Anonymous at Sun, 13 Oct 2024 20:53:40 UTC No. 16429398

1x1=2

Anonymous at Sun, 13 Oct 2024 20:59:54 UTC No. 16429410

>>16429372
>i can't understand this.
>this can't be right.
The papers are pretty readable on their own, but there is a ton of commentary available too. Ask chatgpt to explain the parts you don't understand.

Anonymous at Sun, 13 Oct 2024 21:13:27 UTC No. 16429461

>>16429410
you yourself don’t understand it. This is just an appeal to authority. Yeah I’m not gonna study formal logic and advanced math to get through 10 pages of autistic notation for something that’s bullshit. Self-referential statements are retarded, that’s the only thing Gödel proved.

Anonymous at Sun, 13 Oct 2024 21:15:10 UTC No. 16429464

>>16429372
He used arithmetic to show this. Basically encoded mathematical statements into numbers and used their arithmetic properties.

Anonymous at Sun, 13 Oct 2024 21:16:52 UTC No. 16429465

>>16429464
ok so tell me what string of numbers represents “this” and “proof” and “theorem”

Just because each symbol is linked to some number by a code he invented doesn’t mean anything. Numbers don’t talk about themselves.

Anonymous at Sun, 13 Oct 2024 21:18:02 UTC No. 16429469

>>16429372
> this theorem is not provable
This is incorrect. What he said was given a set of axioms there will exists some theorems that cannot be proven. It says nothing about *which* theorems those will be. You can't know beforehand.

Anonymous at Sun, 13 Oct 2024 21:20:19 UTC No. 16429473

>>16429465
Just read the original paper. The point isn’t to give meaning to some numbers. The point is to provide a one-to-one function between mathematical statements and natural numbers so that one may the properties of the latter to work with the former.
>Just because each symbol is linked to some number by a code he invented doesn’t mean anything.
It doesn’t on its own. But if it’s a bijection, one can always map the results from numbers to statements.

Anonymous at Sun, 13 Oct 2024 21:22:53 UTC No. 16429477

>>16429473
Here’s the problem: not every number maps to a wff. The number with Gödel number G doesn’t map to a statement that is related to math. It’s an empty, self-referential statement that cannot be defined by the axioms or definitions of a typical formal system. The only thing we’ve proved is that self-reference is retarded

Anonymous at Sun, 13 Oct 2024 21:26:43 UTC No. 16429491

>>16429372
>what the fuck does this have to do with arithmetic?
It's an explicit statement about the natural numbers.
>It’s not even talking about numbers
Not as you stated it, but it is as Godel formulated it.
>Show me the axioms and laws of inference that allow such a statement to make sense in a formal system concerned with arithmetic
Simple consequence of the church turing thesis and fixed point theorem.

Anonymous at Sun, 13 Oct 2024 21:28:36 UTC No. 16429496

>>16429477
>Here’s the problem: not every number maps to a wff
Correct.
>The number with Gödel number G doesn’t map to a statement that is related to math
Yes it does. It maps to a wff that's an explicit statement about the natural numbers.
>It’s an empty, self-referential statement
Self reference is not well defined mathematically. It's an explicit statement about the natural numbers like any other.

Anonymous at Sun, 13 Oct 2024 21:29:05 UTC No. 16429499

>>16429477
>The number with Gödel number G doesn’t map to a statement that is related to math
It maps to a mathematical statement ie some string of logic symbols. Whether that string has something to do with Euclidean geometry or is just pointless gibberish doesn’t matter. It’s still a perfectly valid statement following all the rules of mathematical statement.

Anonymous at Sun, 13 Oct 2024 21:30:34 UTC No. 16429502

>>16429491
> Not as you stated it, but it is as Godel formulated it.
So what was wrong with how I stated it?
>>16429499
I find it interesting that what you say is at odds with >>16429496

It seems the cultists can’t get their own story straight

Anonymous at Sun, 13 Oct 2024 21:31:55 UTC No. 16429504

>>16429502
I don’t see how this is at odds with the other anon’s post. Just because some statement doesn’t carry utility we assign to it doesn’t mean it’s not a valid mathematical statement.

