Walstad's Paradox

[subversion]

I would like to share with you all my most recent development. I am super super excited about it right now because I just thought of it like thirty minutes ago.

INTRODUCTION
As many of you may know, I have solved Russell's paradox. I have found that in theory, something which exists, contains itself. Therefore the set of all sets which do not contain themselves is the empty set, in theory. Furthermore, there is a complete set, which contains all things, including itself, in theory. However, now I have been following this trail, I have discovered the other half of Russell's paradox! I have discovered that it is uncertain whether or not everything contains what it is not!

I'm not sure if anybody else has noticed this paradox or not, but I am going to call it Walstad's Paradox, and state it as follows:

We know that everything contains itself, but we do not know if it contains what it is not. Conversely, we know that nothing does not contain what it is not, but we do not know if it contains itself.

Hmmmm interesting. So what do ya'll think? Another way to state the paradox is "does nothing form a meaningful part of everything?" Also, Russell's paradox reduces to "Is the empty set full of itself?"


any ideas?

[WithoutMe]

Ok... how can u solve a paradox? If its a Paradox, then its unsolvable, & if u have solved, then it means that u have solved something that corresponds to the idea that u have of the problem in the paradox, but not the paradox itself, coz "by solving a paradox" wud mean that the paradox is solvable, so how come it is a paradox.... so if anyone claims that s/he demystefied a mystery, it just cannot be a true, coz all such talk of INVERTING, like "demystefied the mytery", "solving a paradox", "talking the untalkable" & all such will but always be a greater paradox... a sort of metaparadox, i.e., the paradox of the paradox being a paradox but simultaneously being able to be no more a paradox (coz its being solved now)!!!!
Similarly, the meta-paradox will have another paradox of its own... thus, existence in its very nature is like the scales of a Onion, with paradoxes reeling on on another -- paradox with the meta-paradox, the meta-paradox with the meta-meta-paradox.... ad infinitum!

Hell! If any of you reading this have been able to understand any but & have been able to solve the mystery (which I am trying uselessly) of existence by reading abt this "meta-meta-...-paradox...ad infitum", then that wud mean that the idea is not a paradox, hence another paradox. Now, if u try to avoid it, then that wud mean that it is avoidable, again a paradox, & if u accept it, u'll have a jump to the next level of "meta"-paradox..... thus, paradoxes all the way, even in the way I am expressing myself!!!!

[WithoutMe]

Does Transcending then mean going from a paradox to the "meta"-paradox, & then transcending the meta-paradox, will mean going from the meta-paradox to the "meta"-paradox..... but in all this, do we go inwards more & more or do we go outwards more & more!!! Now, a Quantam Physicits will say "inwards", whereas an relativistic Physicists might say "outwards"....lol!

Then again, it might very well be that it is our Psychology which sees the worlds in its own way (the "human-all-too-human" view that one is so bound to), & it is due to this, that our thinking tells us that "paradoxes indeed exists", that things contain themselves, whereas in reality it is our perception which sees the things around as if seeing a reflection of all this inside & even vice versa. ............... Now that may be the explanation of a Psychologist.

& a Physicts might say that: "no no! Psychologists r dead wrong, its the Quantum tunelling that is responsible for transcending some thing", & the Mathematician might say that: "no no! its all set theory"..... so its not a case of Russell or God knows who else, instead, the point is simple, & what is that?





I just answered, did u miss it!

Rgds,
wM.

PS. I just answered, did u miss it!

[becomingagodo]

sorry you have not solved the russel paradox because
<I have found that in theory, something which exists, contains itself. Therefore the set of all sets which do not contain themselves is the empty set, in theory. Furthermore, there is a complete set, which contains all things, including itself, in theory>
if something exist and contain itself their fore a statement this is true contain itself. now the statement this is true would be a set that contain itself. so what if their is another set saying no statement is correct. now then we add up all set and we see a paradox because then the set of all set is a class and this class their statement this is true and a statement no statemnet is correct to form a paradox. Also failed to grasp it a mathmetical paradox so no amount of word could fix it if their was a solution it would be about hundred page worth of mathmetics going down to some TOE that can allow it to exist.
however the point you do raise some good question i found the anwser to the first on a paradox website everthing does contain everything it not simple this that everything is all that could be and that could not be. and the anwser to the other nothing is undefine look in website dr math for explantion so nothing is what you make it even if that nothing is the universe and also according to big bang before their was nothing which created the universe so it will yes as well.
if you believe sorry to leave with the bad news see you foggot their more to math and the only way to solve it is proof by contridiction which is limiting or by brute force of mathmatics.

