Any of you morons wanna explain why you believe on faith that empty sets are instnatiable objects inside any symbolic manifold?

Literally nothing in the universe behaves that way.

As a hypothesis, it's as empirically justified as the tooth fairy.

Think you're smart? Prove me wrong.

Oh, wait...

You can't.

>>16705910 (OP)
The existence of the empty set is implied by the axioms of ZF. You are free to use any other axiomatic system, nobody cares.

>>16705910 (OP)
empty bag, you baboon, {}

>>16705910 (OP) >>16705922
also the set of bitches you get

>>16705910 (OP)
You're obviously an obese basement dweller so just think of the empty bag of party size doritos on the floor next to your bed

>Literally nothing in the universe behaves that way.
>imagine thinking the universe has to observe mathematical conventions

>>16705922
Uhuh...

So there's nothing else in the universe except the emptiness inside the bag?

Go get your PhD then come back so I can crush your soul. It's not as fun unless you wasted your life on nonsense first.

>>16705921
So, you just... admit that it's complete nonsense?

That was easy.

>>16705936
I know that there is no "canonical" axiomatic system in math. As I said, if you think it's nonsense, then use some other axiomatic system. Be my guest. But picrel showed that no axiomatic system is better than some other. You can't even show that it's self-consistent.

>Why yes, I would like {} apples please

>>16705910 (OP)
Time for your meds.

>>16705938
Yeah, except for the uninstantiable empty-set causing an ontological paradox.

The uninstantiability of empty-sets (monadic objects) inside any symholic manifold produces a recursive chain of consequences (morphisms) which interact with one another (time) as a means of negating a collapse into a monadic mode of relation.

Think about it...

To define any object in reality you need:

1. Where the object is
2. Where it isnt (the manifold)
3. Where it is in relation to other objects inside the manifold

Consider the manifold itself an object is moronic.

>>16705961
If the manifold isn't an object, then there are things which can be explained without objects. So why not put everything in terms of manifolds?

Am I reading this correctly?
Things that don't exist aren't real? This is something that has to be said?

>>16705967
Because you need fluctuations in modes of relation between constituents elements of objects.

There's no difference between an instantiable mathematical object and the manifold in which it inheres.

Manifolds that exist as distinct "substances" from the objects that comprise them is a superstitious belief brought over from religion.

>>16705910 (OP)
What about your skull?

>>16705910 (OP)
Let's say you have a basket, and there's nothing in it. That's what the empty set is like.

Your list of arguments is an empty set

>>16705961
Meds, now. You’re spouting jargon you don’t know anything about.

>>16705978
*pile

>>16705985
Looks like someone hasn't studied C.S. Peirce and thinks they're a psychologist because they listened to 1500 hours of Jordan Peterson podcasts.

What's that little Timmy? You don't know how to transpose objects across worldsheets with incommensurate axioms?

>>16705999
No, a pile implies an ordering (because things in the pile can stack) and the empty set is an object.

>>16706006
>no, a pile implies ordering
...how fucking brain dead are you? The set is a formality, not a fucking basket. AKA a fucking pile. An empty pile is a place you would put a pile, if you had one.

>>16706004
>manifold
a topological construction, nothing to do with set theory
>morphisms
category theoretic term meant to formalize the notion of "structure-preserving maps" between mathematical structures. Nothing to do with set theory in particular.
>produces a recursive chain of consequences (morphisms)
If one even tries to interpret your nonsense, you're saying that the initial object in a category produces some recursion. This contradicts the universal property of the initial object. Also, the initial object in Set is strict.
>Consider the manifold itself an object is moronic.
I assume by "manifold" you mean "category". The initial set is an object in a category, not the category itself.

I don't even know why I'm typing this, I'm just bored and want to entertain myself with good old /sci/ schizophrenia.

>>16706009
>it is not a fucking basket
Obviously, it's a set, I'm using an analogy. It's not like a pile because the objects in a set are not stacked.

>>16706012
You'll do.

https://zenodo.org/records/15653461

Have fun.

>>16706014
>he thinks a pile is stacked
You are only proving my point. Please see yourself to the nearest landfill to evaluate "stacking."

>>16706020
>dude shady links lmao

>>16706022
Maybe you could do something like define your terms.

