/lit/ - Literature

>>18819878
logic = Spook

>>18819878
analytic philosophy is sophistry

>>18819916
Socrates was king of the Sophists.

You can't be a shit cunt bantistani if you can't fuck analyticals in their own arsehole. If you need more inspiration watch this video regarding flipping cunts with their own Jabroni logic and getting their asses back over here: https://xxx.tubedare.net/video-i6wb5e3/lords_of_the_lockerroom_boss_of_this_gym_

>logical operators
>laughs in incompleteness

>>18819943
Gödel (pbuh) knew exactly the importance of logic for philosophy.

>>18819878
Reject the false dichotomy; choose the third position and become a theologian

>>18819969
Theology is the first position. Philosophy is for the second class of mere aristocrats.

>>18819943
Yeah let's just stop doing mathematics because it's incomplete right? ? ?
I can't stand normies that think that Gödel somehow invalidated mathematics and mathematical logic. It's like saying Turing made computers obsolete by proofing the Halting problem.

Logic is merely a tool. It demonstrates nothing on its own. Stop fetishising it.

>>18819943
Do you even know what mathematical incompleteness means? It is a trivial result "proved" with convoluted logic... later co-opted by writers and philosophers to derive all kinds of results and meanings with a little wordplay.

>>18819987
>I can't stand normies that think that Gödel somehow invalidated mathematics
Who's saying that? He certainly BTFO the naive FACTS AND LOGIC positivism in OP

>>18819987
Both those are true; and foucault//chomsky on language. Simulationism. Cogito being limited to cognition not identity.

Proof is "special," not normal. Normally we get proof with contingent agreement on givens.

>>18820015
All meanings are derived from a little wordplay. Think about it

>>18820015
Sounds absolutely based.

>>18819985
True. Well, read theology in any case. Plus, there is a bit of an academic movement nowadays in theology ("Radical Orthodoxy") which hopes it can restore some notion of truth to the world after all the epistemic doubts of the last century by offering an alternative. It's not very convincing though.

>>18820023
And...? If someone with some pull and connections "derived" some other result completely trivial but superficially deep result in mathematics, "philosophers" would be all over it, trying to co-opt it to whatever their interest and agenda.

>>18820006
>Language is merely a tool. It demonstrates nothing on its own. Stop fetishising it.

>>18820023
YOU NIGGAS WANT WORDPLAY
BUT I'M BOUT BIRDPLAY
FIRST OF THE MONTH YA WE CALL THAT BIRD DAY

>>18820023
And...? If someone with some pull and connections "derived" some other completely trivial but superficially deep result in mathematics, "philosophers" would be all over it, trying to co-opt it to whatever their interest and agenda.

>>18820006
>Math is merely a tool. It demonstrates nothing on its own. Stop fetishising it.

>>18820043
How is something superficially deep? Being "superficial" is the complete opposite of being "deep".
Your wordplay needs some work.

>>18820069
It means it looks deep, but isn't.
You required me to explain this to you.

>>18819943
You just outed yourself as a logiclet. Gödel himself proved that first order logic is complete. The incompleteness theorems refer to aritihmetic.

>>18820006
>>18820035
>>18820049
Cognition is merely a tool. It demonstrates nothing on its own. Stop fetishizing it.

There is only the Absolute, and the Spirit which is the Absolute viewing Itself as absolute otherness, sublating this difference, and returning to Itself as Its self.

>>18820006
My penis is merely a tool. It demonstrates nothing on its own. Stop fetishising it.

>>18819878
Discrete mathematics was probably the easiest course I've ever taken.

>>18820043
We WILL misunderstand your tinkerings
We WILL ignore the implications of your work
We WILL continue doing whatever we were doing before
You WILL be unable to stop us
We WILL define your ideological boundaries for you so you are unable to act in ways that hinder our praxis

>>18819878
I agree everyone should know FOL, especially if studying philosophy, but they should just get the mathematicians to teach it. Philosophers aren't the best at teaching set theory or logic, and the topics really don't require any mathematical background.

>>18820006
Who said otherwise? You need both tools and materials to build anything.

The only thing confusing about logic is the formal notation system.

>>18820077
sounds like a problem with the beholder, not the beheld

>>18820295
>Cognition is merely a tool. It demonstrates nothing on its own.
>There is only [proceeds to describe products of his cognition]

>>18820015
The incompleteness of arithmetic isn't a trivial result, at all. It ended a longstanding research program into the foundations of math, and allowed for other avenues to be pursued.

