DESTROYING SET THOERY BIT BY BIT

[Anonymous No.9784077]

the madman is doing it
https://www.youtube.com/watch?v=U75S_ZvnWNk

[Anonymous No.9784078]

>>9784077

[Anonymous No.9784081]

>>9784078
[YouTube] Modern "Set Theory" - is it a religious belief system? | Set Theory Math Foundations | NJ Wildberger (embed)

[Anonymous No.9784082]

>>9784081

[Anonymous No.9784084]

>>9784082

[Anonymous No.9785380]

I'll never understand this dude's problem with set theory. He thinks that real numbers don't exist or are not well-defined?

[Anonymous No.9785398]

>>9785380
Maybe he just wants to test it, like any other theory

[Anonymous No.9785425]

>>9785380
He doesn't like the reals because they rely too much on the concept of infinity, which he really hates.

[Anonymous No.9785439]

>mfw someone needs consistency to do mathematics

[Anonymous No.9785440]

>>9784077
Set theory will always rule no matter how hard you category theory freaks bitch and moan.

[Anonymous No.9785471]

>axioms are religious beliefs
he is kinf of right

[Anonymous No.9785483]

>>9785440
set theory fairly young in the grand scheme of things, don't be surprised if it happens to fall out of favor

[Anonymous No.9785491]

>>9785471
Autism

[Anonymous No.9785502]

>>9785491
thi s is what i say to everything i disagree with and it makes me automatically correct

[Anonymous No.9785550]

>>9784077
there's actually nothing inherently wrong with set theory itself. it does prove all of the things it purports to. his problem with it is mainly one of interpretation, IE the meta-mathematical concept of infinity, in particular infinite processes, such as in the axiom of choice. however, we don't have to interpret the axiom of choice as a process. we can just say it's a statement in first-order logic and work from there. same thing with axiom of infinity.

IMO the only reasonable criticism of set theory (ZFC in particular) is one of aesthetics, in that its axioms are kind of ugly

[Anonymous No.9785568]

>>9784077

[Anonymous No.9785571]

>>9784077
That was a great video, once again I am reminded of the genius of Wildberger. But that said, I have a different opinion. I was very captivated by his description of the problem with axiomatic mathematics: You simply assert what you want to be true. This is obviously in contrast to Wildberger's view that you should not propose axioms but definitions, and then use semi-intuitionistic (for the most part constructive and tangible) logic to produce results.

This is a very interesting point of the view. It is true that your theorems lose value if you prove them using things you have just asserted to be true. We have seen that with the axiom of choice. Proofs that use it are heavily dismissed and even called paradoxes, while proofs that manage to circumvent its use are praised as genius and desirable. But in my opinion what axiomatic mathematics actually does is push down the problem of "what should be true" one level down. By that I mean that we may do axiomatic mathematics here at the top with analysis and even set theory itself, but when it comes to what axioms we ought to accept, it is only intuitionistic logic we can rely on.

However, it is quite clear that Wildberger sees this is as only a crutch for mathematics and I appreciate his view because he is probably the smartest person alive today. I genuinely hope that he can push this new series and genuinely change my opinion. And if there is one thing I am willing to concede to him unconditionally is that the axioms we assert to be true were hugely convenient for the mathematicians at the time. So convenient in fact that we ought to listen to Wildberger and be sceptical.

[Anonymous No.9785609]

>>9784077
>mathematicians are different from logicians

uncle norm lost me there lads

[Anonymous No.9785623]

>>9785609
He is right in the sense that most of the mathematicians who use the given foundation do not even care about looking into that foundation. The number of mathematicians today that work on logic is minuscule and even they have mostly moved on to other things. Wildberger is basically the only person heavily crash testing the current foundation.

[Anonymous No.9785632]

>>9785623
so I've been following his videos for a while, I understand that he's a staunch Finiteist and that this can be productive for discrete structures like digital computers (there are analog computers btw), but he never really truly defends his stance on this metaphysical crisis in the foundations of mathematics with anything other than "well Pythagoras didn't believe in irrational numbers"

what would I need to read or watch to understand his take that there is a crisis in mathematics, why would I care about logicists "interfering" in mathematics as long as their structures remain useful in daily life, what is NJW's argument for a definition of mathematics that requires finitism and his hardon for pythagoras

[Anonymous No.9785652]

>>9784077
Taking set theory as an elective this fall (the most immediate pre-req was Linear Algebra, and before that, the intro to sets and proof-writing class). My train of thought is that it and its older brother Foundations of Math will make me learn mathematical logic or die trying (ntm bolster my proof writing skills). What to expect? How fucked am I?

[Anonymous No.9786472]

>>9785632
>there are analog computers
Are there any actually being used? As far as we know, the Turing machine encompasses all the computational processes that we can utilize.