>>16706023
Itll be in Entropy shortly, don't worry.

I gotta have fun while I still can.

>>16706027
>calling a stack a pile
>we're disputing the usage of "basket"
It's almost like you're arguing in bad faith and recognize the merit of an unbounded collection of disparate sourcing that one is evaluating together by virtue of them being in the same place.
Dune? Do we have to go with dune? The point is the "construction" was not constructed. There is no weaver. The basket isn't real.

>>16706034
What you're describing ("pile" or whatever you call it) isn't like the empty set. The empty set is a mathematical object that contains things (a set) with nothing in it. It IS like an empty basket.

>>16706037
>I am unable to conceptualize nothing
The fuck is wrong with you?

>>16706038
I don't know what you're talking about. My point is that the empty set is not nothing.

You idiots do realize there's a section on monadicity in my paper, right?

It's like, a 3 minute read.

Machine-checkable.

>>16706042
Correct.

It contains an uninstantiable paradox that has recursive consequences.

Because these consequences formulate the sum of the axioms, you end up with a system that wherein the rules are self-validating.

I.e., my calculus.

>>16706051
>It contains an uninstantiable paradox that has recursive consequences.
Source?

>>16706055
>>16706020
I'm a scholar of C.S. Peirce.

I finished his ontological calculus by proving that monadic instantiation is impossible, dyadic instantiation is insufficient (via Peirce) and that triadic morphic closure is irreducible (Peirce).

It's the grand unified theory of everything.

Machine checkable in about 10 seconds.

Ignore the part about prime-gated Poisson emergence, my math was way off.

The next version (the one being published) fixes that (none of the other axioms depend on it. It was just an aside).

The fact I'm not going to be able to shitpost anymore is perhaps the biggest downside to becoming the greatest mathematician of all time.

>>16706060
>I'm a scholar of C.S. Peirce.
Nice try. Who is/was your advisor?

>
I finished his ontological calculus by proving that monadic instantiation is impossible, dyadic instantiation is insufficient (via Peirce) and that triadic morphic closure is irreducible (Peirce).
That's nice, where's the paper?

>It's the grand unified theory of everything.
Sure it is.

>>16706067
>Who was your advisor.
Nobody worth studying under, that's for sure.

>Any of you morons wanna explain why you believe on faith that empty sets are instnatiable objects inside any symbolic manifold?
Hi, moron here. First of all, you misspelled instantiable. Secondly, one does not believe on faith. Faith is belief without evidence. The phrase "believe on belief without evidence (faith)" is nonsensical. Despite this I believe I understand what you meant, right up to the phrase "symbolic manifold". There is something called a symplectic manifold, and you may do numerical calculations on something in a topological space such as a manifold, as opposed to with mathematical expressions, i.e. algebraically, but it rather seems to me you are mixing up terms from computer science and algebra here.

>Literally nothing in the universe behaves that way.
Plenty of things in the universe can behave as if they are empty. On the largest scale we have the cosmic voids, containing barely any or indeed no galaxies, and on the smallest scale the space between an atom's nucleus and its electrons.

Now, before you object, even without mathematical training you should be able to intuit that the empty set captures the idea of emptiness, i.e. the state of containing nothing. Nothing is a word, a semantic construct not without context. If in casual conversation, I say a room is empty, I most certainly do not mean it is somehow in true vacuum, and I have exhaustively checked that there are no particles there, no radio waves going through it, and so on, but rather that there is no furniture there. But to make such an idea of nothing precise, we turn to systems of logic, such as mathematics, with their rigid definitons. An empty set indeed is a set that contains nothing. And not nothing as in a thing labeled nothing, but no things at all: zero members.
>As a hypothesis, it's as empirically justified as the tooth fairy.
Irrelevant, mathematical definitions do not require empirical justification. This is a crucial aspect of math, separating it from the sciences.

>>16706083
And I suppose you're going to explain to me how a universe where big exists but not small can instantiate?

How can you define nothingness unless you've also defined somethingness? Ya can't.

Peirced proved that. He just didnt realize it applied to ontological structures.