It was also absolutely proved, no scare quotes.

>>18820599
A former philosophy major described a logic course he had taken as the first third of Discrete.

>>18820741
Ok then. Tell me the 2 results of Godel's incompleteness theorems in a clear and concise fashion (to avoid arguments about definitions and to avoid word games).

>>18819987
>>18819969
I'm going to college soon and want to study theology and mathematics/physics together. What am I in for?

>>18820718
Fine then. Answer >>18820765

>>18819969
Keep in mind that I don't know shit about theology, but doesn't God non-statue as an object in the universe mean he/it can't be treated with logic or the conventional rules of thought? Isn't that why mystical experience is impossible to articulate?

>>18820765
1) You talk like a fag
2) You're shits all retarded

>>18820295
>There is only the Absolute, and the Spirit which is the Absolute viewing Itself as absolute otherness, sublating this difference, and returning to Itself as Its self.

Hegel is proud.

>>18820765
*sweats, pulls GEB from shelf*

>>18820792
GEB is a philosophical work that co-opts a simple mathematical result into endless speculation and discussion about "the nature of things". Much like the co-option I talked about earlier.
I asked you to state the 2 results from the mathematical derivation. And not to prove my superiority or anything, just to show they are extremely trivial. But of course you can say "oh it took us such mathematical sophistication to prove things we take for granted".
So state the 2 results in clear and concise language.
>>18820787
Down to the insults? I don't mind. Do me (and yourself) a favor. Go through the actual mathematical derivation and the results that follow. Not second and third hand info about the theorems, especially from "philosophers".

>>18819878
A doesn't always equal A, true contradictions exist:
https://plato.stanford.edu/entries/dialetheism/

>>18820819
>Go through the actual mathematical derivation and the results that follow
Who gives a fuck about that shit other than nerds? All I care about is, one of the nerds proved the other nerds wrong, so we don't have to worry about what the nerds say.
>muh mathematical derivations
Do you listen to yourself?

>>18820599
>Discrete mathematics
Is this still the king?

>>18820836
I trust your judgement. So tell me what exactly did Godel prove wrong about other nerds.

>>18819878
That book doesn't exist. It's parodying Russel and Whitehead's Principia Mathematica which took an insane number of pages to get to the proof of 1+1=2, but that's only because before they could get to basic natural number addition they had to explain and justify the choices they made for their own logic.

>>18819943
Incompleteness theorem refers to any axiomatic system containing Peano axioms. His inconsistency theorem is more interesting, where an axiomatic system cannot prove that it isn't contradictory somewhere. This means people need to essentially find an interpretation of an axiomatic system irl which contains the axiomatic system you want to prove consistent.

>>18820019
You have absolutely no idea what you are talking about jfl

>>18820006
>Logic is merely a tool. It demonstrates nothing on its own.
Every propositional tautology and contradiction would like to have a word with you.

>>18820934
>So tell me what exactly did Godel prove wrong about other nerds
I don't know, and don't really care. Why would it matter?

>>18821055
Why are you in this thread then? To shitpost and berate every other poster?

>>18820767
Schizophrenia

>>18821004
Second part is correct. You didn't state what mathematical incompleteness means. Hint: it has nothing to do with the common english definition. So all pop culture versions of Godel's theorems that say something like "our knowledge is always going to be incomplete" is wrong, but it is the version that most "philosophers" use because it makes for interesting discussion and assimilation into their own bodies of philosophy?

>>18819878
Imagine bragging about being able to do logic.

>>18821064
He probably is; that's the biggest issue I think on boards like these, you just get people trying to tear you down and there's really no way to tell them to fuck off.

>>18821072
Well, by my recollection Cantor, Gödel, and Grothendieck were all metaphysically/spiritually inclined mathematicians who died in mental institutions or with some kind of mental illness. That said, I take solace in the fact that I have only a minuscule fraction of their intellect at best and this will prevent me from going schizo.

>>18820765
(I'm the guy you were responding to, the people who responded to you with insults aren't me)

Okay. To be concise, I'm going to assume you know what logical completeness and consistency are.

