/sci/ - Science & Math

It didn't need Gödel to arrive at the conclusion that "truth" is not something you can every be sure of, especially not in something like Arithmetic.
Just read Descartes.

Gödel's contribution is that for syntactic theories T, systems include at least Robinson arithmetic (arithmetic but not even induction, but with predecessor number existence), there will be sentences G such that you can't find a proof for either G or not(G).

Even if you hypothetically could prove such theory were consistent and if it were the case that it wouldn't have such Gödel sentences G, then we would still not be certain of any "truth". We'd just have a more neat axiomatic framework at hand. It's adoption - of the theory and interpretation of its implied inferences - is a choice on our side either way.

>>15194007
>"this sentence is a lie"
>therefore mathematics is incomplete
Yeah, I'm thinking he was retarded

>>15194019
His result is a straight formal claim that in some structures (arithmetic theories in this case, with their strings of symbols and rules to move between them), the existence of certain computable paths (the proofs) is not consistent.
It tells us that if we were to find a sequence (of strings and rewrite rules in the theory T) with certain properties (e.g. proof of consistency of the arithmetized theory itself), then this mathematically means that this theory T has some other very unpleasent features. In that regard, his result isn't much different than any theorem in ring theory. And nothing we have to second guess. Just stick to the formal statement of "if a theory is nice in the sense of exhibiting X, then the theory also has the un-nice property Y".
It's a mathematical non-existence result that we can study also without describing its content in a trivializing liar-paradox kind of analogy.

>>15194007
>It didn't need Gödel to arrive at the conclusion that "truth" is not something you can every be sure of, especially not in something like Arithmetic.
You're talking shit and know nothing about Godel. If that is your take away from Godel then you need to put down your shitty popsci pamphlets and start reading actual mathematical logic books.
>Even if you hypothetically could prove such theory were consistent and if it were the case that it wouldn't have such Gödel sentences G
Clearly you demonstrate you don't understand his results. It can't be the case that it doesn't have godel sentences, because Godel showed exactly how to construct them for any such theory.
>then we would still not be certain of any "truth"
You're just talking out of your ass again. There's nothing in Godel's results to make anyone doubt about whether arithmetical truth is a real thing or anything of the sort.

>>15194038
>then you need to put down your shitty popsci pamphlets and start reading actual mathematical logic books.
My understanding is fine, thank you. Indeed, it's strong.

>Clearly you demonstrate you don't understand his results. It can't be the case that it doesn't have godel sentences
The sentence literally starts with
>Even if you hypothetically could

>There's nothing in Godel's results to make anyone doubt about whether arithmetical truth is a real thing or anything of the sort.
The doubt is indeed not contingent on Gödel, as I try to make clear. You can always doubt already. E.g. there's no disproving solipsism, we can always doubt. We can however choose not to bother with it.

Please stop seething, I'll not reply to unnecessarily aggressive posts like that beyond this.
In case you're trolling, then I can understand that as it's kinda fun. However for your own sake don't expect more replies.

>>15194025
Of course it's logically valid as a formal statement, but it doesn't have any implications to things which (non-logician) mathematicians actually care about

>>15194007
just use non-axiomatic systems. english language is non-axiomatic so it dodges the incompleteness theorems. Only bad thing is it isn't formalised. Linguists have tried. Best attempt I have seen so far is the semantic primitive attempt.

>>15194025


Yeah yeah but at its core, it is, as goedel himself put it, ' the liar's paradox in disguise'. Which is in turn just another self referential/ diagonalization type paradox.

Really goes through all of CS.

>>15194038

Not OP but there is a similar result for the term 'truth' known as Tarski's Undefinebility of Truth, once more due to the ability to construct self referential formal statements within a turing complete (in the sense that all recursive functions can be expressed) theory.

Gödel does not undermine the concept of truth. He merely says there are some theorems you cannot prove to be true or false.

>>15194109
>says there are some theorems you cannot prove
poof there goes the notion of a deterministic casual universe that has predictable cause/effect relationships.

shit makes some people uncomfortable by feeling small and powerless

>>15194194
>poof there goes the notion of a deterministic casual universe that has predictable cause/effect relationships.
the universe isn't axiomatic, it isn't affected by the incompleteness theorems.

>>15194007
>linguistic paradox
>linguistic paradox, mathematics

>>15194208
>linguistic paradox
it's specifically NOT just a linguistic paradox though.
>The incompleteness theorems apply to formal systems that are of sufficient complexity to express the basic arithmetic of the natural numbers and which are consistent and effectively axiomatized. Particularly in the context of first-order logic, formal systems are also called formal theories. In general, a formal system is a deductive apparatus that consists of a particular set of axioms along with rules of symbolic manipulation (or rules of inference) that allow for the derivation of new theorems from the axioms. One example of such a system is first-order Peano arithmetic, a system in which all variables are intended to denote natural numbers. In other systems, such as set theory, only some sentences of the formal system express statements about the natural numbers. The incompleteness theorems are about formal provability within these systems, rather than about "provability" in an informal sense.

>>15194221
FACT

>>15194208
Guess how I know you're one of the illiterates who post frogs and sperg out about philosophy in every thread?

>>15194221
A formal system is just a specific class of languages.

>>15194208
Pic related also explains at the very begging of the paper the sort of systems which it applies to

>>15194227
Mathematics is just a "specific class of languages", then. Fuck off, retard.

>>15194234
You're confusing mathematics with formal languages, that's your problem.

>>15194221
>"this sentence is false"
>"this sentence is false", mathematics

>>15194237
You are confusing your delusional mental illness for intelligence.

>>15194249
Notice how frustrated you get when your fallacies are presented to you

>>15194254
Notice how you are too lacking in metacognition to even have basic heuristics to help you assess the plausibility of your ignorant opinions, like "is it plausible that I'm smarter than every actual living mathematician or maybe I'm just misunderstanding something?"

>>15194238
>never read the paper

>>15194237

Mathematics is the collection of all formal theories allowed by the >language< of ZFC ( that is the axioms of PL + FOL + ZFC axiom scheme).

Within that system its common to talk about specific formal theories like fields or natural numbers which are defined by axioms in the lang. Of ZFC

>>15194257
It looks like your frustration is causing you to have hallucinations. You certainly don't represent 'every living mathematician', in fact, you're not even a mathematician yourself. Take your meds.

>>15194267
Take your meds.

>>15194266
>Mathematics is the collection of all formal theories allowed by the >language< of ZFC
Wrong. ZFC is just a convenient way of formalizing most useful mathematics.

>>15194272

Ehh, most mathematicians are somewhat aware they operate in ZFC - it would certainly NOT be accepted by the larger mathematical community if you were to proof a significant theorem (outside set theory, because they push boundaries further either way) using an axiom not in ZFC :)

>>15194287
You're missing the point. As I said, ZFC is just a convenient formalization. Mathematics was done well before ZFC or set theory were developed. There's also no dogma that all the non-set theoretical mathematics which is done in the future should also be necessarily formalizable in ZFC.

>>15194317
Is your future mathematics going to be done without axioms and formal logic, retard?

>>15194320
Have you taken your meds yet? See >>15194267 for a reminder

>>15194325
Cringe. See >>15194320

>>15194317

If you are a mathematical platonist like me, it is true that ZFC is just one possible axiomatization which allows to talk about the 'platonic reality'.

