Russell's Paradox no more!

[subversion]

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.

I'm not sure if I was fully able to understand what was written above, but I do appreciate your attempt to explain better.

Anyway, I will state my solution to the paradox again as such
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.

Please if you can you should be able to disprove this solution in a single sentence just as I have proven it in a single sentence. If we men can not agree that I have solved Russell's paradox, then I see no reason at all for me to provide us with the theory of everything because it would obviously not be fully appreciated.

[dleviwing]

Guille;
Sub does not need to read books to acquire knowledge. Only we mere mortals need to do that.
A set that is defined to contain everything must contain itself. An empty set contains no elements and is referred to as a null set if I remember right.

[subversion]

Guille;
Sub does not need to read books to acquire knowledge. Only we mere mortals need to do that.
A set that is defined to contain everything must contain itself. An empty set contains no elements and is referred to as a null set if I remember right.

again you are exactly and ironically correct dleviwing. I DON"T need to read books to acquire knowledge, because all I need is my brain. This is a good thing, because afterall, the TOE does not currently exist in any books. You should have known that! Sadly, however, I am mortal.

A set that contains everything must contain itself, I agree. Also an empty set is null, I agree. So how does it change this fact?

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.

[dleviwing]

There are no paradoxes in nature! Thus all paradoxes are manmade.

[michellemfry]

David, I tend to view paradoxes as little stop signs on the road of logic. Yes, we built that road. Engineering leaves a little bit to be desired, but man-made a road is. My grammar could use some engineering.

[Guille]

again you are exactly and ironically correct dleviwing. I DON"T need to read books to acquire knowledge, because all I need is my brain. This is a good thing, because afterall, the TOE does not currently exist in any books. You should have known that! Sadly, however, I am mortal.

A set that contains everything must contain itself, I agree. Also an empty set is null, I agree. So how does it change this fact?

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.

The explanation f why your solution is wrong is not only 1 sentence, but is short, here I give step to step. Please don't carry on arguing that it reduces to your solution, because it doesn't:

The logical idea of a set that contains something is refeared to the fact that the set, for example S is equal to the following elements {a,b,c,d} such that S contains {a}, {b}, {c}, {d}. In some cases, the requierements to enter a set include that set itself, and then S={a,b,c,d,S} which means that S contains itself. But there are many sets that dont' containt themeselves. For example, the "set of all dogs" isn't a dog itself (the set), so it doesn't contain itself. But the "set of all sets that can be described in less than 30 words" includes itself as it is described in 12 words and a number.

Therefore the set of all sets that do not contain themselves is not an empty set or irrelevant.

[subversion]

The explanation f why your solution is wrong is not only 1 sentence, but is short, here I give step to step. Please don't carry on arguing that it reduces to your solution, because it doesn't:

The logical idea of a set that contains something is refeared to the fact that the set, for example S is equal to the following elements {a,b,c,d} such that S contains {a}, {b}, {c}, {d}. In some cases, the requierements to enter a set include that set itself, and then S={a,b,c,d,S} which means that S contains itself. But there are many sets that dont' containt themeselves. For example, the "set of all dogs" isn't a dog itself (the set), so it doesn't contain itself. But the "set of all sets that can be described in less than 30 words" includes itself as it is described in 12 words and a number.

Therefore the set of all sets that do not contain themselves is not an empty set or irrelevant.

I congratulate you very highly for coming closer to disproving my solution then anyone else was able to do. This is surely a testament of your intelligent and inquisitive nature so you should feel proud of yourself because I am happy that you've tried to logically disprove my solution.

However, despite your notable effort, I deduce that your disproof is still incorrect, and here's why. If a set is a set it automatically contains the set which is itself, and this is what we mean when we say the set contains itself. So to use your example, the set of all dogs is not a dog itself, you're correct, but that doesn't pertain to the fact that the set of all dogs IS the SET of all dogs, therefore the set of all dogs contains itself because itself is the set of all dogs. So for the set of all dogs to contain itself doesn't mean that the set of all dogs has to be a dog itself, just that it has to be the set of all dogs itself. So you're incorrect assumption that you made was that the set itself is a dog, whereas the set itself is a set, therefore the set contains itself.

Therefore I again state that any set automatically contains itself as it's own set not necessarily as a member of it's own set but as the set itself, but this is not NECESSARILY true of the empty set because the empty set is not a set, because it has no value i.e. contains nothing, so whether or not the empty set necessarily contains itself is a non-applicable question. Therefore any set which does not necessarily contain itself must automatically be the empty set because it CANNOT be a set otherwise. So my solution still stands but thank you so much for trying to disprove it because I enjoyed the challenge and I feel my proof is more valid now that I have effectively been able to defend it. Please carry on arguing if you are still not satisfied until we both reach an agreement so that we can consider progress is made.

honestly, SubVersion

[Guille]

Sub,

Thanks for your mature words, I feel for once that we are constructing. Abotu your question to dave, there is no paradox in nature, but that doesn't impply that we should invent any solution to the paradoxes. For example, the paradoxes of Zeno are the probably the strongest ones (by the way, I propose you to try and solve them) developed by humans ever. The solution that has beeen doen of it is absurd: that an infinite amount of space can be covered in a finite amount of time.
In your reply you come again to a circular discussion. The thing is that there is from the start a mistake. I agree with your idea that a set must ALWAYS contain itself, as it contain all it members, and all it's members is what it is. So basically if something is itself (and if something is, neccesarilyl something is itself for itself is it) then neccesarilly it contains itself, for these tow mean the same really.