Any logically consistent system of axioms which describes arithmetic over the natural numbers (zero plus the integers), there will always be true statements within that system whose truth is not provable through the axioms of that system.

Further, any such consistent logical system as the one described above is also unable to prove its own consistency.

The result was significant in how it altered the research programs within logic and the foundations of math at the time.

There's also a nice computational interpretation of the results, which can be summed up as: for any computer program which outputs statements about arithmetic, that program will either produce untrue statements, or fails to produce all true statements, given enough time.

Because I see you deriding philosophers below, I'll mention that I learned the theorem in a course on logic taught in a math department. I read a lot of philosophy in high school, though I have a low opinion of most of the stuff from after about 1930 now. I was trained in physics and math.

>>18821178
Based upon the way you write I wouldn't be so sure. Diagnoses of schizophrenia tend to be based upon misunderstanding rather than an actual "illness" however, so as long as you pace yourself you should be fine. And stay away from psychs. Meditation helps if you get a bit too manic.

>>18821193
Excellent.
Few questions:
1. Related to the second result, isn't this just a triviality? This has been assumed ever since western logic was formulated (and even older in the east). It has been taken as a granted. Sophistry usually revolves around self-evidence and self-proof. The fact that it has been mathematically "proved" is an achievement, but it is still a trivial result.
2. Related to the first result, Godel's theorem can be extended to all 1st order logic systems too. Not just arithmetic. And it says it is possible to construct "paradoxical" statements from a sufficiently complex system of statements that are unprovable. Not true statements. But sure, you can argue the contra-positive statement too. That aside, isn't this another triviality that the Greek's avoided by avoiding self-reference? Or if they didn't it usually led to a clever "paradox" to give some insight upon solving it. Again, this is something we take for granted and it is a mathematical achievement to prove it.
3. Your example about computers is another triviality. A system of statements that allows for self-reference or back-reference can have infinite combination of statements that are true, making it impossible to produce all of them. The production of untrue statements by a computer is impossible unless you program it to produce the combination statements that evaluate to false.
I deride a specific group of philosophers who are interested is endless discussion and promoting their careers or an agenda by co-opting statements from other field completely out of their context. Like mathematical completeness is taken at face value to mean instead "we can never have a complete body of knowledge, we are doomed to permanent ignorance". Or metaphysical self-reference word games that lead nowhere except perhaps make for interesting discussion.
My point is that when people post shit like >>18819943, they are taking the second hand and nth hand versions of the original meanings that have been mangled to mean something else entirely and end up looking fucking stupid.

>>18821336
>that have been mangled to mean something else entirely
Those meanings are as valid as your own dumbass
Phallogocentrists getting exposed hard in this thread

>>18820827
Wrong. The only way 'A' could equal 'not-A' is if 'not-A' was defined to be 'A'. In which case, A=A.

>>18820032
There is no truth in this world, the only truth is in our Lord and Savior Jesus Christ

>>18819907
Is this logically true?

>>18821078
Incompleteness means not all sentences in a formal system can be proven true or false.

>>18821356
>Phallogocentrism
Lmao.
>Those meanings are as valid as your own dumbass
Then those philosophers can state their initial statements in a vacuum and proceed from their. They instead choose to explicitly use Godel or Russell or whoever else to lend credibility to their arguments, which might not be believable and be exposed to more scrutiny had they not done so. It is about selling books, promoting their careers and/or an agenda.
But eh what am I doing arguing in good faith with you? Carry on.

>>18821407
Exactly. See >>18821336 and >>18821409
for my problem with these "philosophers".

>>18821336
>Related to the first result, Godel's theorem can be extended to all 1st order logic systems too. Not just arithmetic. And it says it is possible to construct "paradoxical" statements from a sufficiently complex system of statements that are unprovable.
Nice way to say you dont know what youre talking about.

>>18821336
No, the fact that logical systems are unable to prove their own consistency was not assumed since 'western logic' (whatever that's suppposed to mean, syllogistic logic from the Classical period is extremely different from the misleadingly-named classical logic, which was developed in the 19th century) was formulated.

I'm unaware of any definition analogous to 'consistency' in eastern philosophy.

Godel's incompleteness theorem CAN NOT be extended to any system of first order logic. In fact, Godel's completeness theorem proves that first order logic IS COMPLETE. This is part of why the incompleteness theorem is fundamentally non-trivial.