I can shoot myself into a higher dimensional space with a sufficiently large amount of DMT but I can only communicate the mathematical properties of that place to someone else using some common notion of mathematics, which is usually ZFC.

Me being a platonist doesnt imply that I have an issue with formal systems. My believes about platonic objects shape the form of the axioms I am willing to accept :)

>>15194258
>read the paper
>it's a proof that any formal language strong enough to express its own syntax and provability predicate can encode linguistic paradoxes of the form "this sentence is not provable"
>suddenly it's not a linguistic paradox because proofs n shiet

What about we all have a discord voice call to discuss this rn? Could be funny :)

>linguistic paradox

Suppose we replace "truth" with "hammer"
https://www.youtube.com/watch?v=otCpCn0l4Wo
I mean...a capital "T" looks a bit like a hammer, or a cudgel or sledgehammer
So we aren't completely off base here
Look, u do u
>Hammer Time
Can't Touch This
>Break It Down

>>15194402
so much this. it isn't even a paradox in natural language.

>>15194287
>Ehh, most mathematicians are somewhat aware they operate in ZFC - it would certainly NOT be accepted by the larger mathematical community if you were to proof a significant theorem (outside set theory, because they push boundaries further either way) using an axiom not in ZFC :)
I don't like that formulation.
I agree with the last sentence, but that's because ZFC is already super strong, so postulates of things that don't have a model in ZFC will typically be odd (yes, you can find counter examples of course).
So you say "most mathematicians are somewhat aware they operate in ZFC" but I would disagree with that part - exactly because the are not operating in ZFC, just in a weaker theory also captured by ZFC.
Roughly, most math surely happens inside [math] V_{\omega\cdot 2} [/math].
And unless you do higher algebra (unless you need natural transformations, say), you usually won't need a _set_ as big as the class
[math] ({\mathbb R}\to{\mathbb R})\to({\mathbb R}\to{\mathbb R}) [/math]
holding integral transforms.
That is, you don't actually need
[math] ({({\mathbb N}^{\mathbb N})}^{({\mathbb N}^{\mathbb N})})^{({({\mathbb N}^{\mathbb N})}^{({\mathbb N}^{\mathbb N})})} [/math]
(lel)
to be a cardinal number.

>>15194416
"Can't Touch This" inspired the folk hit "Can't Name a C Identifier After This Reserved Keyword" by Ritchie & Thompson
https://www.youtube.com/watch?v=4fWyzwo1xg0

>>15194287
>larger mathematical community
>le wtf
mathematicians are huge faggots
>why
would you care what faggots think
>go
read a book
>go
watch gay porn
>browse
/lit/
>shit

>>15194287
this is just nuts because you faggots should be able to prove theorems formally using, say, Fitch notation in ZF+!C
>BUT
YOU
>CAN'T
because absolutely fucking nobody learns that
so ZFC fanboyism is cancer, not orthodox pedagogy
suggesting that we don't slay that dragon is STUPID

>>15194448
you can argue that equivalents of AC are easier and more constructive in ZF+!C because !C gives you a set (like axiom of infinity) with certain specific properties instead of ruling out their existence
If you have !C, then you should be able to construct a set that has no well ordering using ZF and vice versa. There might be a nonconstructive proof, but it seems unlikely.
Also, I'm pretty sure ZF minus axiom of infinity plus negation of axiom of infinity is a perfectly reasonable theory, although I haven't investigated the details myself.
A "finite math" movement that studies this theory seems entirely reasonable, possibly even fashionable
Why not simply ban infinity? You can prove theorems about all of the sets in finite ZFC, as there are infinitely many of them, but each set is itself finite.
Note that C is a theorem of ZF-I+!I as we can just write down a choice function by induction.
In ZF-I+!I, ordinary induction serves to exhaust all sets, so at least in theory we have a big hammer we can use to build theorems
Also, you can just prove theorems about the set of hereditarily finite sets in ZFC
At least in theory, these are different topics, but one is a model of the other, in the sense of model theory

>>15194483
I pity da foo' who doesn't study models of ZF-I+!I in ZFC
>and yet he won't study models of ZFC in ZF+!C
I think this is a job for the A-Team

ZFC is underpowered T_T need more axioms, right to the edge of known inconsistency

>>15194501
Our university has a paraconsistent introduction to non standard analysis course, so there is progress. Inconsistencies should be accepted and handled!

>>15194513
What's the point of paraconsistent logic? Wouldn't anything that's true in a paraconsistent logic without invoking the principle of explosion be provable in classical logic with a consistent subset of the relevant premises?

>>15194524
https://arxiv.org/pdf/0812.4852.pdf
>A fundamental goal of Inconsistency Robust Direct Logic is to effectively reason about large amounts of pervasively inconsistent information using computer information systems.
>inconsistent information
>computer information systems
sounds like a secretary at a large company

>>15194423
>what is a veridical paradox

>>15194483

As you say yourself, ZF-Inf models the hereditarily finite sets. And the colleciton of those are also a model of ZF-Inf (and ZF-Inf and no Inf).
iirc that theory has a bisimulation with arithmetic, so it's not really a new theory to research much.

>>15194524
I've seen approaches to set theory using paraconsistent logic, and in a way that again permits unrestricted comprehension without breaking the (paraconsistent) system. That ended up looking extremely ugly for my eyes, pic related

>>15194076
The Collatz conjecture is a good candidate for being undecidable.

I can't think of a single ZFC definition with an admissibility condition that isn't a theorem of ZF
Every modern math definition I've seen has an admissibility condition that is a consequence of ZF
>!

>>15195405
by the way...on the topic of C
I proved to a bunch of Harvard undergrads (my classmates) that a topological space is compact iff every open tower cover contains the whole space way back in 1998
https://en.wikipedia.org/wiki/Compact_space
Wikipedia has neglected to incorporate this unpublished result into their records even though my loyal and adoring minions (i.e. nobody) should have pestered the Wikipedia editors continuously on such a minor and inconsequential point!
How fucking anal of them!
Fuck them!
Now you know the truth!

>>15195405
that's because ZFC is essentially unenlightened (lightswitch off)
clearly ZF+!C is enlightened (lightswitch on)
the whole point of a definition is to separate the strata
if you say
>EVERY SET HAS A CHOICE FUNCTION
then there isn't much need to define different types of sets without choice functions because there aren't any
for example
let X* = { U[i=1]^n X[i] : { X[1],...,X[n] } is a finite subset of X }
and let X*^alpha = { U[beta<-alpha] f[beta] : f : alpha -> X is a map }
so X*^omega = X*
now we can talk of choice-infinite sets, *-choice-finite sets and alpha-choice infinite sets
>choice-infinite: no choice function, doesn't have a choice function, yes we have no choice function, choice function is kill
>X is *-choice-infinite: X is choice-infinite and X* is choice-infinite
>X is alpha-choice-infinite: X is choice-infinite and X*^alpha is choice infinite
here alpha and beta are ordinals

>>15195710
this is one way to go
another way is to say
>X is choice-finite if one X = {}, {} <- X, or X has a choice function
and then say that a choice-infinite set Y is *simple* if every element of Y is hereditarily choice-finite

>>15195731
So ZF+(there exists a simple choice-infinite set) is somewhat appealing because it seems plausible that we can find a model of ZFC here, maybe using transfinite recursion
also ZF+(there exists a model of ZFC) is a natural progression beyond ZFC

>>15194007
Truth is your sister's name, and yes, I will arrive in her not at her.

