Russell's Paradox no more!

[subversion]

Good news!

I was just driving around after having done some posting and I realized something. I know the solution to Russell's paradox!

I only just became familiar with the paradox a few days ago when it was mentioned on this site but now I think I've solved it. This reiterates to me the fact that I have the ability to solve any paradox and that since I solved this paradox I must be correct about my other theories as well.

Anyway, here's the solution. Correct me if I'm wrong because as I said I haven't studied Russell's paradox in depth, but from what I gather it essentially asks the question "does the set of all sets which do not contain themselves contain itself?" The simple answer is this "no, the set of all sets which do not contain themselves does not necessarily contain itself because the set of all sets which do not contain themselves is simply the empty set." Now I say necessarily because whether the empty set, which is nothing, contains itself or not is actually an irrelevant question. For clarity we say by default that the empty set does not contain itself, but this is not necessarily true. To understand this we must look at the simple definition of something.

Anything which is something automatically contains itself by simply being itself. In this manner the Earth contains itself because it is itself. Nothing (i.e. the empty set) on the other hand is not considered to be something and thus either it simultaneously contains AND does not contain itself or it simultaneously neither contains nor does not contain itself OR it simultaneously neither contains itself nor doesn't contain itself while simultaneously containing AND not containing itself. So that's basically a really long and confusing way of saying that whether or not the empty set contains itself is an irrelevant question because the empty set has no value. So in conclusion I will state that the solution to Russell's paradox is that the set of all sets which do not contain themselves is simply the empty set and whether the empty set contains itself or not is an irrelevant question because the empty set has no value.

Now the purpose of this thread is two fold. First of all you will tell me if you think my solution to Russell's paradox is correct or not (also tell me if I have even stated the paradox correctly or not). The official solution I am positing is what I have underlined above. Second you may offer any paradox you wish for me to solve. It is my firm belief that as the Theory of Everything is correct I should likewise be able to solve any paradox I am presented with. So this is an open invitation. Here is a list of paradoxes which I have already solved and the name of who originally devloped the theory/paradox

The Incompleteness Theorem (Kurt Godell)
The Axiom of Choice (Ernst Zermelo)
Russell's Paradox (Bertrand Russell)
The Law of Laws (Lee Walstad)
The Theory of Everything (Lee Walstad)
Guille's Time Paradox (Guille)

thanks for reading, I look forward to yall's opinions and paradoxes. I'm not guaranteeing I can solve all paradoxes but I'm fairly confident in my abilities.

best regards, SubVersion

[michellemfry]

Your ability to achieve solutions seems connected to an eye on the definitions. I would not disagree with such an approach.

Here's to staying defined...

Sincerely,

[Guille]

Sub,

It's an original approach but I logicworld is incompatible with originalityworld. There is a difference between being and containing. Containing is an external relationship, if something contains itself it is from an external condition, just as if it contains any other thing. But being is the thing itself, it is nothing if it doesn't be, it is to be, that's all.

[subversion]

Sub,

It's an original approach but I logicworld is incompatible with originalityworld. There is a difference between being and containing. Containing is an external relationship, if something contains itself it is from an external condition, just as if it contains any other thing. But being is the thing itself, it is nothing if it doesn't be, it is to be, that's all.

Good point Guille, the proof does rely on the definition that something always contains itself and that nothing is irrelevant to the notion of contents. In other words, whether nothing contains itself or not is an irrelevant and meaningless question according to the definition of nothing which is that it has no value and no contents. For clarity, we should arbitrarily say that nothing does not contain itself, because something does contain itself and this way we define the two "things" as different. However we always remember that in reality you cannot truely answer the question of whether nothing contains itself or not because the question is irrelevant to the definition of nothing.

Furthermore I think it is a good definition of something to say that something is something that exists and since it exists that means it is it's own contents. Therefore it does contain itself in a very technical sense. The definition of containing would be that for something to contain something most efficiently (i.e. with the least wasted space) it must be the same thing. This is a special case of containing in which the container is more than infinitely close to it's contents because they are the same thing. So if we accept these definitions, and I do think they are good definitions, then we have a solution to Russell's Paradox and we also have a new definition of set theory.

Here is the new definition: Sets are defined as something which contain themselves. The empty set is the one set that does not necessarily contain itself and thus the empty set is really a false set and should not be defined as a set but as a not set. Defining the empty set as a true set was a mistake by Set theorists and if they adopt this new definition of set it will probably help them out. Not that they'll ever read this but you know, I try.