>>16706094
>And I suppose you're going to explain to me how a universe where big exists but not small can instantiate?
You suppose in vain.
>How can you define nothingness unless you've also defined somethingness?
I actually explicitly mentioned that nothing in context of the empty set is the set with the total absence of things and said things are indeed defined in the same context (as members which are not there). Now to be precise, it is not neccessary to define what those are beyond that they have the property of being able to be contained within the set. For example I can say a room is empty of furniture without specifying that I do not consider ceiling mounted lights as furniture.

>>16706104
Exactly.

You can say that.

You.

The third element in the dyad.

Yourself comprised of a reflexive-dyad pair (you/not you).

There is no instantiation without a mediating third. Otherwise, well... imagine a universe where only two things existed. How could they interact? They couldn't. They'd form a monadic structure.

A crystal.

Kinda sucks being the one punch man of metaphysics.

They all just run away.

>>16705921
>>16705910 (OP)
You must assume at least one set exists, otherwise you possibly speak of no-things.
You may assume this set is the empty set, or assume it is any other set and then immediately construct the empty set from it.
Your choice.

>>16706107
>There is no instantiation without a mediating third.
You are making giant leaps here without explaining anything. What does any of this have to do with the empty set?

By the way there is no "me" and "not me" precise definiton. We already know our bodies are ships of theseus as all atoms of our bodies are replaced, and these aroms are not even mine merely borrowed. I am merely part of the world in a transient and abstract sense.
>imagine a universe where only two things existed. How could they interact?
What do you mean here by universe with two things it? Why is interaction necessary? And what is this nonsense about a crystal?

Honestly you sound unhinged. I have been trying to argue here in good faith, but you are starting to read like an /x/ schizo.

>>16705972
>Manifolds that exist as distinct "substances" from the objects that comprise them is a superstitious belief brought over from religion.

Seethecope
(a+bi)/(c+di) = (b-ai)/(d-ci)

>>16706133
Buddy, you're arguing against Charles Peirce here.

You know.

The guy who invented statistics as a goof.

The guy who wrote a paper describing the possibility of employing electronic switches as logic gates... in the 1850s.

Maybe do a little research into semiotics before tangling with the big boys.

>>16706141
I dont follow.

>>16706163
And I'm not going to explain it ;)

>>16706163
>the father of pragmatism needs a mediating third
how pragmatic

>>16706178
Actually, you insignificant worm of a mind, he spent his last 30 years in poverty attempting to finish his magnum opus, of which I am now responsible.

He built a custom designed drawing desk for his existential graphs that could accommodate working while laying down because the cancer that killed him was so severe towards his last decade that he couldn't sit up straight.

He worked through the constant haze of unbearable pain and morphine haze for the betterment of mankind.

You're a joke.

His work was nothing less than the crown jewel of science.

There's no joke.

You are the joke.

You'll speak when spoke to.

>>16706177
Yeah but I'm too tired to think.

The funniest thing is that he's constantly invoking an empty set but calling it by a different name. There can be no agreement when one person talks about epistemology and the others about math.

It's instantiated without le spooky third crystal eye because here it is. It exists in this universe. We are talking about it right now, therefore it is. The universe with the empty set doesnt give a shit about le peirce's rewuirements for it to exist, it exists anywaym Also you are a gay avatarfagging loser kys.

>>16705936
There might be other things to, but there is also emptiness, you can't put something somewhere if that space is already fully occupied by other things besides emptiness.

>>16705961
Yes you have discovered the trilemma, but either way you need an infinite recursive chain, it just makes more sense for it to be infinite emptiness than infinite matter underlying every single atom of matter.

>>16705970
There definitely really are things that don't exist, though, you can open any fantasy book and find lots of things that don't exist, you can even easily make up things about yourself that don't exist like your fifth ear.

>>16705978
Baskets necessarily have things in them, like the material of the basket, though
If you put a basket in a basket is it still empty?
What about if you fill an empty set with an empty set, is it still an empty set?

>>16706022
A pile is a collection of objects that are piled on each other, though. How exactly can you have a pile without some kind of order? Also, a set is necessarily ordered, it just might not be well ordered in any sort of logical way and could be ordered arbitrarily.

>>16705921
>The existence of the empty set is implied by the axioms of ZF.
It's not implied, it's a literal axiom, retard.