>>15195783
babyfag, go read a fucking book

Our guy Gödel doing God's work by bringing down to earth arrogant atheist like Hilbert and Rsusell.

>>15196042
based [math]\pi(X,x)[/math]

>>15195405
>admissibility condition
Can you explain?
I know set theory but I'm not familiar with the use of this notion.

>>15196478
Hodges, "A Shorter Model Theory" p. 53.

It's more annoying that you'll never even know the things you can't prove, just that they exist. So you could waste your whole life working on an solvable problem without even knowing it.

>>15197725
There are, however, also enough problems of which you can prove that they are not decidable.

>>15194093
>as goedel himself put it, ' the liar's paradox in disguise'
more specifically it's the liar paradox shifted from alethic to epistemic mode

>>15194047
totally fucking delusional

>>15194203
>the universe isn't axiomatic,
So your universal framework has just that single axiom?

>>15199639
kek
okay you win

>>15194007
>here's a proof that you can never know if any mathematical proof is correct
>except for my proof of course hehe

>>15195417
this is introductory textbook exercise tier m8

(=>) Any open tower cover not containing X can not have a finite subcover (since the union of such a subcover would be the largest element in the subcover)

(<=) Suppose every open tower contains X. Let C be a cover of minimum cardinality kappa with no finite subcover. Well-order the elements of C and let T be the open tower obtained by unioning initial segments of C. By assumption, X is in T. So X is the union of <kappa many elements of C; therefore C has a subcover of size <kappa, and by minimality of kappa, this subcover has a finite subcover, which is therefore a finite subcover of C as well, a contradiction

>>15194007
If he said that, he is a good stand-up comedian.

>>15200471
>here's a proof that you can never know if any mathematical proof is correct
not even close to what it says

>>15201345
It's what the incompleteness theorem implies. They are kind of like a hole at the bottom of mathematics

>>15201363
leaving aside the fact that you can prove things in systems to which the the incompleteness theorems don't apply (e.g. presburger arithmetic), still no. they establish an upper bound on provability. gödel established the lower bound a few years earlier.

>>15196042
Sure, the group that doesn't believe some magical sky daddy is going to save them needs to be brought down to earth.

>>15202816
hilbert tried to destroy brouwer's career over a difference of opinion in philosophy of mathematics.
russell advocated systematic state-sponsored murder of anyone intelligent enough to be his peer and not indoctrinated from birth into his philosophy.
gödel tried to warn his immigration judge of a logical flaw in the us constitution.
gödel was a good guy. be like gödel.

>>15202854
>gödel was a good guy.
Yes, for the most part he was pretty moral it seems. He went against the anti-metaphysics attitude of the vienna circle jews for instance. He basically defended Aryan greco/Germanic idealism against it's enemies. He hung around those guys, but had largely opposing views. And he seemed to be right about just about everything.

>>15204525
This isn't math.
This is math-flavored hand waving.
People in this thread are waving their hands just like Gödel.
>lol, didn't do math
>take my word
>the proof is good
of course the proof is good
it's a beautiful proof...FOR THE PHILOSOPHY DEPARTMENT!!!!

>>15202854
based

>>15194007
Truth is an ill defined term. Its predicated on what we call reality which is a relative consensus. You want something non-deterministic the current definition is giving feedback.

>>15204683
Its like wanting unclaimed territory when you claim everything you see.

You are cursed to never arrive at a copy of truth that has all of the properties of truth but is not truth itself, and to make matters worse, you have no proof that establishes that it is a copy of truth that you are cursed to arrive at and not genuine truth, and to make matters even worse, you have no way to verify a putative candidate proof that could, if it were sound, establish that it is a copy of truth and not truth that you are cursed to never arrive at?
t. read about the pumping lemma in pic related

>you are cursed to arrive at truth
I don't actually see how this is better. I mean, you're damned if you do, damned if you don't.
>you are not cursed to arrive at truth, nor are you cursed to never arrive at truth
zzzz....

If we accept ZFC, why not accept Con(ZFC), and Con (Con(ZFC) + ZFC) and Con(Con (Con ... etc ?

>>15204683
>you are cursed to never arrive at accuracy
this is literally the pragmatic philosophy
just keep evolving, never get to the end
endless refinement of the truth
whir...

>>15194194
a deterministic system doesn't have to be predictable.

>>15204801
yep, this is the core idea of the halting problem

>>15204792
because you have to learn model theory in order to understand what Con(ZFC) means, and the other ones are nested models, and nobody studies that
there's no proposed notation to differentiate between, say |= one model deep and another |= that is two models deep or zero models deep
you would have to learn model theory and develop a theory (and notation) for nested models
besides, ZFC is more like a target we shoot at in order to subvert it than the foundation...the proofs are just there to organize education, outside class nobody cares about proofs unless something really crazy is happening, and it almost never is

>>15204807
You're missing the point. If you believe ZFC is consistent, why not accept Con(ZFC)? Which is just saying ZFC is consistent. Any why not accept the consistency of that new theorem Con (ZFC + (Con (ZFC)))? And so on and so on through out all the ordinals.

>>15204826
>you believe ZFC is consistent
you're trying to cover for the fact that you don't know what "ZFC is consistent" means
you're trying to cover for the fact that you don't know that "ZFC is consistent" means "ZFC thinks ZFC is consistent"
you don't know what you're talking about, and you're posting out of embarrassment

>>15204834
Con(ZFC) is just talking about the function of some turing machine that searches through every proof of ZFC looking for a contradiction. If it finds one, it halts. So it's about saying such and such function is total.

>>15204826
>why not accept Con(ZFC)?
you're trying to make this a sky daddy conversation
you're trying to say this is about a trick to get people to believe things
no
the trick is to get you to attack ZFC by coming up with proofs that ZFC is not consistent
that's the only thing going on
only game in town
this is the carnival, not church
ZFC is the dummy, we're taking shots
you're not allowed to protect the dummy
you could get hurt
>oh noes
>u guize tricked me into believing ZFC!!!
no
you're just supposed to use ZFC until it breaks, and then we fix it, and you're supposed to use that...

>>15204842
Take your meds

>>15204843
ZFC is the meds

>>15204840
I doubt Kunen uses this
If I recall correctly, he doesn't really define it properly, he just says
>well, just take my word that it's defined
and then he uses it poetically

>>15204872
So you're saying such a program can't exist? Like you cannot even imagine some program which searches through every possible proof of ZFC looking for a contradiction?

>>15204843
>I
WANT
>MY
Z
>T
V
https://www.youtube.com/watch?v=wTP2RUD_cL0

>>15204878
this is also not math
this is CS people moving their arms and making noises and thinking they're doing math

>>15204886
Please read an introductory book on logic.

>>15204842
People barely ever use anything bigger than P(P(P(N))) in practice.