The fact that you didn't understand this shows that it's non-trivial, and the fact that you thought the incompleteness of first order logic is "something we take for granted" speaks to the profundity and importance of the theorems.

My example about computers isn't trivial at all, and the fact that the theorems were proven before digital computers even existed, or Turing completeness was defined, are evidence of their importance. In fact, they were pivotal in establishing a mathematical definition of computation, without which we wouldn't have the digital computers of today.

Your statements about computers show that you really don't understand the incompleteness theorem, or even the definitions of completeness or computability.

"The production of untrue statements by a computer is impossible unless you program it to produce the combination statements that evaluate to false." is a simply incorrect statement, and the bit about the impossibility of producing every true statement because there will always be more (a form of a diagonal argument) shows that you don't understand what computability or decidability are -- I suggest looking into this before talking about this topic further.

I agree that the person who posted that Godel image is retarded, and I'm also happy to deride philosophers, though for different reasons than you (I actually understand their arguments, for one).

I don't know of any philosophers who misinterpret the incompleteness theorems in the way you're describing. Many of the better philosophers are very mathematically literate, though I still think they're wasting their time for the most part.

>>18819878
>not a philosopher
>can't do logic
No shit Sherlock.

>>18821427
Yawn. Fuck off to some other thread and shitpost there.

>>18820827
This makes no sense. That a=a is true by virtue of the definition of "=". It's like if I was to define a symbol "#" such that #a is true for any a. If you were to say #a was false for some a, you would be wrong by definition. The only way you could argue against this is:
1. Say you can't define things and create definitions, in which case nothing you say has any meaning and I acn ignore your post, or
2. You change the definition of "=" so that it means something that no one else takes it to mean.

>>18821445
My bad. I meant 2nd order logic. You even stated his first theorem wrong. You said that some true statements will be unprovable. But the first theorem states that it is possible in a sufficiently complex system of statements to create a paradoxical statement (ie neither true nor false) that cannot be proved by that system. But we'll move past that.
> fact that logical systems are unable to prove their own consistency was not assumed since 'western logic'
>The fact that you didn't understand this shows that it's non-trivial, and the fact that you thought the incompleteness of first order logic
False. Self-evidence has always been taken as sophistry. This is something that has always been taken as a granted. It has been formalized only recently. Doesn't mean it didn't exist prior. It has existed forever. The only place where self-evidence has been allowed historical is pure metaphysics and religious apologetics.
>My example about computers isn't trivial at all... without which we wouldn't have the digital computers of today.
False again. Turing completeness has nothing to do with Godel's theorems. You even created a nonsense example of "computers being able to produce either untrue statements or being unable to produce all true statements", which is retarded because, like I showed, it is impossible for a computer that generates all the true combinations of a system of statements to produce a false one as it has been programmed that way.
>even the definitions of completeness or computability
Lmao YOU since when did computability have anything to do with the 2 theorems of Godel?
> I suggest looking into this before talking about this topic further
No I suggest you really understand what you think you were taught. A lot of university courses are designed to get through the syllabus and not much else. The proofs that the lecturers choose are often the most convenient, even if they gloss over the entire theory. Same with special and general relativity taught in university.
> though for different reasons than you
What are these reasons. Please articulate.
Or perhaps even you are a product of nth hand information and you have just swallowed it whole without once taking a step back and actually thinking about it.
Whatever. No skin off my back. No personal attacks. Just discussing the point, which you couldn't help but make personal.

>>18821427
It's true, they really exposed themselves there. You're not shitposting.

It's honestly amazing to me how people will just stake out positions that they have no actual justification for. "The incompleteness theorem can be extended to all systems of first order logic" is straight up untrue, and something (the completeness theorem) one should already be well aware of before even talking about the incompleteness theorem.

That person just needs to stop talking shit on 4chan, and just get a fucking textbook and work through it.

To anyone that's interested, here's a textbook that ends with the incompleteness theorem and will take you all the way through from scratch:
https://www.ibisc.univ-evry.fr/~belardinelli/Documents/Logique/Mathematical-Logic-ChiswellHodges.pdf

Do the exercises!

>>18821522
>You said that some true statements will be unprovable. But the first theorem states that it is possible in a sufficiently complex system of statements to create a paradoxical statement (ie neither true nor false) that cannot be proved by that system.
That isn't what his first theorem says jfl. You don't even know the meaning of completeness.

