Can you solve it, anons?

>>16704874 (OP)
>Self referencing sets can't be built
Wow, that was easy.

>>16704874 (OP)
>solve a paradox
Are you retarded?

>>16704893
Philosophers solve paradoxes all the time

>>16704895
This is math. If there’s a paradox (aka a contradiction) in your axiomatic system, then the system is inconsistent and you dump it.

>>16704889
>casually breaks all of modern mathematics

>>16704874 (OP)

The set is clearly empty then. What is the problem, do the mathematicians find no fancy way to write down such a basic statement? XD

>>16704907
>It is empty
Then it does not contain itself. Then it contains itself. Contradiction.

Sets can't contain themselves, OBVIOUSLY.
>But the notation we use—
is completely stupid. Sets can't contain themselves, only be themselves.
(Pro-tip: This fact also debunks some of Goedel's nonsense, too.)

>>16705022
Based on what principle?

>>16704900
>all of modern math isnt already broken
good try einstein

>>16704874 (OP)
>infinite sets
stopped reading there

>>16704980

If you see it mathematically, yes. But it is simply contradictory, nothing would satisfy the criteria of the set except, well ... nothing.

>>16705031
It's not broken.

>>16704874 (OP)

Mathematicians deal with ideas and artifacts that do not exist or are contradictory to the 'real' world

>>16705051
im afraid it is libtard

>>16705058
which is why its filled with contradictions.

>>16704889
>equations can't be solved ever
Retard.

>>16705097
cool strawman libtard

>requirement
>this set does not belong to itself
>there is more after this required condition
>this is somehow a paradox

>>16704899
No, otherwise they would have to rid math of 0 since it has to be its own opposite number, a self-contradiction, yet there is still nothing more logical as an arithmetic base than -0=0.

>>16705022
So then what exactly does a set that is itself contain if it can not possibly contain that which is itself?

>>16705058
So is this the mathematical explanation of spooky action at a distance since even atoms that are really separated completely still conceivably intersect at some i?

>>16706347
No, explanation of that is way simpler and lame. The idea is spin is conserved hence if particle A in one corner of the universe has spin 1/2 then particle B in the opposite extreme (both where close to each other at first) has to have spin -1/2. If it didn't have it then spin conservation law is rekt. You can do that with all variables you could think of and know what happens on the other corner of the universe at instant speed.

It's closer to solving x on a first degree equation than it is to a spooky stuff.

>>16706375
>If it didn't have it then spin conservation law is rekt
That could be tranferred via angular moment to particles it comes into contact with, the spin doesn't have to magically instantly affect another particle on the other side of the universe for the spin to be conserve, with the continuity it shows that actually the two particles are still in contact, so its fine for the spin to transfer to the distant particle instead of the ones in obvious real direct contact.

>>16704874 (OP)
The solution to the paradox is to observe that Russel first must assume the set S exists. This is like the axiom that the universe of discourse D is nonempty, i.e. in ZF/CA that some set exists, or that the empty set exists in particular.
Since assuming S exists leads to a contradiction, S does not exist. Therefore there is no paradox: the paradox doesn't exist.

>>16706344
people on this board genuinely belong in a human zoo

>>16706417
I accept your concession, if you want to be in a human zoo, go check yourself into a human zoo or at least start a vlog, so everyone can marvel at your lack of argument.

>>16704874 (OP)
No, it's not something to be solved. It's proof that set theory is just nonsense.

>>16704874 (OP)
it has been solved over a century ago.

>>16706437
If your 'solution' consists of just positing arbitrary axioms, that's no solution at all.

>>16706437
>>16706438
I solved it here >>16706387

>>16706438
>fixing naive theory that leads to contradiction that in consequence destroys the entire theory (principle of explosion) is not a solution
also, you arbitrarily assumed that object like this can exist therefore you introduced contradiction in your naive theory, making it as useless as your posts

Russell Paradox is a falsehood on the basis that the set of all sets is no longer the set of all sets if it has any additional context conditionals. Therefore russell's example set has no barring on the set of all sets, and is being logically conflated by fools. It is no more than a weak gotcha for those with more limited expressions in logic. It is an absolute certainty that the set of all sets would indeed be self containing as any possible missing information would have to be included within it for it meet totality standards. The set of all sets is the definition of completeness, it is ontologically impossible for something to be completely incomplete, they are oxymoronic and I don't care what what idiots who get caught up into systemized patterns of thinking try to soothe themselves by trying to represent Russell's claim.