>>15204878
if you want to do math, you have to flip that delicious char broiled sentence over and get the proofs to say things about the machines
https://www.youtube.com/watch?v=RijB8wnJCN0

>>15204894
>shills for logic
not in a post-anacon world, motherfucker
pic related
>very large hardcover advertisement for tied software product subject to a proprietary software license
this is about logic entryism and Bill Gates' 1976 "Open Letter to Hobbyists" where he demanded academia not study the source code of the computer software products sold by his outfit

>>15204912
Right, so you have to figure out what the hell is going on here. It's a primary source. Gates is trying to intimidate people he regards as thieves.
Gates is writing this pretty far from the research centers of California
A place like Menlo Park, you wouldn't be able to write this letter
Think about it
There are a whole bunch of students and professors who want to test the performance characteristics of Altair BASIC because they are linguists, they study language, they study essentially the same stuff that Gates and his team are working on

>>15204912
>>15204925
So what you get here, a quarter century later, is one professor going
>wait, no
>no, wtf
>you can just say
>DON'T READ THE SOURCE CODE
>oh shit
>let me try this out
>HEY PEERS
>SUCK IT
>USE MY FUCKING COMPUTER PROGRAM
>NO, YOU CAN'T READ THE SOURCE CODE
>IM'MA DANCE ALL NIGHT
it's a punk move

>>15204794
You hit the end but you ignore it because it doesn't look like you want it to.

>>15204956
that's literally math
>okay, get this, motherfucker
>x = x
>got that
>good
now some badass walks into the bar, orders a rainbow daiquiri
>did I overhear somethin' about somebody's ex
the other guys decide that we don't have to drag girlfriends into a math discussion
>Okay, fuck it
>y = y
badass looks pleased, takes a look at the blackboard, a big smile comes over his face
>so, uh
badass takes a sip
>why do we have a blackboard in the bar
a group of 10/10 models enters the bar
one of them goes up to the blackboard
writes
>xx = xy;
and gives the boys a sexy look
>that's why there's a blackboard on the Vegas strip
a bit of her spittle lands in the rainbow daiquiri, she looks slightly inebriated
badass takes another sip

>>15204982
When you put it like that it sounds like sex.

>>15204956
>You hit the end but you ignore it because it doesn't sound like you want it to.
https://ia803401.us.archive.org/8/items/heart_of_darkness/heart_of_darkness_1a_conrad_64kb.mp3
https://mp3.hardnrg.com/MadamZu-March_2004.mp3

>>15194007
We are cursed to never arrive at a recursively enumerable axiom system that lists all the things that are obviously true.
If you believe in the existence of semantics of an axiom system T, then it's obviously true that Con(T), and Con(Con(T) + T) and so on. Yet Godel says that you cannot encode this set of beliefs in a recursive formal system.
It still might be true that all true statements in arithmetic are provable, just not from a single recursive axiom system.

>>15194018
>It didn't need Gödel to arrive at the conclusion that "truth" is not something you can every be sure of, especially not in something like Arithmetic.
Provability is the word that sometimes gets used instead of truth.
>is a choice on our side either way
Ah, yes, CHOICE, ie none-algo/programmatic input. Yes. And this is why, or part of why, no doubt, Gödel came to his conclusion AGAINST the computational theory of mind. He also later took turing to task for this view. Though, to be fair, turing DID mention a 'choice machine' whose 'motion is only partially determined by the configuration' which 'cannot go on until some ARBITRARY (my/anon's emphasis) choice has been made by an external operator.' And so even he intuitively was tapping in to the idea of non-programmatic/algo mind and non-local, non-virtual/physical/formal language-istically constrained thought, IE FREE WILL AWARENESS UNIT THOUGHT.

>>15194018
more on this
>>15206694
idea in terms of why, being that the physical world is virtual, ie emergent from non-local (outside of spacetime) info processing, that brains can not be the seat of consciousness/mind, and why mind is non computational and only INTERFACES with algorithm and is CONSTRAINED in some ways by algo, as in any virtual experience, but is not resultant OF algo or formal language. This is why the AI will never have internal experience in a first person/subjective way. Also, even in terms of on/ off switches arranged in a certain structures cycled MIMICKING some of the things mind DOES and some of the CONTENT of mind, the AI orientated enterprise of creating a free will awareness unit is doomed.

>>15194425

Forgot to reply a few days ago because I was on a low dose acid minitrip.

> "I agree with the last sentence, but that's because ZFC is already super strong"

Super strong relative to what? What is supposed to be the norm?
Aren't we obligated to add more axioms until the whole system is right at the edge of inconsistency?

"Vω⋅2."

Not familiar with the notation from whichever hierarchy this is :)

However, I would be okay with adding
https://en.wikipedia.org/wiki/Absolute_Infinite

as an informal axiom to ZFC just for the fun

>>15206694
Provability is the word that sometimes gets used instead of truth.

If you don't have a concept of sematics defined by model theory and don't have something like the completeness theorem defined for your theory.
If you have not shown your formal system to be sound, you could not just replace 'provable' with 'true'. One is a syntactic property, the other a semantic one. You first have to show them to be matching for some formal system.

>>15206726
>If you have not shown your formal system to be sound, you could not just replace 'provable' with 'true
I didn't say you could. I am just stating that that is the way it is usually put instead of using truth. Truth is determined by minds ultimately. Something outside of syntax or formal systems.
>One is a syntactic property, the other a semantic one
Yes, I know. Semantics are grounded in minds only. Semantics are not grounded in syntax, see the chinese room experiment. though, syntax CAN, of course, be utilized to CONVEY semantics and meaning to minds. Minds are semantic generators or meaning generators, not programs. We also give qualitative-ness to quantities or quantifiables. We turn data into INFORMATION, just as we take the physical data stream and through interface we create qualia or qualitative experience INFORMATION. We also are uncertainty resolvers. This is what we are doing in life. Creating information.

>>15207019
>Yes, I know. Semantics are grounded in minds only. Semantics are not grounded in syntax, see the chinese room experiment. though, syntax CAN, of course, be utilized to CONVEY semantics and meaning to minds. Minds are semantic generators or meaning generators, not programs. We also give qualitative-ness to quantities or quantifiables. We turn data into INFORMATION, just as we take the physical data stream and through interface we create qualia or qualitative experience INFORMATION. We also are uncertainty resolvers. This is what we are doing in life. Creating information.


Astonishingly, I would not have written it much different :)

Without qualia coming into place at some point, usually when we talk about the interpretation function that assigns truth to a formal statement, these strings just have no meaning.

>>15206647
Con(...) is always meant in a philosophical or poetic sense. No author actually goes to the trouble of figuring out that complex scoping rules must be defined in order to actually represent the structure of genuine proof. All authors using Con(...) lie and claim that a list of formulas with no explanation of how variable scoping rules are enforced is a proof system that is adequate to handle what we ordinarily call mathematical proof. This started with Gödel. Gödel is lying when he says "there is no proof" because he is claiming that something that is not proof and isn't powerful enough to enforce variable scoping rules is proof. Gödel claims "proof is this" but he's simply incorrect, and part of this stems from his prank: submitting a "theorem" to PNAS that makes reference to make-believe, namely "semiintuitionistic logic"
see for yourself: https://www.pnas.org/doi/epdf/10.1073/pnas.24.12.556
like other logicians such as Russel, Gödel is selling snake oil
All while Conrad is witnessing a destruction of truth of another kind and channelling it through Heart of Darkness

>>15207242
What's wrong with gentzen's sequent calculus LK?

>>15207212
>
I agree. Good to see another non-bot player.