Anonymous at Sun, 13 Oct 2024 21:34:02 UTC No. 16429508

you are philosophically illiterate and yet you come here and ask a philosophical question with indignance
get the fuck out of here you troglodyte

Anonymous at Sun, 13 Oct 2024 21:34:55 UTC No. 16429511

>>16429461
It is really not that bad. Once he setups up Godel Numbering it starts to move quickly, but honestly it's high school level maths after that.

Anonymous at Sun, 13 Oct 2024 21:36:14 UTC No. 16429515

>>16429502
A string of symbols isn’t necessarily “valid.” It’s neither true nor false. It’s meaningless. There’s no reason to bring this up unless you think the Gödel sentence is meaningless, which would just be agreeing with me.
>>16429508
Cope. You simply don’t know how to explain the theorem. No one does.

Anonymous at Sun, 13 Oct 2024 21:53:24 UTC No. 16429545

Gödel has already been debunked by a guy who understands the theorem, and no one can explain why he’s wrong

https://www.jamesrmeyer.com/ffgit/godel_flaw

Anonymous at Sun, 13 Oct 2024 22:10:39 UTC No. 16429591

>>16429545
Godel's incompleteness theorems are elementary theorems that are taught to all undergraduates who study mathematical logic.
They have been proven in the proof system Isabelle
https://www.isa-afp.org/entries/Incompleteness.html#

Anonymous at Sun, 13 Oct 2024 22:12:50 UTC No. 16429597

>>16429515
>A string of symbols isn’t necessarily “valid.” It’s neither true nor false. It’s meaningless
That’s not at all what makes a statement valid. If a statement is consistent with the rules of mathematical logic, then it is valid. You are turning a very simple deductive set of arguments into meaningless semantics.

Anonymous at Sun, 13 Oct 2024 22:18:06 UTC No. 16429613

>>16429597
He literally doesn't know basic shit like what soundness and validity are. He is a fucking mongoloid who shouldn't have been entertained.

Anonymous at Mon, 14 Oct 2024 14:10:54 UTC No. 16430912

>>16429477
> The only thing we’ve proved is that self-reference is retarded
>>16429461
> Self-referential statements are retarded, that’s the only thing Gödel proved.
Wait, but every statement contains in itself an implicit statement that says "I'm true".

Anonymous at Mon, 14 Oct 2024 14:13:38 UTC No. 16430918

>>16429511
>>16429464
Godel Numbering, Unicode, ASCII - what's the difference?
They're essentially the same thing.
You can't claim that you proved some profound truth just because you encoded a string into utf8.

Anonymous at Mon, 14 Oct 2024 16:06:40 UTC No. 16431213

>>16430918
Close. Keep reading. You'll get there. We're all rooting for you.

Anonymous at Tue, 15 Oct 2024 20:49:51 UTC No. 16433437

>>16429545
>Gödel previously defined that an italicized word, such as number-string indicates the number calculated by his Gödel numbering function Φ, when applied to a given sequence of symbols of the formal system P (the system for which Gödel is claiming incompleteness). In other words, he is claiming:
>Z(n) = Φ(n)
he isn't claiming that though

Anonymous at Tue, 15 Oct 2024 21:01:33 UTC No. 16433445

>>16429461
>I'm not gonna study advanced math to understand advanced math

Anonymous at Thu, 17 Oct 2024 03:38:31 UTC No. 16435689

>>16433437
not an argument

Raphael at Thu, 17 Oct 2024 03:48:06 UTC No. 16435705

>>16429372
His thorium is bullshit read the ctmu and understand physics and algebraic topology

Anonymous at Thu, 17 Oct 2024 03:49:16 UTC No. 16435707

>>16429372
Anon, you don't have to believe his fake proofs just because everyone else does.

