doronshadmi
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A hidden assumption
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doronshadmi
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A detailed example, please.
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Indeed!
Indeed!
jsfisher
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And you don't see that "non-local ur-element real-line" is gibberish in any sort of accepted mathematical nomenclature?
This whole thing of yours is an invention, a fantasy.
No, logic was not involved so much as hand-waving and presumption. You assumed a conclusion, then through a sequence of excursions into the irrelevant or meaningless, arrived back at your destination.
Here's is an excellent example:
doronshadmi
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Please look at http://www.geocities.com/complementarytheory/NXOR-XOR.pdf in order to understand the logical basis of non-locality.
My conclusions are the results of a simple question, which is:
How the multiple (or the multitude) is defined?
( In my opinion, critical thinking is a very important method for fruitful development.
One of the most important things that we can ask ourselves is:
Are we sure that we do not act in the same way that is criticized by us? )
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PixyMisa
Persnickety Insect
Remind me not to play baseball with you.
PixyMisa
Persnickety Insect
That makes no sense.
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Complexity
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jsfisher
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Nonsense. All you did in that document is make meaningless statements as you renamed things that didn't need to be renamed. Here is my personal favorite, by the way:
Why not just represent it as {x}? For that matter, why did you even bother since you never referred back to either representation?
Be that as it may, let's explore that document a little. Assume we have the four elements, a, b, c, and d with relationships in and out defined as follows:
Code:
[FONT="Courier New"] in out
+---+---
a | 0 | 0
b | 0 | 1
c | 1 | 0
d | 1 | 1[/FONT]What would be your underlying System Z? Be explicit. Is a an element of the resulting set? Is d?
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doronshadmi
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No problem. Have a nice day.
doronshadmi
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The main principle here is very simple:
Any given collection of logical connectives is reduced into common (invariant under exchange) \ non-common (variant under exchange) relations.
We know that the fundamental property of Symmetry is its invariance, and the fundamental property of Asymmetry is its variance.
By using Symmetry on 2-valued logic, we have noticed that NXOR connective is the symmetrical state of A,B pair , where XOR is the asymmetrical state of A,B pair.
Let a 2-valued framework be represented by A B.
A B relation is:
A B
A A
A B
B A
B B
These relations can be reduced (without a loss of generality) to
symmetric (AA or BB) \ asymmetric (AB or BA) relations, represented as:
AB
XX is AB symmetry --> A=B (AB is the same)
XY is AB asymmetry --> A≠B (AB is not the same)
A=B can be reduced (without a loss of generality) to a single value X.
A≠B cannot be reduced to a single value without a loss of detail X or Y.
Furthermore, in order to conclude that A≠B, they must share the same realm.
So 2-valued framework is at least X (symmetry or sameness) \ XY (asymmetry or difference) relation.
Let us use SA (Symmetry\Asymmetry relation) on 2-valued Logic:
T F NXOR
F F considered
F T not considered
T F not considered
T T considered
T F XOR
F F not considered
F T considered
T F considered
T T not considered
T F NXOR\XOR
F F considered
F T considered
T F considered
T T considered
T F generalization of NXOR\XOR
X X considered (Symmetry)
X Y considered (Asymmetry)
Well English, as you have probably noticed, is not my first language so by representation I mean a particular value in this case , where x is used here as a variable.
This is system Z, which is the outcome of Symmetry\Asymmetry relation:
T F generalization of NXOR\XOR
X X considered
X Y considered
As can be seen, True\False are generalized to Symmetry\Asymmetry relation.
Some examples of a,b,c,d membership with system Z:
The truth table of OR membership:
in out
0 0 --> F (a is not considered)
0 1 --> T (in , out are not the same) = { }_ (b is out Z (b is local))
1 0 --> T (in , out are not the same) = {_} (c is in Z (c is local))
1 1 --> T (in , out are the same) = {_}_ (d is in AND out Z (d is non-empty non-local))
In this case the non-local membership is non-empty, and the local membership is empty or
non-empty. The empty non-local membership is ignored.
The truth table of AND membership:
in out
0 0 --> F (a is not considered)
0 1 --> F (b is not considered)
1 0 --> F (c is not considered)
1 1 --> T (in , out are the same) = {_}_ (d is in AND out Z (d is non-empty non-local))
In this case the non-local membership is non-empty. The local memberships and the empty non-local membership are ignored.
The truth table of NOR membership:
in out
0 0 --> T (in , out are the same) = { } (a is in NOR out Z (a is empty non-local))
0 1 --> F (b is not considered)
1 0 --> F (c is not considered)
1 1 --> F (d is not considered)
In this case the non-local membership is empty. The local memberships and the non-empty non-local membership are ignored.
