

 

[zooterkin]

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

No, it doesn't. Try again.