Anonymous at Thu, 17 Oct 2024 04:04:08 UTC No. 16435724

>>16435689
James R. Meyer claims in his argument that 1+1=3. Since this is obviously false, his argument is flawed

Anonymous at Thu, 17 Oct 2024 04:14:21 UTC No. 16435740

>>16435724
You should read his articles on the sub function where he explains more in depth what the issue is.

Anonymous at Thu, 17 Oct 2024 04:31:12 UTC No. 16435755

>>16435740
If he's gonna say ridiculous shit like 1+1=3 then why would I want to read more of his articles?

Anonymous at Thu, 17 Oct 2024 04:38:10 UTC No. 16435761

>>16435755
feel free to explain directly (to him, even) how he’s saying 1+1=3. If you’re right then you should be able to explain his error.

https://www.jamesrmeyer.com/ffgit/godel_sb

Anonymous at Thu, 17 Oct 2024 04:40:16 UTC No. 16435762

>>16435761
not an argument

Anonymous at Thu, 17 Oct 2024 04:47:57 UTC No. 16435769

>>16435762
he explains the error in every mainstream proof, formal or informal. Nobody can refute him. You’ve been duped.

Anonymous at Thu, 17 Oct 2024 04:59:56 UTC No. 16435781

>>16435761
>This means that Gödel has to assume that Sb(x, v, Z(x)) is precisely equivalent to the entirety of the requirements of a correspondence by Gödel numbering, which is:
>Sb(x, v, y), where y = GN(Y) and x = GN(X) and x = Y
>since the free variables of Sb must be Gödel numbers.
I don't get where he's getting x = Y from, can you explain?

Anonymous at Thu, 17 Oct 2024 05:19:36 UTC No. 16435794

>>16429372
he wrote a programming language and then showed the halting problem is unsolvable in that programming language. it's really basic stuff. note that everything on a computer is represented with numbers and arithmetic operations, exactly as in the proof of incompleteness encoding for arithmetical statements

Anonymous at Thu, 17 Oct 2024 05:41:09 UTC No. 16435813

>>16435781
If you read further, he talks about the Gödel number of a Gödel number. So when he says x = Y, he’s saying that y = GN(GN(x))

And his point is that Gödel is conflating the language of the formal system with the meta-language

Anonymous at Thu, 17 Oct 2024 05:47:15 UTC No. 16435817

>>16435761
yeah the section "The Gödel number of a Gödel number" is absolutely retarded
The third term in Subs(x,v,Z(x)) is not "GN(GN(X))". This guy is correct that this is an ill-typed expression, since GN(X) is a number and GN takes formal expressions as values. Gödel doesn't consider GN(GN(X)), he considers GN(t) for a specific formal expression t. The formal expression t is GN(X) many S's followed by a "0".
I can't tell whether the author doesn't understand this, or if he's like "I know that Godel is actually plugging in the formal term and not the number itself, but he can't do this because... HE JUST CAN'T OK":
>Now, while one could force the formats for numbers to be the same in both systems, that would not somehow magically make the conflation of meta-language and sub-language logically valid. in short, that would be a fudge that should fool no-one. The entire notion of Gödel numbering is that, for every relationship between expressions A and B of the formal system there is a corresponding relation between numbers a and b, where a = GN(A) and b = GN(B) (and similarly for more than two expressions). But Gödel’s construction is an illogical distortion of the correspondence between formal system expressions and Gödel numbers.

Anonymous at Thu, 17 Oct 2024 06:03:22 UTC No. 16435831

>>16429469
>You can't know beforehand.
which sucks big time, and also the number of unprovable theorems i not even known

Anonymous at Thu, 17 Oct 2024 06:17:25 UTC No. 16435839

>>16435817
Here is a challenge to you:

Re-write G using only the language of the formal system, and determine an exact formula for calculating the Gödel number of G. For convenience you can type “sss…sss0” but you can’t use notation like “Sb” or “Prov” or “Dem(x,y)”

Anonymous at Thu, 17 Oct 2024 06:18:53 UTC No. 16435842

>>16435839
>Here is a challenge for you: Write an internet browser in assembly code

Anonymous at Thu, 17 Oct 2024 06:22:03 UTC No. 16435844

>le theorems cannot be proven in this model
>...
>just make a new model bro

Anonymous at Thu, 17 Oct 2024 06:35:13 UTC No. 16435859

>>16429372
the proof only works "inside infinity", otherwise it doesn't work.
But logic inference in infinity itself hasn't been proven...

