What if Godel was just... wrong?

What if Godel was just... wrong?

His conclusions have been taken as gospel and have informed the development of math for decades. But what if a few years from now, someone finds a crucial mistake in his work that upends it?

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>His conclusions have been taken as gospel and have informed the development of math for decades
Nope. I'm pretty sure his proof has been read by a lot of people.
>But what if a few years from now, someone finds a crucial mistake in his work that upends it?
Then he'd be wrong. But that won't happen, Russel.

I didn't mean "taken as gospel" to mean "accepted uncritically", I meant "treated as absolute truth".

what if his proof is incomplete

what if godel was an interdimensional space lizard trying to sabotage our progress

wouldn't sabotaging our engineering or physics be a more effective means?

No, because humanity has overcome bullshit Aristotelian physics. Godel's plan was much more sinister. Rather than suggest a demonstrably false mechanism of action for reality, he sowed a seed of doubt that our mathematics was not powerful enough to be trusted. That the god that man created was not omniscient.

>proof
>a finite sequence of terms in a language with finitely many symbols
>treated as absolute truth

What if Wittgenstein was right about math?

>accusing a mathematical Platonist of trying to undermine mathematics as truth
The postmodernist cries out in pain as he strikes you.

I also accused him of being an extradimensional space reptile from Omicron Perseii 8
Surely if he was capable of falsifying his humanity he could falsify his philosophical beliefs

You have to have stories to make stories but the stories you have limit the stories you can make. The Ouroboros of the Narrative vomits itself up from nothing. Then creates its own head and a tail to fool mathematicians into thinking there is something called a given or a conclusion, a cause and an effect, a before and an after, a big and a small, then use these stories to build their Dialectic Myopia called "Proof".

Math, like everything, is a story that is either useful to be believed for its Intent because the World allowed it, or it stops because the World didn't.

The only reason you don't like Godel is because he wasn't a Platonist or a Sophist, and didn't have a story that the World could ever be known.

Your question says it all: you think you can know the World, when all you can ever know is a representation you made from differentials. Even the story of you is just a story that is useful to be believed for moving around.

Godel simply said that stories have intentions that limit what the story can say. He glimpsed the circularity and utter nonsense of the Narrative to say anything about the World, and the fallacy and rhetorical persuasion at the heart of all our stories. But like all the rest before him, he was too much the coward to see it all.

>The only reason you don't like Godel is because he wasn't a Platonist or a Sophist, and didn't have a story that the World could ever be known.
But Godel was explicitly a Platonist when it came to his understanding of the nature of math.

You completely miss the point of Godel. Incompleteness in no way says mathematics cannot be trusted. It simply entails that there are borders to be dressed around mathematics. Our math is still correct, but there are true statements which we cannot prove.

I would have never expected the ghost of Bertrand Russell to haunt Veeky Forums

A Platonist has a story of determinism: that the World is and cannot change. A Sophist has a story of free will: the World changes depending on our choices. Both believe the World can be known.

Both together - free will and determinism - are what is called a Bootstrap Paradox: one cannot exist without the other and forms a loop from which a base, or a "given" can be constructed. They need each other to work.

Godel used logic, which is a Rhetoric to persuade using only the story of the story, and not the story of the action that is useful to be believed for the action's sake.

His Axioms (stories) changed. The acceptance that Axioms other that those found in living in a Euclidean Representation (story) makes him fundamentally NOT a Platonist or a Sophist.

But he deceived himself by not seeing how the way he made stories affected his story of the World means that the World cannot be known. He, like all westerners, Reflected his Perspective from "The World allows this story to be useful" to " The World must be this way" which is a story that is created by the Reflection.

Mathematicians should know this: You deal in alternative Representations to make stories that are useful to be believed for their own intent; Yet you use the same feeling of inference trained in a Euclidean Space to move from your given to your conclusion, after your conclusion has chosen the givens based on that Representation that trained your inference.

That is why you get so confused with spaces that are divergent. You can't use deduction - big things can't fit into small things - in a space that has sinks and sources. you can't use induction - time as a constant - in a space where time is not invariant.

Godel just showed this for arithmetic, which is the foundation upon which you fool yourselves with the shell game of what you allow yourself to see.

please let this be some obscure copypasta

it is now, i'm saving it

Stop Randomly capitalizing Words you're triggering My Autism

>Both together - free will and determinism - are what is called a Bootstrap Paradox: one cannot exist without the other and forms a loop from which a base, or a "given" can be constructed. They need each other to work.
"The Bootstrap Paradox is a theoretical paradox of time travel that occurs when an object or piece of information sent back in time becomes trapped within an infinite cause-effect loop in which the item no longer has a discernible point of origin, and is said to be “uncaused” or “self-created”."

Prime example. You have to have stories to make stories but the stories you have limit the stories you can make.

This is the Dunning Kruger effect: you cannot possibly have, understand, or make a story if you don't have the stories from which it is made.

You are too stupid to know you are too stupid.

So you lash out with an appeal to the crowd, because that is all you have...