Not all statements available in all grammar and vocabulary will be decidable within that grammar and vocabulary.

>>16706476
Russel's paradox is not an undecidable statment, it is a contradiction.

>>16706476
Your raving has nothing to do with Russell's paradox which is not about the non-existent set of all sets

>>16706487
>>16706486
>>16706476
>>16706455
why are you ignoring me >>16706387

>>16706494
you just rephrased in a weird way what ZFC and others did.

>>16706496
damn im good

>>16704874 (OP)
The solution is defining sets to contain themselves always (and the empty set); this makes the definition of S contradictory.

>>16705022
Yes. We say that:
∀A∃B∀x(x∈Bx∈A∧ϕ(x))
>Pro-tip: This fact also debunks some of Goedel's nonsense
No.

>>16704874 (OP)
Russell already solved it himself, with types. A set of sets has type Set[Set[T]]. BOOM problem solved.

>>16704874 (OP)
S is not a set. This is literally a proof by contradiction

>>16708533
Or set theory is fallacious. Literally a proof by contradiction.

>>16704874 (OP)
yeah use a different foundation

>>16708536
>Or set theory is fallacious
Big gamble. I’m sure you’re smarter than every logician to ever live. >>>/reddit/

>>16708544
>trust the looogicians
You're the one that belongs on >>>/r/eddit buddy

>>16708548
Stay mad all you want lil broe. I’m right. You’re wrong. Simple as. Don’t believe me you can look it the fuck up on G00gle

Axiom Schema of Specification, it ensures that you can only use set builder notation like that when taking subsets of sets that are already well-defined. No "set of all sets" or anything like that is allowed.

Once you construct numbers and arithmetic and all that from the ground up with the empty set and axioms, you can then use set builder notation to cut up those sets you have already constructed.

Thank the autists for doing the hard work to make sure that math is calculably valid even when we are free to work in abstract ways.

Just let set membership be non Boolean

>>16704874 (OP)
Is there a calculus of paradoxes? Like how proof theory treats proofs as mathematical objects?
Use the paradox as a measuring device to measure/encode/construct higher order paradoxes.

>>16705022
>Sets can't contain themselves
uhhh... source?

>>16706531
Gödel is all about modal logic, not logic.

>>16704874 (OP)
The problem is that your symbolic language has no real referent. All paradoxes have no real ontological status. The only consistent logical system that can be made is one which refers to actual reality and not simply logical syntax. Read Aristotle.

>>16704874 (OP)
>An object that exists must, by definition, exist relative to all other objects that exist
>Given the fact that matter and energy can neither be created nor destroyed, each individual quantum of mass-energy that exists is its own cause and its own effect
>Propositions 1 and 2 are simultaneously true
>Therefore, the axiom of dependent origination and Democritus' postulate prove that a set that is not a member of itself is necessarily "not real"
Ez pz. Paradoxes like this already got solved thousands of years ago, and we're currently in the process of rediscovering their solutions.

>>16711128
The definition of sets. A lot of math is just shit being arbitrarily defined as whatever's most useful in calculations while still being self-consistent.

Those are ultimately the only things that matter until and unless someone comes up with a working and useful system of paraconsistent math.

You want to redefine sets, feel free. Just remember you have to adjust your axiomatic system to avoid provable contradictions.

>>16711128
This is not even true.

You can consider the anti-foundation axiom (i.e. corecursive sets) instead of the foundation one, and you'll get a perfectly consistent theory with a lot of sets which contain themselves. You can even carve out the inductively defined sets out of the coinductive ones by relativized quantifications and you'll get exactly ZF.

The problem with Russel's paradox is rather a size issue, just like OP's dick.

>>16704900
If modern math can be broken by such a intuitively simple truth ("self-referencing sets can't be built") that's more on the realm of semantic/language than real math, then modern math is way more convoluted than it should be for its own sake, and therefore all of you retards should all lose your jobs and academic positions and go back to square 1.

>>16704874 (OP)
Don't Gödel's Incompleteness Theroems explain that shit already? Just consider it an incomplete system impossible to encompass everything and move along. Call it an exception for the rule, and that's it.

Jesus, you mathematicians are way too prone to put yourselves into corners because of meaningless shit that could be easily bypassed by simple ontological conventions.

>>16704874 (OP)
>Consider a literally impossible construction
>Herr durr contradiction
No fucking shit? How the fuck is this revolutionary