>>16706352
No, you dont need it. All you need is that the universe of discourse is nonempty

>>16705941
u get no cake if u not eat fruit & veg

>>16706060
>monadic instantiation is impossible, dyadic instantiation is insufficient (via Peirce) and that triadic morphic closure is irreducible (Peirce).
wadabout nulladic instantiation, you quadruple chuckle-nigger?

>>16705910 (OP)
Don't you mean "non-sets"

>>16705910 (OP)
anything beyond calculus is out of my scope therefore non-existent. I hate math because there is no "calculation" there is no "optimization" there are diffeomorphism shit shit shit bla bla bla without any application! Physics is shit either, to filter out non-physicsts they interchange between notations to a point of incomprehension. Bra-ket notation is the biggest piece of dogshit in this entire galaxy.

Think of it this way... the wavefunction is always collapsed everywhere simultaneously.

>>16706323
That's why all universes curve into themselves.

>>16706324
No, I've solved the paradox.

Do you know what an empty set contains? The impossibility of its own instantiation in isolation.

That's what Peirce meant by the irreducibility of triadic modes of relation. Get into string theory. It should clear it up.

I'm a string theorist more than a mathematician. I hate math. It's for dorks.

Geometry is for absolute gigachads like me.

>>16706429
What about it?

It's a nonsense idea.

>>16706264
Of course I am.

My model (full proofs and prime-gating statistics coming in next version) demonstrates that the empty set contains the impossibility of its own instantiation sans any other mode of relation. How can you define nothingness without a relation to something?

Think of it this way... let's go newtonian, because that's where most human monkey meat robots are at intellectually (no offense).

How the hell can you calculate the velocity of an object in a perfect vacuum? Let's imagine that literally nothing in the universe existed except a bowling ball.

Is it moving? How do you know? That's the problem of moandic instantiation. This is why you need a mediating third. All measurements are ratios contrasted against other ratios that are reflexively dyad and triadically mediated via observation.

You, the observer, must interact with both objects in order to draw meaningful conclusions about their relative/reflexive modes of relation.

>>16706331
I can tell you what this thread is a pile of.

>>16706352
It isn’t. You prove it from the other axioms. It’s basic proof too.

You know what, I'm not doing the translation.

You idiots can extract the formalisations yourselves and machine-check it.

Github can suck my dick.

>>16706611
>It's a nonsense idea.
lol, lmao even & odd

>>16706611
>How can you define nothingness without a relation to something?
>he doesn't know about the empty relation
math ain't for dorks, it merely filters retards

I sorta get where you're coming from, OP. I've gotta brush up on my logic, but what I'm seeing here has something to do with actual existence (not simply logical existence like the empty set) being necessarily contingent on a thinking subject, is that right?

>>16705961
This reads like ChatGPT.

>>16706706
You got it, man.

See, these dipshits >>16706678 conflate reality with the fantasies inside their fucking heads.

They differentiate between their own subjective frame of reference and reality because they're afraid of ths fact they're metaphysically entangled with the "objects" they dissociate from their own cognitive processes via sinulations drawn on symbolic manifolds, i.e. math.

There's no differentiation between an instantiable object and the subsequent consequences of the initial conditions of a system. They're basically playing video games inside their minds and trying to convince you it's reality.

It isnt.

Reality is reality.

You're either describing it or you're not. My calculus can produce zeta-zeroes without arithmetic.

I'm right. They're wrong.

End of story.

You're basically fucking monkeys.

You know why I'm posting Rick? Because you're all so stupid that I can hypnotize you all into paying closer attention to my thread by aligning my syntax with icons that produce involuntary associations between genius and insanity.

This triggers projective identification with Rick, which, because you're mostly all unconsciously identified with him, produces a cognitive dissonance that elicits frustration,which as Kernberg pointed out is automatically converted into aggression.

Ergo, engagement.

Fucking morons.

>>16706715
Very nice. I had a feeling that had something to do with it. I haven't really gone through Pierce yet, but what you've come up with is somewhat similar to an intuition I've gotten from studying classical Aristotelian logic for the first time (which makes the difference between actual vs. logical existence explicit, something I've never seen in modern logic), so this is very motivating.