Sad...

can I see your katana collection user

I'm not the same user, but your delusions of intelligence are transparent. You sound like you've read ancient philosophy by yourself but never had any formal training in it, which would explain your poor understanding of it.

You can't believe everything you read on the Internet. That is not a Bootstrap Paradox. that is just an Inductive Paradox - something came before it is created. It is an oscillating Paradox.

A Paradox can be deductive, inductive, or semantic (equivocation). A Paradox is a story structure that violates your feeling of inference

Deductive: big things can't fit in small things (ex. Russles Paradox)
Inductive: things can come before they are created (time travel paradox)
Semantic: Things are global or locally defined and the definition chages. (ex the liars paradox)

They can also be destructive, constructive, and oscillatory.

A Bootstrap Paradox is any two givens which are defined in terms of each other. Nature versus Nurture, free will versus determinism, space tell matter how to move and matter tells space how to curve.

They are Narrative Objects used as Rhetorical structures that give the impression by looping back on each other, that these objects are valid and are not up for debate. They turn these Narrative Object into Givens, or Axioms from which BOOTSTRAPS the story.

Any sources for your claims?

And you sound like a dick who uses the fallacy of Appeal to Authority who can only know what someone else has taught him and cannot find out things for himself.
Enjoy your job at McDonald's with your Associates Degree in Math.

HAHAHAHA!!! Try your own brain. Try your own life (if you are not 12)
Try working it out. Take the list of Paradoxes and organize it by what I just said.

Philosophers say paradox is a statement that contains its own falsehood.

But that definition is a Paradox itself!
So leave off the [cit needed] crap and start to think on your own.

Evidently I was correct. You've never had any training and exhibit your profound misunderstanding of philosophy.

Evidently I am correct: you cannot debate the issue or come up with a cogent counter argument to my argument because you cannot see past what you have been taught.
This tells me you don't even know what you have been taught, and just parrot back to teacher, because you cannot present it or defend it.

Pathetic.

>training in philosophy
No.

A cogent argument to being called a dick who works at McDonald's?

You are playing the victim card, mate. It really is ridiculous since you probably do it instinctively.

No. I'm asking what argument there is to be made against being called a dick. This is simply pointing out that you request an argument where none is to be given.

He was being emotional by calling you a McDonald's employee. He wasn't making that by logic but by frustration. Why do you want to cloud your world with useless comments rather than analyzing the data.

>and have informed the development of math for decades
No they haven't: he was upset that his work didn't change the way mathematicians work in the way Einstein's work changed the way physicists work.

>Einstein's work changed the way physicists work.

What they call a "Platonist" in the context of Russel, Gödel, and 20th century foundations of math is only tenuously connected with Plato.

>A Platonist has a story of determinism: that the World is and cannot change.
>He took a Philosophy 101 class and thinks he understands Platonic cosmology
You can't be a determinist if nothing changes. There's nothing to determine. [math]Timaeus[/math] details all of this.

>Philosophers say
>So leave off the [cit needed] crap and start to think on your own.
user....

God I hate fags who think they have their own philosophy/theory of the universe. It almost always dissolves into drawing incoherent parallels between tangentially related things like there's some broad pattern that only they've seen. DMT and other psychedelics posters do this all the time.
Also this

You can draw your own conclusions, one of which might be to deny the validity of his work to begin with. As many do.

he was

Well, I'm clearly not as smart as the wordy cocksuckers earlier ITT, but if his work can be coherently reduced to "this statement is false" being unprovable, no big fucking deal.

Honestly, all those crazy fucking posters from earlier were doing some real hand waving.

There isn't much interesting about logical fallacies being unprovable. It just means faulty bases are faulty.

I don't think the conclusion is that paradoxical statements are unprovable, I think it's more like "there are statements in mathematics (or any similar system) which are true but cannot be proven".

Well, I'd only read a marginal summary in "Gödel, Escher, Bach..." before this, but it wasn't far off.

Recursion that doesn't resolve (in this case, resolving indirectly) approaches circular logic, in my opinion

Pic related

What other sorts of languages exist?

>inb4 something laughably wrong

this fuckin guy right here

Has it been proven that there are any such true statements outside self-referential claims/ sets?

If not, why can't we just chalk this up to some (potentially current) limitation in describing self-reference?

Where can I get a hold of what you're smoking?

Languages with infinitely many symbols? Here's one that you might have heard of:

en.wikipedia.org/wiki/First-order_logic#Alphabet
>There are several logical symbols in the alphabet, which vary by author but usually include ... An infinite set of variables
>For every integer n ≥ 0 there is a collection of n-ary, or n-place, predicate symbols ... For each arity n we have an infinite supply of them
>For every integer n ≥ 0 there are infinitely many n-ary function symbols

For arithmetizable syntax you can use an equivalent version with finitely many symbols by representing non-negative integers as iterators (i.e. x, x', x'' ...) but the infinite-symbol convention is far from obsolete, Mendelson uses it for example.

Actually, it has been proven that the incompleteness theorem is a special case of the halting problem, so the unprovable truths are most likely just self-referential claims.