>>15207212
>we are this
>we are that
>we are happy :)
we are not
we are not happy
we are not :)
we are not :(
I simply am not. I invite you to refute it, to play your idiotic mind-games. Those are yours, you are someone who plays idiotic mind-games, and I am not.
I simply am not.
Your words are yours.
Your idiotic mind games are yours.
Math is not idiotic mind games.
Go to /lit/, motherfucker.
You aren't doing science, and you aren't doing math.
https://www.youtube.com/watch?v=fcrexKS8kxA
Get the fuck out of here.
Didn't you see the sign?
No short dicks allowed.
>THAT
HAS
>GOT
TO
>BE
THE
>SMALLEST
DICK
>I
HAVE
>SEEN
IN
>MY
WHOLE
>LIFE

>>15207254
you're changing the topic to testing logics, and you are demanding a /lit/-tier philosophical response, not a math or science response
>what's wrong with it
what the fuck is wrong with you
math isn't about reading your fucking mind and trying to figure out what the fuck you mean when you say "what is wrong"
what the fuck is wrong with you, motherfucker
do science
do math
get the fuck out of here
take your shit to /lit/ or /his/

>>15207258
the greentext is in PUAtalk
>he wants an A.I. that can add a hypnotized slave girl to the GIF
yes, and use pic related as artistic inspiration, graphics design A.I.
>tfw you raise SPP and sell hypnotized slave girl gold items to the masses because...MOTHERFUCKIN' PUA MOTHERFUCKER
>SHOVE
THOSE
>RED
PILLS
>UP
MY
>ASS

This thread convinces me that our future extinction is justified.

>>15206708
this is like pre-math waffles, circa late 1800's
>delicious pragmatic emotive philosophical products for your enjoyment and entertainment
Now I must play some emulated vintage Apple Macintosh™ video computer games after making my selection browsing old issues of Computer Gaming World
https://www.cgwmuseum.org/galleries/issues/cgw_40.pdf

>>15207309
you're one of those people that bought Gödel's snake oil, aren't you??
it's a very nasty formula
it was developed during
Colonial exploitation
Great White Hunters used to go to Africa and just fucking violently assault people and kill huge animals and take their tusks.
This created social conditions where the reports of Conrad and Orwell are properly understood as news reports filtered through a difficult communication environment.
You cannot understand "Shooting an Elephant" and "Heart of Darkness" along the neo-liberal bs lines and have anyfuckingclue what actually happened and why those pieces of literature, primary historical sources claimed to be "English Literature"
>BLAM
BLAM
>BLAM
BLAH
you realize the Buddhist natives just wanted lunch meat, Elephant lunch meat, nutrition for days, weeks, perhaps months, supplementing an impossibly impoverished diet, the diet of the Buddhists

>>15207317
I watch this video every morning with my coffee, Anon.
But I like your spirit.
https://www.youtube.com/watch?v=mAvEmzjL_lA

>>15207317
You understand that the Buddhists warped Orwell's mind and exploited him because they wanted Elephant lunch meat, and "Shooting an Elephant" is about how Buddhists can brainwash elephants and white people
https://www.orwellfoundation.com/the-orwell-foundation/orwell/essays-and-other-works/shooting-an-elephant/

>>15194007
Because you’re a low IQ faggot incapable of comprehending the implications of his work

>>15207322
I just have to say
I don't think I have a better life than these people
They get to work nekkid

>>15207339
so you drop a bomb and you don't give us a reference
you are such an asshole
https://www.youtube.com/watch?v=XGdjKvivJA8
>KEEP
FIRING
>ASSHOLES

>>15207339
one could argue that mathematicians shouldn't attempt to "submit code to the C compiler that attempts to use a reserved keyword as an identifier"
In other words, it's absurd to accept a mathematical document that attempts to "define" any of a list of reserved keywords such as
>muh proof
>muh truth
note that the grammatical form of "true" in model theory
>X is true in Y, a.k.a. Y |= X
is distinct from the generic form in logic and math
>X is true
so we can take a C++ism and say that model theory is "overloading" true and it's okay because the grammatical form of usage clearly differentiates between the logical meaning of true and the mathematical meaning

>>15207366
>programming analogy
https://en.wikipedia.org/wiki/Meta-circular_evaluator

>>15207309
this thread is essentially a core war vampire trap
here are my comments
>>15194416
>>15194427
>>15194436
>>15194448
>>15194483
>>15194493
>>15194609
>>15195405
>>15195417
>>15195710
I know full well a "voodoo programming pragmatism" argument using the difference between C reserved keywords and identifiers is absolutely fucking killer. Clearly humanity is being forced to accept the difference between a C reserved keyword and identifier and it's
>le end of the world
THIS
>IS
BIGGER
>THAN
GLOBAL
>WARMING

>>15207385
part of the issue is that the difference between a C reserved keyword and an identifier went through a mushroom process
we can easily blame Dennis Ritchie and Ken Thompson for this
however
it was trivial when they created it and did everything necessary to essentially create a condition whereby nobody could save humanity from the difference between a C reserved keyword and an identifier
the politicians were helpless
nobody wanted to teach them computer programming
we never had a chance
https://www.youtube.com/watch?v=fShlVhCfHig

>>15207396
We can only shudder in horror as we contemplate the incalculable ecological damage wrought by the plague of distinguishing between a C reserved keyword and identifier. Indeed, humanity must reckon with its semantic past, with its rough and tumble parsing, its Knuth-Pynchon "Crying of LR Parser vs. Dark City Hits" mutants lurking in, in, oh, I just can't say it
https://www.youtube.com/watch?v=aPKbxYBSK7c
https://www.youtube.com/watch?v=DdYoSfQrHI4
https://en.wikipedia.org/wiki/LR_parser
>fucking anti-historical currents
fuck
>GO DIRECTLY TO /LIT/
DO NOT PASS "GO"
>DO NOT COLLECT $200

>>15207385
I'll believe you.
If only /sci/ used IDs.
>>15194609
Heh.
>There is much work to be done!
>This article is dedicated to...Ludwig Wittgenstein.
I guess someone didn't really understand Wittgenstein. Oh well, more publications must follow!

>>15194007
>you are cursed to never arrive at truth
Why?

>>15207420
Your answer is meta.
Think about it.

>>15207415
he passed last december

>>15207413
>LURKING
IN
>THE
Æther

>>15207443
Is that a good thing?

Anon, I need you to understand this by Monday morning. We are doing highly important scientific research in artificial intelligence, and your input is vital to the success of the project.
We're counting on you, Anon.
https://en.wikipedia.org/wiki/Actor_model
https://www.ijcai.org/Proceedings/73/Papers/027B.pdf

>>15207533
I'll get right on that as soon as a $50k grant shows up in my checking account

>>15207533
Fuck no
I can recognize that '68 "Mother of All Demos" style from a mile away
I ain't takin' no commie jobs
That iz sum Electronic Labyrinth THX-1138 shit rite dere m8
>I
CANNOT
>RELATE
2
>DIS
KOMMIE
>HATE
https://www.youtube.com/watch?v=yJDv-zdhzMY
https://archive.org/details/electroniclabyrinth

>>15207425
>Your answer is meta.
A bit yes. But >>15207420

>>15207603
because truth was defined to be that which you can never arrive at, and a "logical trick" was played on you to get you to think that it is natural or reasonable to play with a linguistic system that is nothing more than a parlor trick

>>15207603
If you have been tricked into believing that you will never arrive at truth, then you never will
because you clearly will never see through this trick
see through the trick, arrive at truth
very easy

>>15207614
>>15207621
So you've arrived at truth?

