Paradox Theory

[bowmore]

If A = B then (a and b) = True.

If A = True
And B = True,
the (A = B) = (True = True) = (True). What I've noticed here, is that in order for the statement to be True, Both statements have to inherently match up. And what do you call a statement that matches up? You call it True. That's why I equate "True" with And.

Equating the operators with the values doesn't add clarity. Frankly I wonder why you do it at all. What's worse it looks like you're actually changing the old algebra in the process.
I'm also wondering why you think operators must match a value. With what value does the "not" operator corespond or the "implication" and "equivalence" operators?

On top of that you seem to reach different results with one notation vs. the other :

(I've underlined the difference)

(Null) True (True) Not(=) False, therefore, (Null) True (True) = (Null) or (True) = False!

(Null) False (True) Not(=) False, therefore (Null) False (True) = (Null) False[/i] (True) = True!

At this point I'm not very convinced you're on to something at all.

[Wechtlein Uns]

ok. I've thought about this for a good long time.

The problem of Godel statements, or actually, what I had percieved as godel statements, but that were actually reflexive statements, originally struck me as a fitting challenge. I set out to define what was meant when one uses the term statement. But I have found that you can not know what is meant, and yet at the same time, you can grasp it's underlying structure.

A statement is not a thing. It is a pointer. In computer science, we have things known as pointers, which do not contain values in bits, but contain the address location of another location in memory. I think this is an elegant metaphor, because statements do not contain data in themselves. They point to data. When you read a book, and your eyes look over myriad statements, it becomes crystal clear that the word "tree" does not made a giant block of wood grow out of the page and into your eye. But rather, it directs the attention[/i] to the phenomena in question.

I believe this is why, when someone asks, "what is the meaning of meaning?", we get an error. Meaning, is, in essence, a translation mechanism. It is nature's way of switching "formats" so to speak. For example, If I were to make a statement that utilized large, obtuse sounding words to indicate that my keyboard is black, there is a chance that you will not understand the words and ask me for their meaning. If I say, "such and such means", I am utilizing the axiom prinicple. The two statements are equivalent, but not in the way you might think.

Statements that are equivalent to each other are not so because they are identical things[/b]. They are equivalent because they point[/i] to the same thing. The "meaning" I am speaking of, is simply a translation tool, to switch the data from one format to another, so that another person might understand.

This is important, I believe, because there are statements that do not point to the same phenomena, and these are not equivalent. But even more importantly, there are statements that point to statements, just as in computer science there are pointers that point to pointers. But, my point(pardon the pun) in all this, is the one underlying principle that Statements are not Inherently existent. They do not exist. In computer science, a pointer doesn't exist. It simply points. This is proven when in programming, it is revealed that "no data can be extracted from a pointer, that is itself not a pointer."

In this challenge, I have thought to create a third bit that would resolve the issue, but only now do I see, that I was, in essence, simply labeling the situation. There can be no third bit, or third value, because a bit or value is just that: data, value. In reality, however, when you come across a reflexive situation, there is no data that can be honestly extracted. And yet, there is data in this bizzarre situation:

The concept of Zero. In computer science, Zero is not equal to Null. It is an actual value. And yet, the two ideas share the same value. Truth is, zero is the concept of absolutely nothing. No data. No value. It is here that I believe the answer to reflexive statements may be found. A reflexive statement, by itself, points to another statement. But the system of reflixive statements as a whole, holds no data, and thus it's data is zero. It's data is null.

But Null is very different from true and false. However, I think that the statement "something is true" is also a statement about a statement. Only this time it is a statement about a statement with it's relationship to some data. In the same sense, to say "something is null" is to make a statement about that statement with it's relationship to zero. This relationship is, in fact, the very thing we have started with to define true. It is the axiom of identity. Null = Null. To say something is Null, is, if it is null, then it is True. If it is not, then it is false.

But what of the original system of reflexive statements? Are they true, or are they false? To this I have realized that the terms True, and False, only apply when there is something. Some data. I have all ready shown how to make a true or false with the systems relationship to zero, but when you take that relationship away, you are left only with zero.

And the only comfort that can be sought is that in computer science, Zero is false.
What is false? It is, of course, the idea that the statement and reality don't match. In other words, the statement, and the phenomena it points to, do not exixt. This might lead to the idea that Reflexive statements do point to data. But if they did, that phenomena would not exist. Thus, as a whole, they would be false.

[bowmore]

In this challenge, I have thought to create a third bit that would resolve the issue, but only now do I see, that I was, in essence, simply labeling the situation. There can be no third bit, or third value, because a bit or value is just that: data, value. In reality, however, when you come across a reflexive situation, there is no data that can be honestly extracted.

So no more algebra  

And the only comfort that can be sought is that in computer science, Zero is false.
What is false? It is, of course, the idea that the statement and reality don't match. In other words, the statement, and the phenomena it points to, do not exixt. This might lead to the idea that Reflexive statements do point to data. But if they did, that phenomena would not exist. Thus, as a whole, they would be false.

I on the other hand can live with the fact that human cognition is limited, and by extension that the systems we build to describe reality are in themselves limited, which is ultimately what Gödel's incompleteness theorems prove.

BTW zero is false is not a universal in computer science. In Java for instance '0' is not the same as 'false', and both are not equal to 'null'.

[Wechtlein Uns]

I on the other hand can live with the fact that human cognition is limited, and by extension that the systems we build to describe reality are in themselves limited, which is ultimately what Gödel's incompleteness theorems prove.

Heh. Yeah. I am still young and arrogant, and I feel a call to prove some major theorem or teard down the established walls. There's revolutionary blood in my viens. It's just of the scholarly type.  

Thank you for hanging with me through this, bowmore. You're a great guy to give me an ear when I wanted to talk to someone about my crazy ideas. Thanks a lot.

[bowmore]

Heh. Yeah. I am still young and arrogant, and I feel a call to prove some major theorem or teard down the established walls. There's revolutionary blood in my viens. It's just of the scholarly type.  

np

Thank you for hanging with me through this, bowmore. You're a great guy to give me an ear when I wanted to talk to someone about my crazy ideas. Thanks a lot.

You're welcome.
I was curious for that algebra, as it would constitute a new formal system, and it would in fact be subject to Gödel's incompleteness theorem again.  
You concluded the algebra thing wasn't going to work before I could show that, so kudos to you.