Anonymous at Thu, 17 Oct 2024 06:35:26 UTC No. 16435860

>>16435842
what a convenient excuse. You will never see that you’re wrong because you refuse to think about what a statement would look like because it’s le heckin big. As I said, you don’t have to write out all the successor symbols. So what’s stopping you?

Anonymous at Thu, 17 Oct 2024 06:50:16 UTC No. 16435877

>>16435860
I'll write out G if you write out the formula defining the function
>n -> godel number of "SS...S0" (n S's)
using only the formal notation of the language. Since the expression for G will use this formula, this is much less of an ask for you than yours is for me.

Anonymous at Thu, 17 Oct 2024 07:04:16 UTC No. 16435892

>>16435877
Are you seriously asking me to do the hardest part for you? Lol.

It shouldn’t be difficult for you to write as much of the statement as you can, and then explain why you can’t write out the rest. In the case of “sss…ss0” the answer is that there are too many symbols to list. But we at least understand what you’re trying to convey. You should be able to do the same for the whole expression, if not write it in its entirety.

Anonymous at Thu, 17 Oct 2024 07:57:12 UTC No. 16435939

is the godel theorem constructive or it work only in classical logic?

Anonymous at Thu, 17 Oct 2024 08:33:29 UTC No. 16435977

>>16435892
So you can't or it's just too much work?

Anonymous at Thu, 17 Oct 2024 12:47:36 UTC No. 16436175

>>16435977
That’s literally what I’m asking you, retard

Anonymous at Thu, 17 Oct 2024 16:51:12 UTC No. 16436539

>>16436175
My answer is that completely disallowing formula abbreviations an impractical request that would need thousands of characters, akin to asking for assembly code. I still comprehend that my software *is* in the form of assembly code, even if I am not able to write that assembly code down. I don't know why it's so hard for you to comprehend that

Anonymous at Thu, 17 Oct 2024 17:55:15 UTC No. 16436648

>>16436539
You haven’t explained exactly what’s so hard about it. I understand that you can’t write so many s characters. You haven’t explained what’s so hard about constructing the rest of the statement. I think it’s because you simply don’t understand even a vague idea of what the statement looks like in the formal system. You rely on the meta-language to even make sense of it.

Anonymous at Thu, 17 Oct 2024 18:04:04 UTC No. 16436663

>>16436648
>disallowing formula abbreviations would require thousands of characters
what did YOU mean in >>16435892 by "the hardest part"? I disagree that that function is the hardest part of the proof

Anonymous at Thu, 17 Oct 2024 18:09:09 UTC No. 16436673

>>16436663
Your task is very simple. All you have to do is write out the statement using as much of the formal language as you can, then explain why you can’t write out certain parts in the formal language. You should be able to explain precisely what it would look like even if you aren’t able to write down each symbol. You keep deflecting for some reason so this is the last time I’ll ask you to make an attempt.

Anonymous at Thu, 17 Oct 2024 18:17:11 UTC No. 16436691

>>16436673
Nobody has ever said the formula can't be written out in the formal language, the problem is that it would be thousands of characters.

Anonymous at Thu, 17 Oct 2024 18:24:15 UTC No. 16436703

>>16436691
…and you still haven’t explained why it would require so many symbols, aside from the successor symbols. Maybe someday you’ll realize the truth.

Anonymous at Thu, 17 Oct 2024 18:37:36 UTC No. 16436723

>>16436703
because it's typically defined in terms of abbreviations of formulas which are defined in terms of abbreviations of formulas which are defined in terms of... many layers deep
your argument is kinda like "I don't believe that 20x20 matrices have determinants. Prove me wrong by writing out the entire formula"