>>15207614
Not 'truth' in general, just ULTIMATE and complete mathematical truth. He didn't have an attitude that there were no truths at all. The opposite is true. He believed in apriorism, against the spirit of the time by the way.

>>15207614
He actually did specifically believe in accessing ULTIMATE truth, just not with REASON via a completely formalizable system. it's a good thing. There's always new knowledge/truths to search for because mind can bounce outside of these systems and gain new insights. pic related is interesting.

>>15207857
>>15207889
shockingly enough, metaphysical discussion is confined to /lit/ and /his/
if you want to do
>le forum topic creep
go to plebbit
by the way
I suggest you go to /lit/ and /his/ and read what the fine folks over there have to say about this.
You get
- retards
- child races
- idiots
- morons
- STEMcels
over here, and they just can't handle /lit/ and /his/
actually
most of them can't into Catholicism, either
they're stuck in child race Buddhism or Hinduism

>>15207857
>>15207889
>we should discuss the metaphysical beliefs of 2nd rate snake oil salesmen attempting to peddle their wares as "mathematical proof"
this actually isn't mathematics
it's some kind of sophistry or false argument
math isn't equipped to handle Gödel's anti-math tricks

>>15207857
>>15207889
Gödel is not part of
- pragmatism
- William James' theory
- criticism of metaphysics
and specifically the reference to "semiintuitionistic" in his 1938 publication is pure bullshit
https://www.pnas.org/doi/epdf/10.1073/pnas.24.12.556
this guy is full of shit, and people actually believe his lies
he went insane and starved himself to death for a reason

>>15207857
He's simply asserting
>this is a fact
>that is a fact
like a nazi thug or Rush Limbaugh

>>15207889
This is 2nd order snake oil. This is some weirdo listening to Gödel, thinking
>okay, now le math is le poetry
and then he tries to continue Gödel's snake oil cantos

>>15207889
>human beings can never formulate a complete and correct description of the set of natural numbers
presburger would like a word with you

>>15207889
Rudy Rucker is selling snake oil. He is working with Bruce Sterling, a sci-fi writer. It's a disgusting zombie bullshit experience.

>>15207889
I mean, you have to read the New Testament to understand that Jesus Christ peddled this goddamn fucking snake oil.
>Jesus is Lord
Yeah, right.
Jesus is talking like a snake so we can recognize snakes.
That's how we're going to use Jesus Christ.

>>15207927
>>15207942
>>15207947
>>15207953
all these words to cry about how this isn't math when if you actually knew the math you could just point to the glaring inconsistencies like >>15207948

>>15207889
You have to read the Holy Bible and browse /lit/ because people like Rudy Rucker are going to pull this bullshit and try to play philosophical homosex games with you and pretend it is
>le math
when it is not
>le math
at all

>>15207962
if it were math and I said
>it isn't math
then it wouldn't matter
clearly it does matter
so we can conclude that you are full of shit and trying to pretend that your bullshit philosophical theory worthy of Wittgenstein is math
you want to point at bullshit and say
>it's math
>you have to discuss it
but you're simply full of shit, and nobody cares
we don't have to discuss topics according to your schedule, nazi thug

>>15207962
you're trying to be a nazi thug
you're trying to push me around and tell me what to do
you suck
you suck hard

>>15207962
>if you didn't suck, you would do what I tell you to do
damn you're fucked up
you are a fucked up nazi thug
>FUCKED
UP
>NAZI
THUG

>>15207967
>>15207971
i'm not usually an advocate of antipsychotics, but you might want to give them a try.

>>15207927
>>15207932
>>15207942
>>15207947
>>15207948
>>15207953
>>15207959
>>15207964
>>15207923

>>15207976
we don't have a /med/ical board because 4chan doesn't want to encourage this idiotic speech
if you guy actually gave a shit about what you say
then maybe we could
imagine that
actually intelligent 4chan readers
you guys wouldn't know anything about that
why don't you shut the fuck up
and stop making it easy for 4chan admins to deny us a /med/ical science board

>>15207977
no, really. a consistent and complete description of the natural numbers is no problem, it just can't include multiplication
https://en.wikipedia.org/wiki/Presburger_arithmetic

>>15207366
Provability is purely an arithmetical notion. It's even been formalized in Theorem Provers like Coq.

>>15194084
Yeah, and that system consequently can't provide a complete and consistent truth, the same problem we had originally.

>>15207987
That wasn't meant for you, that response. it was a mistake to add that post in there. I have to read some of the sources from the article to get an idea of how it relates to the incompleteness theorems. I found this short thread on it
https://math.stackexchange.com/questions/2211149/presburger-arithmetic
Which included this interesting statement
>In your question you say Presburger Arithmetic "proves its own consistency". Really? It's provably consistent, as the wikipedia article notes, but isn't the proof done in a metalanguage?
At any rate. This all sends me on some interesting leads, so I will refrain from saying anything about the matter until I research it.

>>15207987
So are you more concerned with the phrase "the complete description of the natural numbers"? Because by that I he was meaning 'capable of proving all truths about the arithmetic of natural numbers'. And this would include multiplication. And so I don't see how this system could fullfill the the idea of the systems he was talking about. So it's supposed 'to decide ALL mathematical questions which can in any way at all be expressed formally in the systems concerned'.

>>15208061
>by that I he was meaning 'capable of proving all truths about the arithmetic of natural numbers'. And this would include multiplication
pretty sure that any number that can be constructed by multiplication can be constructed by iterated addition. all you're losing out on is existence proofs, so congratulations, you've discovered why existence proofs are controversial.

>>15208026
i would suggest you start with the wiki article on conservative extensions
https://en.m.wikipedia.org/wiki/Conservative_extension
there's a link to the same article in the top response to your question
tl;dr it's kind of a metalanguage but it can't say anything that the language itself can't say

>>15208026
as far as how it relates to the incompleteness theorems, most of the plain-language attempts to state the first theorem say something along the lines of "any sufficiently powerful...". this slips under the radar by not being powerful enough.

>>15208082
Thanks. I have run across this concept before, but I will research it in a much more comprehensive way.

>>15208085
I need to read some of those links at the bottom of the wiki article. I will have to wait until next time around to further discuss the matter when my knowledge base has increased.

>>15208026
If your system isn't capable of self reference (usually achieved via a version of the diagonal lemma (you can use it to proof botzh gödels theorems and non halting and other stuff)), you can have a consistent and complete theory.
Dan Willard studied such systems:

https://en.wikipedia.org/wiki/Self-verifying_theories

(Orig. papers linked in article)


The heart of these types of paradox is self reference

>>15208968
>Presburger Arithmetic
And so is Presburger Arithmetic is NOT capable of self reference?

>>15209139

Yes, you cannot form a gödel sentence in PB.

>>15209167
>Yes, you cannot form a gödel sentence in PB
Right, that's what I thought. And so going back to what started this little exchange between me and another anon, which was this pic
>>15207889
what is stated is true.
>that human beings can never formulate a correct and complete description of the set of natural numbers,
Because it was a given, as stated here
>>15208061
>So are you more concerned with the phrase "the complete description of the natural numbers"? Because by that I he was meaning 'capable of proving all truths about the arithmetic of natural numbers'.
But the reason this system of Presburger Arithmetic is not robust enough to be included in the sort of system Gödel idea's covered is not because of multiplication, but because of self reference?