I watched his video including the resolution of the Goldbach conjecture (mostly clickbait, but he gives an interesting perspective). He basically argues that for all the individual numbers that we can name once you go really big the chance of us finding a pair of primes that add up to it is impossible, even if we allow for the computational power of the whole universe. So, there are numbers that cannot be 'expressed as the sum of two primes'. He might interest you whatever you are doing in math and science.

[Anonymous No.9786579]

He quite clearly is not familiar at all with the foundations of mathematics, nor could he be moved to care one bit about it.

It will come back to haunt the academic institution that hired this fraudster. It would be like a hospital insisting on holding on to an MD who is convinced that voodoo is more efficient that modern medicine.

If he teaches, then it will come to hurt the poor students who are gullible enough to lend attention to his mumbo jumbo.

[Anonymous No.9786622]

>>9786579
>set theory is not a religion

[Anonymous No.9786693]

>>9786579
>sophistry instead of arguments
i wouldn't expect any better from a pure """"mathematician""""

[Anonymous No.9786715]

>>9786693
>thinks that direct observation is an example of a false argument

[Anonymous No.9786723]

>>9786715
>i've seen God with my own two eyes! he talked to me!

[Anonymous No.9786783]

>mfw when no "real" mathematician knows the solution to [eqn]\sqrt{2}+\sqrt{3}[/eqn]

[Anonymous No.9786788]

>>9785550
The axioms aren't what matter, since you can always reformulate them into some different-looking set of axioms. What matters is the structures they produce, and the cumulative hierarchy described by ZFC is very nice, aesthetically speaking.

[Anonymous No.9786824]

>>9785652
>being attracted to blonde whores
LOL

Here's a real woman for ya. Thank me later ;)

[Anonymous No.9786834]

>>9786824
>>>/lgbt/

[Anonymous No.9786844]

>>9785380
He's an ultrafinitist. He refuses to accept the existence of anything you can't explicitly construct (i.e. write down the entire object on a piece of paper).

[Anonymous No.9786862]

>>9785380
You are the problem he is trying to eliminate.
Borderline cult type behavior over such unnatural math concepts.

[Anonymous No.9786926]

>the set of all sets not members of themselves
>mathematicians will defend this logic by ignoring it

[Anonymous No.9786929]

>>9785439
t. compsci trash

[Anonymous No.9787131]

>>9786926
>implying it's meaningful to talk about sets defined in non-stratifiable ways
t. New Foundations

[Anonymous No.9787143]

>>9784077

Dam I remember seeing wildberger videos here when I started my math degree, I can't believe he's still going with this, what a beast.

[Anonymous No.9787181]

>>9786862
I want my Hahn Banach Theorem and vector spaces to for sure have a basis. Wildburger go ahead and not assume the axiom of choice and infinity, that's fine. I will continue to do so.

[Anonymous No.9787217]

>>9785380
Many people take issue with the reals. For one, you have uncountably many reals but all statements you can make (or e.g. all books that can be written) can be enumerates.
Informally, choose a language and consider the set D of all real numbers that have a description. E.g. 2 or sqrt(2) (as some infinite sum, say) or pi (as some infinite sum, say). For each of those reals, you can specify them. But since the possible descriptions of things is countable, the set X given by the real numbers that are not in D, i.e. X=R\D, is a "set" of which you can, by constructions, no speak of think about any of "it's members" individually. You can formally write "Let x be an element of X", but by construction, there's no particular x you can write down no matter what.

And further, what's similarly unnice, is that the set of reals contains numbers that are describable, but which are not computable. That is, you can write down a definition and make statements about it (e.g. that the thus described number exists and is between 0 and 1), but provably you can also never even compute a single digit of that number.

https://en.wikipedia.org/wiki/Definable_real_number
https://en.wikipedia.org/wiki/Computable_number
https://en.wikipedia.org/wiki/Specker_sequence

That being said, I'm not against axiomatic set theories or the real in any form. I'm too much of a formalist to dismiss it.
But I understand anyone who, like W., wants to put "set theory" in quotes and point out that it's not about sets.

>>9787181
All good vector spaces have a basis anyway. There's no good in requiring the existence of a set of basic vectors for a space (making the existence provable by the axiom of choice) when you can also at the same time prove from the theory, that if a set of basis vectors exist, you can never state a single one of them. Those non-constructive axioms do just that - they empower you to prove more and more existence statements, but you can't do anything with that existence.

[Anonymous No.9787248]

>>9784084
What are the contradictions he is talking about?

[Anonymous No.9787265]

>>9785425
sounds like a retarded nominalist to me.