The truth table of NAND membership:
in out
0 0 --> T (in , out are the same) = { } (a is in NOR out Z (d is empty non-local))
0 1 --> T (in , out are not the same) = { }_ (b is out Z (b is local))
1 0 --> T (in , out are not the same) = {_} (c is in Z (c is local))
1 1 --> F (d is not considered)
The non-empty non-local membership is ignored.
The truth table of NXOR\XOR membership:
in out
0 0 --> T (in , out are the same) = { } (a is in NOR out Z (d is empty non-local))
0 1 --> T (in , out are not the same) = { }_ (b is out Z (b is local))
1 0 --> T (in , out are not the same) = {_} c is in Z (c is local))
1 1 --> T (in , out are the same) = {_}_ (d is in AND out Z (d is non-empty non-local))
The truth table of NO membership:
in out
0 0 --> F (a is not considered)
0 1 --> F (b is not considered)
1 0 --> F (c is not considered)
1 1 --> F (d is not considered)
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jsfisher
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So, as I said, you are just going to use new names for all things to make it sound more important. You have added no value, only obfuscation.
OR membership? OR membership? You aren't following your own rules. You said in your paper:
You invented these rules; you should at least stick to them. There's no OR, AND, NAND, etc., just XOR and it's negative.
You were the one that said the in and out relations were minimally required for the concept of Membership, and that the concept of set grew from the XOR and NXOR outcomes of the in and out relations. I have provided exactly this information, so where's the set?
By the way, care to explain what, exactly, you meant by "related to the NXOR outcome but...logically not a part of it" in plain English? You seem to just smash the two together and mark all the outcomes as T. Why not F? Why not some of each?
doronshadmi
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If something is generalized it does not mean that the states that are based on it are not used.
NXOR\XOR logic does not mean that NXOR and XOR are the only connectives that are used.
NXOR is the logical basis of non-locality where XOR is the logical basis of locality.
What I did is to show that any given logical system is based on Locality\non-locality relations and the rest of the connectives are the results of these concepts.
The fundamental concept here is Symmetry\Asymmetry relation and without it nothing is comparable (Symmtery-only is total unity. Asymmtery-only is total isolation) and therefore not researchable.
For example, take this:
A B
0 0
0 1
1 0
1 1
If you get it in terms of variance and invariance, then 0 0 ; 1 1 is invariant under exchange and 0 1 ; 1 0 is variant under exchange.
This simple principle can be used as the univeral principle of any given logic.
If you disagree with me than please show a researchable realm which is not the outcome of Symmetry\Asymmetry relation.
A set (or anything that is based on the mutitude) is the result of this relation and not the basis of it, exactly as I show in http://www.geocities.com/complementarytheory/NXOR-XOR.pdf
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jsfisher
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Would it help to point out errors in "The standard notion of the concept of Set" part right at the beginning of your paper? I suppose not. You will continue to believe what you like. Knock yourself out.
Your paper is founded in a lie. You believe that giving things names make them somehow important. You connect terms together to make absolute gibberish out of them. And then the few times you actually seem to be heading towards a coherent thought, when questioned on it you deny it any semblance of sanity.
Well done.
doronshadmi
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True and False are not comparable without Symmtery \ Asymmetry relations.
Symmetry provides the common basis for comparison and Asymmetry provides the objects that are compared.
Please show this universal principle by using traditional Math, because after all you claim that my system is no more than giving different names to well known mathematical concepts.
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Gate2501
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I am mad at myself for thinking that I was in over my head here. It seems that other intelligent posters have echoed what I was saying... I know the definitions for the words you use, but you simply use them outside of the scope of their known meanings. Shame on you for making me feel bad.
At any rate... What are you talking about in the above quote?
True and False. We all know what these words mean. Symmetry and Asymmetry. We all know what these words mean. I however have no idea what you have said in the quote. This time I am not going to get in the mindset that this is all over my head. I think that you are just spouting rubbish, and redefining words.
Are you trying to say that True and False cannot be compared without understanding mathematical symmetry? As in you cannot tell the difference between 1 and 0 if you do not understand that 1=1 and 0=0 and 1=/=0? Why do you need to say this? It is another tactic of obfuscation?
I would hate to hear how you order a pizza.
Olowkow
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Gate2501
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Oh my lord...
But yeah, I think that in the post I quoted, our friend Doron basically said:
*You cant tell the difference between true and false if you don't know the difference between true and false*
It reminds me of how Scientologists will go on these horrible complicated rants about extremely simple concepts. I think that our new friend has taken a simple concept, injected a slew of new definitions and non traditional language, and in turn transformed something simple and well understood into a complete mess of crap.
Doronshadmi, if I give a lecture, but first fill my mouth with jellybeans, and continue stuffing them in my mouth for the duration, it does not make me smarter than the audience because they do not understand me. It makes me an idiot. Take the jellybeans out of your mouth dude.
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