>>15209190
Multiplication is the property that allows the system to self reference in this instance.

It's all explained in detail here
https://libgen.li/ads.php?md5=933a01c91ca78a2e6a8fcfdc9112274e

By the grand master of logic Raymond Smullyan

>>15209213
>Multiplication is the property that allows the system to self reference in this instance
So this anons post
>>15208069
wherein it is stated
>pretty sure that any number that can be constructed by multiplication can be constructed by iterated addition
Such a system is NOT capable of of self reference. Not to repeat the question I already asked and you answered, and I will read this book you suggested, I just want to be crystal clear and I will archive this thread so I can come back for reference.
>It's all explained in detail here
Excellent. I have heard of this guy and seen his name for sure. I already downloaded a file of this book that I was able to find online fre. It's a good thing as well, being that a physical copy is 150$. I get a boner from this stuff, so thanks for the lead. The subject is labyrinthine and endless like mentioned in pic rel here
>>15207889
multiplication can be constructed by iterated addition

>>15209249
i'm the anon who mentioned iterated addition. just wanted to point out that gödel incompleteness / tarski undefinability requires both a recursive binary operation (i.e., multiplication) and also logical negation (i.e., NOT statements). so you can keep multiplication as long as you're willing to give up proving negative claims.

>>15209356
Yeah, I think I am understanding the statements and claims involved in this sub set of exchanges in this thread between me and you and at least one other anon. Thanks for the clarification.

>>15194007
It boils down to something like " A mind with no outside input can't learn anything about how the world really works. " which is actually prety inane.

https://imgur.com/a/Gzp2Ile
This is the "Eye" document, and I've used it like Roundup herbicide on Gödel threads.
I wrote the document, and I'm the only person who does this.
I flunked out of Tom Sawyer's
>get the negro to whitewash the picket fence
school.

>>15210069
The "Eye" document formally distinguishes between a "simulated proof environment" and the enclosing standard of proof by differentiating the "logical deduction" of logic from the "true in a sigma-structure" for some signature sigma of model theory. It is the device for revealing Gödel's garbage proofs and garbage ideas as the garbage they are.
This is about anti-cancer.

>>15210076
There were no Gödel threads for a year because of the level of annihilation this document caused.

>>15210081
Gödel's trick is the following:
1. figure out what the "enclosing standard of proof is" a.k.a. "read my mind and the mind of every mathematician"
2. figure out that I'm lying and demanding you work in my formal system
3. import the standard of proof you painstakingly researched in part (1) and encode that standard of proof in the system I designed and transmitted to you in part (2)
4. Now you are forbidden from ever changing the enclosing standard of proof, i.e. science and math must stand still because if they do, then as my peon, you can say there is a complete and perfect simulation of the enclosing standard of proof at one meta-level deep.
This is why Gödel went insane. He's trying to take nazi thuggery to the blackboard.
You aren't going to make friends that way.

>>15210105
but u can
https://www.youtube.com/watch?v=xixnYk2lSjw
>BOOM
SHACKA
>AHHH
LAK

>>15204925
Gates... Super-genius who needs to hire programmers instead of super-genius-coding it himself.
Myth busted ...

>>15194007
>you are cursed to never arrive at truth
No, you can, just not analytically. Godel proved that math isn't analytic, thereby refuting logical positivism.
>It didn't need Gödel to arrive at the conclusion that "truth" is not something you can every be sure of.
That is not Godel's conclusion. Some truths are self evident. For example, that if equals are added to equals, the sums are equal.

>>15194019
He didn't say mathematics is incomplete, he said formal arithmetic is incomplete. He refuted formalism, not mathematics.

>>15194099
A word doesn't need to be defined to be meaningful. People know what the word apple refers to without needing a definition.

>>15211085
That's like saying a warrior refuted the sword he was using because he fucked up his battles and got hurt.
Part of the problem with Gödel is that he doesn't give any idea how the way proofs are accepted and rejected in reality...in particular the evolutionary fact that what was proof n years ago isn't necessarily proof today...should be modeled mathematically
In short, Thomas Kuhn killed Gödel.
Gödel is just lying about the amount of work he's doing. If he had done the work, he would have been drawn into what is essentially
- machine learning
- agent based calculations (complex adaptive systems)
- artificial life simulations
- introducing errors into candidate proofs and candidate proof verifiers
If Gödel had done the work he claimed to have done, then he would have revealed a rich and vibrant world of "proof accepting machines" that are indeed evolving...he didn't do the work; he waved his hands, and publishers printed the work he submitted

Gödel: The Freud of Math
>available now as a Bantam paperback for $12.95 from fine booksellers all over the world

On the topic of truth, we could argue that Conrad-Orwell-Pinkwater represent a kind of "Thothian truth" intended for the grim task of separating the humans from the animals.
There is a triumvirate of
- Heart of Darkness
- Shooting an Elephant
- Lizard Music
that track various technology separating humans from animals, Thothian tech
ThothTech™

>>15211148
what unites these books is the educators will say "it's about metaphor" and that's a lie
they're all about SHIBBOLETH https://www.youtube.com/watch?v=ZcnhRYSIaf4
and you have to read Kim by Kipling in order to understand the Great Game / British imperial warfare context

>>15211152
skip 1994, forget about it
>Nineteen Ninety-Four never happened
https://www.youtube.com/watch?v=zsrtPvKey-U
Soviet communism falls in '89, leaving only confused chink nazis who think they're commies
five years later, all Western youth get hosed with Disney's paean to communist brutalist racial hierarchy
>Nineteen Ninety-Four: the Year the West Went Soviet
and somehow this has nothing to do with
- truth
- evolution
- metaphysics
>oh no, don't tell the kids that
>you'll spoil the fun
>let them watch the nice film

>>15211164
SOVIET COMMUNISM FALLS BUT WESTERN YOUTH ARE FORCED TO ENDURE THE SECURITY ARRANGEMENT CREATED BY THE CRAZY LOSERS IN FORMER SOVIET COUNTRIES INSTEAD OF MURDERING EVERYONE THAT GETS IN THE WAY OF EXPANDING WESTERN IMPERIALISM
>WHAT
THE
>FUCK
https://eyeofutopia.bandcamp.com/track/twelve-links-of-dependent-origination
Now I'm an adult Westerner, and I want people murdered for the crime of refusing to impose Western imperialism on former Soviet countries at top speed.
That's truth.