But the thing is that the idea of containing itself in set theory is not this containing. The idea of containing itself in set theory is that a set is part of the members of itself, is itself a member.

The basic thing is that your solution doesn't match the set theory problem which is russell's paradox. But it is interesting, as it shows how the logical idea of contention is not the same as the real thing that contention means in the world. And this shows that logic is not neccesarilly true.

[WithoutMe]

First & foremost, yur statement
"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."

was initially said by the Buddhist Logician Nagarjuna in his four-fold logic, i.e.,
1. "This" (but not "Not This).
2. Not "This" (but not "This").
3. "This & Not This".
4. Not "This & Not This".

Basically he used it to counter the Nyayayikas (who basically used the "Neti Neti" line of thought for the Ontological proof of the Brahman & the dependene of the Atman in it).

Now going from Logic to Metaphysics, he stated the case as acausal!

Now going from Logic to Psychological, he used the first as the "Sensation", second as "Feeling", third as "thinking" & the fourth as "Intuition" (Ofcourse am using Jungian Psychological terms to translate it from the original Sanskrit). Similar such connotations can be found if you consider the first three as the specific aspects of the "Reptile Brain" (first case), the "Mammalian Brain (2nd case) & the "Human Brain" (3rd case). As I had posted it in the thread starter, "On an Immoral Ethics" at http://www.toequest.com/forum/showth...newpost&t=1666
Only in the case when the 3 brains work in perfect harmony does the individual live in the acuasal world, i.e., he doesnot have Pschological Time, Though the Chronological Time goes on as usual. I will post on this much details, giving the whole detailed structure of the Mind along with the Brain Dynmics in relation to Nirvana & the Acausal Perception in some other post. If u all r very much interested, then I can make it early as soon as possible!

You said:
"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".
I repeat: "whether the empty set contains itself or not is an irrelevant question because the empty set has no value"

Now, u r using the kind of logic which the much mis-interpreted Logican Wittgenstien used, when he basically said:
"What can be said at all, can be said clearly, & what cannot be said at all, must be passed over in silence, for that lies in the range of nonsense"

Note the words "must be passed over in silence", that is, even by considering such propositions, wud lead to paradoxes (he used the word "nonsense").... yep its true, that's the way we go on in life, whenever we find at a paradox, we dont drop dead while reeling back at a paradox, instead we choose to simply avoid or just "let it be", i.e., we humans have the capability to voluntarily step out of an endless loop..... does it point to the much-perplexing (& often scpetical) phenomenon of Free-Will or does it instead speak of our capability to always be able to multitask using multiprocessers, that is when one processers (neurons, as the experts say) hangs (that is, goes in an infinite loop), the other neurons interrupt it & reset the very signal input to that neuron..... Now, how does another neuron "realise" that some other neuron has hanged? Does it have a time out? Can't eb, coz we just seem to understand a paradox even before going in circles with it!!!!
Is it bcoz all paradoxes have a pattern of toggling output, i.e., "yes/no/yes/no/yes"... if so, then how does the mind differentiate a paradox from a clock? Or are all paradoxes actually the clocks which tick us to Infinity??

PS. I need an answer, not that paradoxes have one....lol!

Infact whether a paradox can have an answer refer to my reply-post of "Walstad's Paradox" at http://www.toequest.com/forum/showth...newpost&t=1681

wat say u ?

Subversion dude,
u deparately need to read up on Object Oriented Design.... read the relationships of "is-part-of" vs "is-a"..... u definetely have confused Containment with Being.

I am what I am, however I donot contain myself, infact my relationship with me is that of a "is-a" (Identity) whereas my relationship with say, my tooth, is a "is-part-of" (Containment)!!!! u dig that?

Note very carefully, The relationship of Identity (that is, "me being me just for the sake of me being me", or in Kantian Language, "in-itself") is itself a paradox & runs the high risk of being mistaken for that of Containment (that is, "me being me just for the sake of all the properties & attributes that whoever is positing my existence is in relation with" (so it depends on the person who is positing my existence, whereas the "in-itself" doesnt need anyone to posit, the "in-itself" is infact self-caused, or as Nagarjuna wud conclude, anything that is self-caused, is actually acausal), or in Kantian Language, Containment points to the "for-itself", ie., the Penomenal World)!!

Now one may very well say (as the Logical Positivists had championed) that the "in-itself" even if it exists is full crap coz one can't even say whether its right ot wong ot true or false, coz its beyond any source of inverstigation (acausal).... & thus, what I call "Isolated Existence"!!!

Wat say u all to that ?

Regards,
wM.

[subversion]

Subversion dude,

I am what I am, however I donot contain myself, infact my relationship with me is that of a "is-a" (Identity) whereas my relationship with say, my tooth, is a "is-part-of" (Containment)!!!! u dig that?

Ahh but ask yourself this question, what is it that contains you and nothing else?

Now one may very well say (as the Logical Positivists had championed) that the "in-itself" even if it exists is full crap coz one can't even say whether its right ot wong ot true or false, coz its beyond any source of inverstigation (acausal).... & thus, what I call "Isolated Existence"!!!

Wat say u all to that ?

In response to this, I would say that if everything exists, then in-itself must exist, for everything is in itself (solution to Russell's other paradox).

ps. I'm interested in checking out some of the philosophers you mentioned