[Anonymous No.9787284]

What a small, hateful man.

[Anonymous No.9787299]

>>9787217
who gives a shit about computable man i'm not a computer numbers exist whether you see them or not

[Anonymous No.9787319]

>>9785471
Not even close to right, axioms are true because we say they're true. We can just define them because it's all abstract.

Religious beliefs in the other hand make claims about the real world

[Anonymous No.9787323]

NW is wrong. The foundations of set theory was not outsourced to philosophers. Everyone working in foundations at the turn of the last century were mathematicians.

[Anonymous No.9787327]

>>9787217
>Many people take issue with the reals
Correction: Many cranks take issue with the reals
take your pills

[Anonymous No.9787338]

>>9786844
I agree with him which is why I always use 3 for pi.

[Anonymous No.9787345]

>>9786579

How interesting that you use the phrases "voodoo" and "mumbo jumbo"

Now go back to your square root of 2, your infinities and your complex numbers.

[Anonymous No.9787347]

>>9787345
(You)

[Anonymous No.9787355]

>>9787347

Whatever makes you happy, Sam. Don't stop thinking that way, We need people like you to mow our lawns and clean our toilets.

[Anonymous No.9787358]

>>9787355
t. brainlet who can't comprehend even the simplest logical concepts

[Anonymous No.9787361]

>>9787358

t. Fuckwit stuck in the stone age.

[Anonymous No.9787362]

>>9787248
perhaps russell paradox

[Anonymous No.9787367]

>>9787338
i can assure you you don't use any real number for pi (or for anything at all really)

[Anonymous No.9787420]

>>9787361
>wants us to go back to pre-greek mathematics
>says I'm the one stuck in the stone age
t. retard

[Anonymous No.9787451]

>>9787217
Your description of definability is unfortunately naive. By Tarski's theorem, first-order definability is not first-order definable. As such, it is perfectly possible to have models of ZFC (complete with sets interpreted as real numbers) where every set is definable.
As far as non-computable numbers existing: who cares? Are you telling me something like Chaitin's constant isn't well-defined?

[Anonymous No.9787525]

>>9786929
reminder both math and logic are simply subsets of computer science

[Anonymous No.9787532]

>>9787525
>imagine being this delusional
I genuinely feel bad for you. I hope that you can get better.

[Anonymous No.9787620]

>>9787532
not an argument

[Anonymous No.9787622]

>>9787620
not that anon but absurd claims need no counter argument

[Anonymous No.9787625]

>>9787361

[Anonymous No.9787626]

>>9784077
>anal

[Anonymous No.9787628]

>>9787620
Here's an argument: By both definition and historical development, the theoretical aspect of computer science is a subset of math. Beyond that there are the engineering aspects of computer science, and as we all know engineering is a tumour on the face of mathematics so you are still contained there.

But still, I really cannot comprehend what would motivate someone to say something that is so wrong as "math is a subset of computer science". I am getting some weird vibes from you. Like, raped by your uncle tier weird vibes. I hope I'm wrong but you are certainly deranged.

[Anonymous No.9787630]

>>9787626
>not doing real anal

[Anonymous No.9787634]

>>9785471

[Anonymous No.9787640]

>>9787628
>ad hom
sorry, but you conceded the argument (which is still not an argument, by the way) right there
therefore, math is a subset of computer science, as determined by rational debate

[Anonymous No.9787642]

>>9787630
>gf won't do nonstandard anal

[Anonymous No.9787652]

>>9787640
This settles it. You are too far gone. Anyways, congrats on "proving" that math is a subset of computer science in a Mongolian board. In the meantime, I and everyone else in academia will keep referring to the standard definitions used by leading researchers and textbooks. If in your schizophrenic delusions you think you have actually achieved to prove anything then good for you.

[Anonymous No.9787696]

>>9787420

t.ultra double retard.

A retard so retarded they cant even begin to understand just how retarded they are.

Best to keep them on a chain and feed them table scraps.

[Anonymous No.9787707]

>>9787625

The difference being water actually exists on the left. Going right ensures death by dehydration.

[Anonymous No.9787771]

He keeps repeating that some things are "problematic" without explaining what the supposed problems are.
Clearly he misunderstands the roles of different theories. It does not matter how you switch around the boxes: Set Theory will continue to contain all the structures that exist in Arithmetic, Analysis, Algebra, etc., and (Peano) Arithmetic still does not contain the structures that exist in Analysis, Algebra, etc.
He is probably thinking of the order in which things might be taught, and then the diagram on the right seems reasonably close to the way in which it happens today.

[Anonymous No.9787773]

>>9787707
my fucking sides

[Anonymous No.9787785]

>>9787696
Did you just describe humanity? We still haven't mapped out the human brain, nor do we understand the mechanical configurations for memories. Just how fucking retarded are we?