>>15211183
It's important to understand what Western imperialism is. It is simply letting Westerners travel to your country, talk with your people, exchange culture, eat drink and be merry.
That is Western imperialism.
That is what you fucking child races have been opposing this entire fucking time.
Bleak & depressing communist brutalist racial hierarchy is developed in the West.
It is then tuned to be acceptable and palatable for an international audience.
The West took up the Bolshevik's burden and ignored the White Man.
Here is George Lucas taking up the Bolshevik's burden: https://archive.org/details/electroniclabyrinth
If you ignore the extent to which the Bolsheviks stole the work of taking up the White Man's burden, then fuck you.
https://archive.org/details/call_it_sleep_situ
Let me ask you: what is more important: the jews or the child races?
Who do you hate more? The Jews? Great, put yourself in pile (A)
Who do you hate more? The child races? Great, put yourself in pile (B)
I go in pile (B)
jews are weak
child races are strong
strong child races manipulate weak jews
don't hate the tool the child races are using to hurt you
hate the child races for being goddamn fucking children

>>15211114
>That's like saying a warrior refuted the sword he was using because he fucked up his battles and got hurt
no, it isn't
>If Gödel had done the work he claimed to have done, then he would have revealed a rich and vibrant world of "proof accepting machines" that are indeed evolving...he didn't do the work; he waved his hands, and publishers printed the work he submitted
It's going to apply to any machine, see pic

>>15204982
>xx = xy

>>15212623
So you're refusing to admit the importance of this line:
>but it can only be finitely long
This line is absolutely crucial. It is the crux of the matter.
By introducing "finite" the author does the following:
- attempt to suggest that "finite" has already been defined as a mathematical concept when it has not
this is selling a very specific brand of snake oil to the reader, namely "Appears to be genuine math but is not genuine math, more like philosophical poetry than math"
Using a term from math that does not have a standard definition, falsely claiming that an undefined math concept applies to the entire world, this is sophistry that should be refuted with philosophy on /lit/ and these sorts of linguistic tricks are a matter of philosophy, not mathematics.
That line contains the entire "haha I got you to believe this is math" trick.
You have to believe the real world is subject to mathematics in order for this trick to work, i.e. it's a con to get you to believe something false.
You say "the real world obeys math" but you won't say what math is.
That's the problem.
It's a recursive problem.
Math is about ignoring these childish self-referential tricks.
Gödel starved himself and went insane.

>>15212623
This is not mathematics.
This is not science.
Take it to /lit./

>>15212623
this is the opposite of math
this is about introducing undefined terms and pretending they have definitions
then playing tricks on the reader and defining some of the undefined terms
this is about idiot playing tricks on each other and tricking editors into publishing crap

>>15212623
Rudy Rucker claims to be a mathematician, but
>LOOK
AT
>THIS
FUCKING
>GARBAGE
This is bullshit. Rucker can get editors to send this fucking bullshit copy to the printers.
He is a charlatan, not a mathematician.
Fuck Rudy Rucker.
Fudy Fucker is more like it!

>>15212623
Math was invented because asshole magicians like Fudy Fucker wouldn't explain their tricks.

>>15212623
Fudy Fucker won't explain the trick because he fears he won't be able to sell books if people think his books are boring exercises instead of stimulating mysteries...he is selling popular anti-math books, not math textbooks

>>15212698
You don't have to reply with 50 posts of nonsense. Next time I see a sort of thread sliding post with your style in a Gödel thread, which is a weird dis-jointed sort of spastic style with nonsense attention seeking provocations, I will just know that there exists some goofball who doesn't like Gödel and who will try to shit up and slide the thread. And so next time I will just ignore your posts.

>>15212623
see
>>15194019
you can see quite clearly now that Gödel is trying to falsely claim that your ability to accept or reject a proof is
(A) subject to Gödel's theory
(B) completely determined ahead of time
in short, Gödel is claiming you're a robot
the problem is in demanding that your ability to accept or reject a proof is finite
Gödel is demanding that your decisions be subject to his theory.
Can you see why he had this personality?
Can you see how this personality affected his life?
Can you see how this personality contributed to his mental illness, starvation, and death?
It's basically evil.
It's a sick, rapey trick.

>>15212708
Gödel was a really nasty person.

>>15212708
I don't like the fact that a whole bunch of idiots are saying this nasty man did nice things.
No, Gödel was a nasty man.
Gödel did mean things.
He was not a nice man.
Gödel played tricks on people.
Gödel was a nasty man.

>>15212708
There are a lot of bullies in academia that think Gödel was okay.
No, Gödel was an asshole.
Gödel fucked things up.

>>15212708
>I like Gödel, and I want to be an asshole bully.
Good for you.
Now get the fuck out of here.
Thanks for sharing.
>Not.

>>15212805
You people don't understand the depth of Gödel's stupidity.
He was a stupid bully, and he played nasty tricks on people.
He was a nazi thug.

It would be such a nice thread without the poltard anon.

Can't wait to have an NN browser extension for this type of semantical content blocking

>>15212970
>NN browser extension
When (large) NNs become feasible on a CPU (rather than GPU) this will be possible. Currently NNs are limited by the necessity to compute a large amount of dot products and CPUs are notoriously inefficient for doing "parallel" calculations.

You don't need NNs for filtering though, since 4chans native extension already allows regex filtering, which I believe is more efficient than NN will ever be (remember NN is just used to extrapolate data, it's not that useful on its own). NN based filtering would involve a large amount of samples (inefficient), while regexes are easy to write (efficient).

I dont think his proof really indicates much about actual trueness. I think it is a cool proof with some cool math that doesn't actually correspond to the nature of truth.

>>15213017
> You don't need NNs for filtering though, since 4chans native extension already allows regex filtering

Yeah i know all that, I use regex extensively alongside adblocking (ofc) and this NN based NSFW filter here https://addons.mozilla.org/en-US/firefox/addon/wingman-jr-filter/

Works well for me - so much less shit that reaches my conscious attention stream :)

>>15212970
You people don't realize what a nasty politician and snake oil salesman Gödel is.
It's shocking how uninformed you are.
You guys are really dangerously stupid.
You should browse /pol./
There are other dangerously stupid white supremacists over there.

At the end of the day, you guys just want Gödel to tell you that you can be a circus freak and everything is going to be okay.
It's mind blowing.
You want to run away from home with Gödel.
He's the fucking antichrist.

>>15212970
>>15213017
>>15213042
>he literally suggests that he is going to get a computer to make him weaker when it comes to reading
you guys are so fucking fucked it's unreal
you're literally asking a computer to make you pathetic & weak
>HOLY
FUCKING
>SHIT
it's like you're fucking afraid of pain or something
fuck
>GET
OVER
>IT

>>15213188
Keep serving us delicious entertainment jester!

>>15204866
I love this comment, holy shit.

>Jech never defines "proof". He switches from math to poetry at p. 157. (Jech "Set Theory" 3/e)
>>15212805

>>15213190

>>15214960
So, I should explain. This is
https://en.wikipedia.org/wiki/Rectification_of_names
vs.
https://en.wikipedia.org/wiki/Pumping_lemma_for_context-free_languages
It's a specific formula for schizobabble
So we can surmise that Confucius brought up rectification of names because someone was feeding him chained definitions out of a can, and of course this is very frustrating.
In modern math terms, the practice is to claim that X has a definition, then when a definition of X is requested, define X in terms of Y and claim Y has a definition.
It's a definition shell game.
>where did the definition go??
>you're an idiot if you don't know!!

>>15215022
by the way
this is a case of academic fraud
see
>>15215073

>>15215228
here is the thread with the details of the fraud case
>>15215294

>>15216084

I love Godel posts. They draw out the fedora-wearers like flies, so they can practice their wordy babbling of simple ideas.

>>15215022
here are some definitions of formal proof systems tho
https://www.cs.bu.edu/faculty/kfoury/UNI-Teaching/CS512/AK_Documents/Formal_Proof_Systems_for_FOL/main.pdf

>>15204866
underrated post

>>15204872
no he defines it in Chapter II.1, at least in the newer version