You have no idea what you're talking about.
Word salads belong on

It's just a Veeky Forums brainlet doing Veeky Forums things.

> You sound like you've read ancient philosophy by yourself
I doubt he's read anything beyond a couple of 20th century French meme "intellectuals".

>You can't be a determinist if nothing changes
ho boy..

citation? and if that's the case, why was Russel wrong? Can't we find a perfect merger short of self reference, acknowledging meta claims as categorically separate? It still seems entirely profound to me.

I don't think you really understand what you're questioning to begin with

No one understands his theorems. The shit pop-math folks say about him are ridiculous. Pretty frustrating desu.

Proof, an extension of axioms you believe in towards the consistency of a statement. Since a proof is a system of the elements called axioms which deductively lead to the statement, a proof can be treated as a model in Model Theory. And also because of the Curry-Howard isomorphism between math and computer science, a proof is equivalent to a program, and the statement it aims for is the class of that program, example: the class of programs "Each number is a prime or a factor of primes" has a number of programs that prove it. Add up the filter of what the compiler accepts or doesn't accept and you got yourself a syntactical formalization of a set of program classes, proofs, that can be called Mathematics. Now consider these axioms: a false statement is unprovable and a true statement is provable. Due to their tautological nature, they lead to: if a statement is unprovable, then it is false, and if a statement is provable, than it is true. Something provable depends on, again, a consistent extension of axioms towards the consistency of a statement. Truthfulness then boils down to the Consistency of a system that is able to prove any true statement, right? Thus any set of axioms that can't be used to prove All true statements is necessarily inconsistent, it implies other axioms which it doesn't include are wrong by definition. A consistent system needs to be able to generate all possible elements used in such statements, differentiate a statement from a non-statement, and necessarily have as many axioms as there are. Is there a finite number of axioms that can be used on proofs? No. Of course, this is just an introduction to Gödel's work, I might write more later.

pic unrelated

What if Godel was just... wrong?

His conclusions have been taken as gospel and have informed the development of math for decades. But what if a few years from now, someone finds a crucial mistake in his work that upends it?

Did you mean to swap Gödel for Boole?

Yeah. The joke is dead now.

>that
>joke
really makes me think

what if one day you put one and one apple together and get three???

>if a statement is unprovable, then it is false
Retardedly wrong.

If A then B and if C then D. Thus if B then A and if D then C. This is basic stuff, my friend. Tautology map: if A then B or D, if C then B or D, if D then A or C, if B then A or C. If every true statement is provable and if every false statement is unprovable, and if there are only provable and unprovable statements, which I expect you to agree with, then a provable statement is true and an unprovable statement is false. Basic logic.

>unprovable statement is false
Retardedly wrong. LEM is not provable in intuitionistic logic, but its double negation is true. The continuum hypothesis is not provable from ZFC while still being consistent with it. I think even a retard such as yourself should know this.

what a load of shit
axiom of choice is unprovable in ZF. you can make it true or false by adding extra axioms

But not every true statement is provable

believe it or not you can read the incompleteness proof if you want to be critical of it and poke holes in his arguments if you think something is wrong with them.

you are the one who is being uncritical OP.

>taken as gospel
>I didn't mean "taken as gospel"
Accepting something "as gospel" means to
accept as true an inaccurate report of a
mistaken rumour about a misunderstood
statement in a poorly-remembered anecdote.

>His conclusions have been taken as gospel
Just like EVERYTHING ELSE in mathematics, the works of mathematicians will be checked by others. It is not accepted without questioning, it is questioned into the smallest detail and then accepted. That is how math works.

If you don't believe it is true CHECK IT YOURSELF, that is the entire point of mathematics. Gödel has made a proof, a sequence of logical arguments. He did not make a hypothesis or a conjecture. He provided a proof which has been checked by others, if you don't believe it there is nothing stopping you from trying to find a flaw in his arguments.

>But what if a few years from now, someone finds a crucial mistake in his work that upends it?
Pointless question. You can ask the same for any other important theorem in mathematics.
The consequences (for the people who are not researchers in mathematics) can range from meaningless to catastrophic, depending how many application the theorem had.
Gödels theorems are on the lower edge of meaninglessness.

"Logic is useless for the discovery of sciences. It is good rather for establishing and fixing errors (which are themselves based on vulgar notions) than for inquiring into truth; hence it is more harmful than useful." - Bacon

"Logic teaches how to know whether or not reasoning and demonstrations already made and discovered are conclusive, but not how to find conclusive reasoning and demonstrations" - Galileo

"Logic contributes nothing whatsoever to the knowledge of truth. It does not teach the method by which something has been discovered. Therefore, it is entirely useless for those who wish to investigate the truth of things" - Descartes

"Logic discovers no new proofs, it is merely the art of marshalling, and ranging the old ones we have already. Therefore, it has been thought more proper for the attaining victory in dispute, than for the discovery or confirmation of truth in fair enquiries" - Locke

>informed the development of math for decades.

xdddd

if logic as a branch disappeared today, not a single mathematician would even notice.