[Anonymous No.9787790]

>>9787217
Yea, but computer science is a subcategory of math (that which is computable).
I don't do that, I care about the overall stuff which is why I study both pure math and computer science.

[Anonymous No.9787793]

>>9787525
computer science is a subcategory of math which is a subcategory of logic.

[Anonymous No.9787801]

>>9787652
Dude I argued with a 4chan pass user who was claiming the same thing for literally days.
I don't know where these retards are coming form. Check this shit out senpai:
>>9776095

[Anonymous No.9788007]

>>9787707

[Anonymous No.9788071]

>>9787771
>without explaining what the supposed problems are.
he explains everything. watch the videos or keep quiet

[Anonymous No.9788262]

>>9787625
More /sci/ related.

[Anonymous No.9788325]

>>9787785

[Anonymous No.9788351]

>>9784077
Is there some good summary of his idea about math without reals? Im interested but his videos are shit. He rants about irreverent things and then spends 10 seconds talking a little bit about his idea instead of just showing it.

[Anonymous No.9789049]

>>9787319
Imagine being this dumb

[Anonymous No.9789361]

>>9784077
>>9786579

to be honest if you blindly swallowed set theory without even thinking about the reals or the strangeness of their definition you should drop math
im happy there's someone finally making videos on this, set theory in current form is broken and not a foundation

[Anonymous No.9790130]

>>9784077
He is not seeing math as the thing it is: Arbitrary but useful definitions and their behaviour.

The first time I learned Lie Algebra I was stocked how much of the definitions are purely arbitrary.
(I.e. for my understanding there is no real reason why one uses an exponential map for a one parameter subgroup. You could use something else.)

Mathematics is not so "fundamentally deep" plebs make it to be. Set theory is fine, irrational numbers are fine, analysis is fine too.

Fuck.

[Anonymous No.9790152]

>>9790130
Brainlet tier counter-argument. It is true that under formalism, definitions are arbitrary but only retards would want that. Most mathematicians agree that there is an inherent natural path along mathematics, that there is objective truth in the structure. Formalism is really just the most recent crutch we use to try to find this path using our monkey brains. Because believe me, way before definitions were arbitrary and we had formalism, people were still doing math. In fact, they were doing just fine all the way up to the discovery of calculus which just produced problem after problem and because no one could decide what was true, that prevented us from going even further along the path.

In this sense, Wildberger's opinion is:
>This crutch is a piece of shit, we ought to go back and use something else to discover truth.
And the establishment opinion is
>This crutch is amazing, let's see how far we can take it.

I'm not arguing for or against Wildberger here so I'll leave it up to you to decide which opinion you hold. Just know that your current opinion is the most pleb tier engineer tier piece of shit I've ever read. May the gods help us and prevent you from ever getting published in a logic journal.

[Anonymous No.9790153]

>>9787420
It's all just a big proof by contradiction. Assume set theory works, do things until you encounter problems which you avoid by throwing them out of your model until you reach a point of inconsistency. This is when people who live in the past try to hold onto the crumbling "modern mathematics" and people free from such constraints see how modern mathematics is the one in which we return to the Greek ways.

[Anonymous No.9790157]

>>9784077
He's repeating himself.

[Anonymous No.9790200]

>>9788262
Good one lad.

[Anonymous No.9790212]

>>9790130
>he thinks the problem is that it's arbitrary and not ill-defined

[Anonymous No.9790217]

hahah anal XDDDD

[Anonymous No.9790226]

>>9790152
Dude.
>Inherent natural path
That's just philosophical. Which arbitrary axioms you choose you use is up to you. Thus there is nothing deep about it. That's my whole argument. Besides that, I doubt that we can somehow create a system without inconsistencies. I think it isn't possible, heck, because of this we have many many systems of logic itself.

I Just had an seminar about Tractatus and Wittgenstein uses a completely projective logical system and says stuff like: 'fundamental logic', 'elementary phrases' but can't give one specific example.

This whole "mathematics is so pure" mambo jumbo is dogshit.

Mathematics is useful and more or less consistent if we ignore some things at the beginning but this doesn't stop it from being rad as hell in describing behaviours of structures.

>>9790212
There is not difference in these two if we move into higher branches of mathematics. Nobody doing numerical PDEs cares about small inconsistencies in set theory

[Anonymous No.9791488]

>>9790226
>I doubt that we can somehow create a system without inconsistencies
Consider the first-order theory of groups. There are clearly no inconsistencies in this theory, since we can exhibit the trivial group as a model.

[Anonymous No.9791499]

>>9787217

holy fucking shit you're retarded. just stop talking about math please.