>>16705910 (OP)
empty sets make perfect sense in computer science. its just these libtard mathematicians that think every 0 happens to be exactly the same.

>>16706729
Hey, thanks man.

I'm just having some fun before it all kicks off.

It was Peirce, man. I really did nothing special. I just applied his framework and realized that empty sets contain a paradox.

Well, and calculated the highest meaningful prime.

I'll give myself that one.

>>16706163
>The guy who invented statistics as a goof
retard

Net slipped.

Thanks, fellas.

Later.

Reverse psychology never doesn't not work.

So you're telling me modern math is built on faith in a magical object that contains nothing, yet somehow exists? Sounds more like theology than science.

>>16705910 (OP)
>why you believe on faith that empty sets are instantiable objects inside any symbolic manifold?
Because they literally are, you midwit.

The empty set is axiomatically constructed in ZFC. It’s not "faith" — it's formal necessity.
We define:
O:={x∣x =/= x}

This isn’t some mystical handwave — it’s a deductively valid object that exists in every single model of ZF. Your so-called “symbolic manifold” doesn’t even count as one unless O is in it.

You’re confusing material instantiation with logical instantiation.
An “object” in a formal system isn’t some physical Lego brick — it’s whatever the axioms guarantee the existence of. If you can’t grasp that, maybe symbolic logic isn’t your domain.

Also, no serious logician is "taking it on faith" that O exists.
It’s built by definition, appears in every universe of discourse for set theory, and is used to define all other numbers. ℕ starts from O. Your keyboard wouldn't exist without it.

tl;dr:
Read a book. Start with Enderton or Jech. You’re not redpilled — you’re just stuck in pre-formal-tier metaphysics.

>>16706817
It wouldn't be an axiom if it was a necessity.

>>16706817
Huh.

Here's another axiom for ya.

You're gay.

Sorry, buddy. Rules are rules.

>>16706830
He hasn't learned about precision yet.

In fairness virtually no one but me has.

>>16706718
no it doesn't if anything the relation it makes is you being a ricky retardo, sechuan sauce, pickle rick, drunkard rube

>>16706928
Hey, bud, look, see that preprint?

That's a rough draft.

My idea of rough.

>>16706718
>i came here to roleplay and avatarpost
>i know that's retarded
>therefore i am verysmart and have psychically dominated anon
lol
lmao even

>>16706951
Hey, buddy.

You're bumping the thead, aren't ya?

Fuck me dead there are so many showstopping logical gaps.
I wish they'd just take my fucking word for it. Vector quantificatuion is for pussies.

>>16705961
>Yeah, except for the uninstantiable empty-set causing an ontological paradox.
>>16706817
>it’s a deductively valid object that exists in every single model of ZF.
>>16706948
>Hey, bud, look, see that preprint?
>>16706020
>https://zenodo.org/records/15653461
>cross-framework embeddings into ... ZFC
>To verify that ROC retains its logical strength across standard foundations, we exhibit faithful and conservative translations into ... ZFC
so your nonsense is interpretable in a theory that your nonsense says is inconsistent by definition... how exactly is that suppose to be a plus towards your nonsense's validity?, God you are going to be chewed out by actual mathematicians...

>>16707325
Oh dude that's just to cement certain ideas.

The actual model is in an entirely different domain.

And holy shit, you were smart enough to see that? Phd?

>>16707325
I mean, obviously I only hinted at or implied embedding.

It's all sketches and, like, "just trust me bro" style theorems.

But it's very impressive that you saw the gaps. Most mathematicians would just dismiss the whole thing outright.

>>16707339
>Phd
not even close, just a hobbyist
>Most mathematicians would just dismiss the whole thing outright
i can see that being the case, never the less and in spite of how abrasive and if im to be honest, repellent, you have come off as, i do wish you the best in your endeavors, take care

>>16705910 (OP)
I have an array with no repeating values but I haven't put any numbers in it yet, how do I represent this? Obviously, it needs to exist in memory before I can put anything in it.

>>16706814
So what, you have never held nothing because there are always over 9000 dicks in each of your hands and holes?

>>16707633
pointers to memory locations

the empty set is implied by the existence of elements and their ability to enter a set.
Why can't midwits compute this simple induction? Sad!