[subversion]

Ok... how can u solve a paradox? If its a Paradox, then its unsolvable, & if u have solved, then it means that u have solved something that corresponds to the idea that u have of the problem in the paradox, but not the paradox itself, coz "by solving a paradox" wud mean that the paradox is solvable, so how come it is a paradox.... so if anyone claims that s/he demystefied a mystery, it just cannot be a true, coz all such talk of INVERTING, like "demystefied the mytery", "solving a paradox", "talking the untalkable" & all such will but always be a greater paradox... a sort of metaparadox, i.e., the paradox of the paradox being a paradox but simultaneously being able to be no more a paradox (coz its being solved now)!!!!
Similarly, the meta-paradox will have another paradox of its own... thus, existence in its very nature is like the scales of a Onion, with paradoxes reeling on on another -- paradox with the meta-paradox, the meta-paradox with the meta-meta-paradox.... ad infinitum!

Hell! If any of you reading this have been able to understand any but & have been able to solve the mystery (which I am trying uselessly) of existence by reading abt this "meta-meta-...-paradox...ad infitum", then that wud mean that the idea is not a paradox, hence another paradox. Now, if u try to avoid it, then that wud mean that it is avoidable, again a paradox, & if u accept it, u'll have a jump to the next level of "meta"-paradox..... thus, paradoxes all the way, even in the way I am expressing myself!!!!

It is a paradox because we can not know whether the empty set contains itself or not. We know that the empty set does not contain what it is not, because then it would not be empty. However, we can't decide if the empty set theoretically contains itself or not. So I have simplified RUssell's Paradox to show that all sets which do not necessarily contain themselves form the empty set, and we can not tell whether the empty set contains itself or not. Luckily, we don't have to worry about Russell's Paradox anymore because we can realize that it is an irrelevant question about nothing (literally the empty set). That is why I say I have solved the Paradox, because I have shown it's irrelevancy.

However, in simplifying the paradox, I have discovered it's other half. The other half of the paradox states that the full set does contain itself (this is the solution to Russell's other paradox) but that we cannot tell if it contains the empty set or not. In other words, we can not tell if the complete set contains what it is not, but we can tell that it contains what it is. Again, the original part is that we know that nothing cannot contain what it is not, but we cannot tell if it contains what it is.


Basically the entire paradox is asking the question, is the empty set a true set, and if so is the complete set complete without it? The answer is that the answer is irrelevant.

[subversion]

sorry you have not solved the russel paradox because
<I have found that in theory, something which exists, contains itself. Therefore the set of all sets which do not contain themselves is the empty set, in theory. Furthermore, there is a complete set, which contains all things, including itself, in theory>

Yes I have solved the paradox, in theory, for I have shown that Russell's Paradox may in fact be an irrelevant question about the empty set. I'm not saying it's for sure, just saying that it seems to be a logical possibility, and it would make a lot of sense.

if something exist and contain itself their fore a statement this is true contain itself. now the statement this is true would be a set that contain itself. so what if their is another set saying no statement is correct.

You bring up a good point but let me just say that in order to consider your example correctly you must consider that the set which says something is true is the complete set and the set which says something is false is the empty set. This is so because the Law of principle shows that any statement which says something is false is a negative statement, i.e. a statement about nothing. Only true statements (statements that say what is true) may be made about everything and false statements (statements which say what is false) refer to nothing. So in your example any statement which says that it is not true must not necessarely contain itself and must be part of the empty set. Now whether or not the empty set forms a meaningful part of the complete set is an irrelevant question, in that we do not know if it is relevant or not, because the empty set has no value.