[zeroca]

Sub,
I hear about Russel’s paradox for the first time. I’m not familiar with it. Can you formulate it briefly anew?
Here’s the paradox from bible, which (together with other paradoxes…) led me to the system “active zero”:
Jesus says: I’m in father and father is in me (this isn’t quote from bible, but only is main idea of told). How would you interpret it?
To say figuratively, can the mug, which contains water, be in the same water, which is placed inside it?
Or another paradox from Dao de Tzin (Lao Tse), which together with the paradox above, led me to mentioned system “active zero”:
Only a few in this universe act by mean of inactivity (this sentence isn’t quote from Dao de Tzin, but only is main idea of told)
Regards,
zeroca

[Guille]

Sub,
I hear about Russel’s paradox for the first time. I’m not familiar with it. Can you formulate it briefly anew?
Here’s the paradox from bible, which (together with other paradoxes…) led me to the system “active zero”:
Jesus says: I’m in father and father is in me (this isn’t quote from bible, but only is main idea of told). How would you interpret it?
To say figuratively, can the mug, which contains water, be in the same water, which is placed inside it?
Or another paradox from Dao de Tzin (Lao Tse), which together with the paradox above, led me to mentioned system “active zero”:
Only a few in this universe act by mean of inactivity (this sentence isn’t quote from Dao de Tzin, but only is main idea of told)
Regards,
zeroca

Zeroca, the best explanation I've seen on the net is here: http://en.wikipedia.org/wiki/Russell%27s_paradox. There is a thread I started with it's title here: http://www.toequest.com/forum/showth...ll%27s+paradox. I give a good explanation of myself and write it in logical form.

[subversion]

Sub,
I hear about Russel’s paradox for the first time. I’m not familiar with it. Can you formulate it briefly anew?
Here’s the paradox from bible, which (together with other paradoxes…) led me to the system “active zero”:
Jesus says: I’m in father and father is in me (this isn’t quote from bible, but only is main idea of told). How would you interpret it?
To say figuratively, can the mug, which contains water, be in the same water, which is placed inside it?
Or another paradox from Dao de Tzin (Lao Tse), which together with the paradox above, led me to mentioned system “active zero”:
Only a few in this universe act by mean of inactivity (this sentence isn’t quote from Dao de Tzin, but only is main idea of told)
Regards,
zeroca

Zeroca,

I think what Jesus is essentially saying is that he and the father are together, contiguous, synonymous. If we consider that something always contains itself then we can deduce that God and Jesus are one according to the paradox. So yes, the mug and the water can both be inside eachother but only if you consider the mug and the water to be the same single object.

Russell's paradox is about set theory and set theory is about grouping numbers together in sets. For example, you can have the set of natural numbers which is just the counting numbers 1 2 3 4 5... etc. You can also supposedly have the empty set which contains nothing, i.e. zero. Now Russell's paradox asks about having a set which does not contain itself. Specifically, it asks if you had the set of all sets which do not contain themselves, then would that set contain itself? Generally you think it would have to contain itself if it contains all sets that don't contain themselves, but then once it contains itself it no longer is a set which does not contain itself and thus we arrive at a paradox. I am solving the paradox by saying that all sets must contain themselves in order to exist and the only set which does not contain itself per se is the empty set. Therefore the set of all sets which do not contain themselves is the same as any set which does not contain itself which is simply the empty set. Therefore the simple answer is that the paradox is based on an irrelevant question because it is a question about the empty set and the empty set is considered to be irrelevant because it has no value and no contents.

[dleviwing]

A real example:
In the Library of Congress there is a reference index book. Within this book are referenced all the documents and books that are maintained by the librarian. Also within this book is a reference to itself as a document.
Sub;
Your solution is false/positive and thus is still a paradox.
Jesus is a member of the set of man.

[subversion]

A real example:
In the Library of Congress there is a reference index book. Within this book are referenced all the documents and books that are maintained by the librarian. Also within this book is a reference to itself as a document.
Sub;
Your solution is false/positive and thus is still a paradox.
Jesus is a member of the set of man.

please explain in greater detail why my solution is wrong because the example you give refers to a set which contains itself, not a set which does not contain itself. Therefore I deduce that you have said nothing of pertinence to my solution of Russell's paradox and instead you are using your bullshit rethoric again to try and discredit others without proof and it is probably because you find it hard to admit that I have succeeded. I do not want you to be jealous, I want you to be glad.

[Guille]

Sub,

I don't know exactly what was in dave's mind but I can assure there is a relationship to Russell's paradox, for anyone with a minimal knwoledge in set theory, at least.

The example set of dave is a set that contains all other of it's kind (in set theory this is called a class) and thus contains itself. The thing is that the set contains all the other sets in it's class that do or do not contain themselves. Therefore, weather or not it contains itself, depends on weather or not any of it's members contain the whole class including them selves. And this is itself,so yes, it does contain itself. But in contradiction, by containing itself it would be a member contained in the class and there would need a set that contains the class including the set that contains itself in that it contains the class. Therefore this one wouldnt' contain itself, it would contain the class, but not itself. And vice versa... It is a strange version of russell's: it jsut introduces the idea of a class and the set that is the class and contains itself but not the class and the set that is not the class and contains itself but not the class and the set that is the class and contains the class but not itself and the set that is not the class and contains the class but not itself. The four of them make a double russell paradox.

Anyway, there actually is a solution to russell's paradox. I read it once in a paper in a university library. Quite complex. Mathematicians introduced the idea of "type"... I don't liek this all logical objects, they are unlogical.