Also failed to grasp it a mathmetical paradox so no amount of word could fix it if their was a solution it would be about hundred page worth of mathmetics going down to some TOE that can allow it to exist.
however the point you do raise some good question i found the anwser to the first on a paradox website everthing does contain everything it not simple this that everything is all that could be and that could not be. and the anwser to the other nothing is undefine look in website dr math for explantion so nothing is what you make it even if that nothing is the universe and also according to big bang before their was nothing which created the universe so it will yes as well.
if you believe sorry to leave with the bad news see you foggot their more to math and the only way to solve it is proof by contridiction which is limiting or by brute force of mathmatics.

Will you please restate the above in a way that I can understand it? Making the logical assumption that something must contain itself in order to exist, and also the assumption that statements of a false nature only apply to nothing, all paradoxes can be reduced to irrelevant questions. An irrelevant question is a question that we don't know if it's relevant or not.

[WithoutMe]

Avoiding a problem (by sayings its "irrelevant") dosnt solve it!!!

[subversion]

what if the problem is irrelevant though? Afterall, isn't nothing irrelevant? Actually let me rephrase that, we have know way to tell if nothing is relevant or irrelevant. WOuldn't you agree to that?

[Lloyd Gillespie]

We know that everything contains itself, but we do not know if it contains what it is not. Conversely, we know that nothing does not contain what it is not, but we do not know if it contains itself.

Sub, the set of all sets, which is a set of itself, and not a set of itself, and does contain itself, and does not contain itself, is intuitive imagination...i.e., it's infinitely extensional in infinite directions, both positive and negative...and mathematicians should use a little more of it to answer more serious quests...don't ya think...?

regards

[Guille]

Sub,

Not only you have not find a paradox at all, but that your own "solution" to Russell's paradox disproves Walstad's paradox.

We know that something does not contain what it is not because it is something in particular containing certain things, which are what it is. In this sense, you are correct when you say that containing is the same as being, but you do not understand that the meaning of containment in logical mathematics sis not the existential containing to which you are referring to. Anyway, everything (if by this you mean the set of all sets) must contain what it is and what it is not, for it is the set of all sets, including the set which are empty sets, or the set which are not part of the set of all sets (there is no set which is not a member of the set of all sets, therefore the set of sets which are not a member of the set of all sets is an empty set, and as I said, the set of all sets contains all empty sets). Also, we do know that nothing does not contain what it is not, as you said, but we know also that as nothing (if by this you mean the set of all empty sets) contains only (and all) empty sets, it contains nothing, so what it is, is nothing, and yes, it contains it.

I have discovered something very interesting. The implication that nothing is the set of all empty sets implies that there is another nothing, which is any empty set. And so, here comes Antonio's mathematical developments. In a recent thread (I can't remember the name), Antonio said that 0 and 1/infinity are both nothing, the same mathematical value, with the difference that zero is absolute and one/infinity is relative. Thus, we can say that the nothing which is the set of all empty sets, is zero, and the nothing which can be any empty set, is 1/infinity.

Also, I have discovered in my disproving of Walstad's paradox a new paradox. I explained that the set of all sets must contain the set of all sets which are not contained in the set of all sets for the set is an empty set, and all empty sets are contained by the set of all sets. Anyway, this paradox is just as absurd as your paradox, because we are using logic to explain concepts like nothing and everything, which are not real. And the fact that we have come to talk so wrongly within logic, is due to the assumption that all sets contain themselves, for they are themselves. A long time ago I told you that not all sets contain themselves, for example 'the set of all dogs' is not a dog itself, therefore it doesn't contain itself. Even though it is itself, that is, the set of all dogs is the set of all dogs, but doesn't contain the set of all dogs, for the set of all dogs contains only (and all) dogs, and the set of all dogs is not a dog.

Russell wrote to Frege in 1902 telling him not to publish his new work (Basic Laws of Arithmetic), for the Rule 5 of his axioms started with the idea that a set must either contain itself or not contain itself, but not none nor both. Frege's work of over a decade had been destroyed with a serendipitous discovery by Russell. Over a hundred years later, you have developed a 'solution' to Russell's paradox and discovered your own paradox out of this solution, and I've proven your solution isn't a solution, and your paradox isn't a paradox. Please, don't work for years on your project as Frege did, if he had known about Russell's paradox he wouldn't have lost all that time, now you know my developments, so don't waste your time.