>>18821536
Ya my bad. Forgot the difference between 1st and 2nd order logic. Everything else I say is true. See >>18821536.
But of course, you will use my one slip up to discredit everything else I say.
Whatever man. Again, no skin off my back.

>>18821559
No retard. That IS what the theorem says. That is is possible to construct paradoxical statements in a sufficiently complex system of statements. Seems like you haven't actually thought for yourself. You just took your uni text book's derivation at face value and ran with it. Like I said earlier, many derivations presented in such courses are the most convenient ones to be able to cover the syllabus fast. Same with other advanced math and physics concepts. But sure insult me some more.
>You don't even know the meaning of completeness
Yes I do. This has been made clear by my multiple previous posts. Clearly if a paradoxical statements is impossible to prove within a system of statements, then that system of statements is incomplete. But you just say this to try and discredit me. Eh. Ok.

>>18821193
I think the problem that arises most often in understanding Godel's proofs is that the "primordial" notions that are of relevance/concern in understanding them, like consistency and completeness, but also "true statements" and their relation to axiomatic systems, are not universal but are specific to late 19th and 20th century understandings of logic. And much more specifically, to the commonplaces of mathematical foundations discourse at that time. But analytics think they are and speak as if they are perennial and simple notions.

For philosophically inclined people coming from other approaches to philosophy, it is confusing to hear these multivalent and loaded words, like "truth," but also "statement," used as if they have a self-evident and simple meaning. Let alone all the other taken for granted conceptual baggage like "computation" and "computability."

A continental would have an easier time understanding Godel and his importance if he spent a little bit of time studying the presuppositions of people like Dedekind and Peano, Frege and Russell, and early set theory in general. For example
>The formalization of arithmetic (the theory of natural numbers) as an axiomatic theory started with Peirce in 1881 and continued with Richard Dedekind and Giuseppe Peano in 1888. This was still a second-order axiomatization (expressing induction in terms of arbitrary subsets, thus with an implicit use of set theory) as concerns for expressing theories in first-order logic were not yet understood. In Dedekind's work, this approach appears as completely characterizing natural numbers and providing recursive definitions of addition and multiplication from the successor function and mathematical induction.
This kind of thinking is just foreign to traditions that don't presuppose it like the contemporary analytic tradition does. But once you understand the conceptual undergirding of a paragraph like this, you are most of the way to understanding Godel's presuppositions and thus the impact his ideas had on other people WITH those presuppositions.

At least that is how I would recommend approaching it if you are continentally or otherwise epistemologically inclined and were not reared with analytic jargon.

>>18821584
Do you want me to fucking quote godels paper for you? Like you are blatantly wrong. There is no arguing on this, Godel's first theorem has nothing to do with constructing paradoxes, it has to do with constructing an unproveable sentence.

Logic is obscurantist. All true philosophy is immediately true.

>>18821522
I didn't misstate his first theorem at all, the statement isn't 'paradoxical' (a technical term you are abusing) because it can't be proved by the system.

You clearly didn't mean 2nd order logic.

Self-evidence is a non-technical notion. Be clear about what you mean and we can actually have a discussion then. If you mean it in the sense of 'self-evident truths' or something like that, that's a notion that's very different from consistency or completeness.

> Turing completeness has nothing to do with Godel's theorems
I don't know where you got this idea. The incompleteness theorems were instrumental in defining computation and computability mathematically, absolutely nobody would say otherwise.

Your example you gave didn't 'show' anything, you just made a (false) statement, one which demonstrates you don't get what the incompleteness theorem means. Again, just learn logic from a math textbook, you'll figure out why you're wrong.

>Since when did computability have anything to do with the incompleteness theorems
You have to be trolling, right? The halting problem is undecidable because of a direct consequence of the incompleteness theorems. Why continue to talk about stuff you don't have the slightest clue about? Literally just Google 'Godel incompleteness computability' before making retarded claims like this.

>>18821598
We should both stop arguing with this idiot, he doesn't even know the basic definitions necessary to discuss this productively.

>>18820295
Daily reminder that Hegel was literally Satan/The Demiurge taking human form and unleashing mental poison into the planet. If memes are like viruses, Hegel is Ebola mixed with AIDS mixed with small pox.

>>18821625
Nah.

>>18821598
Exactly. A paradoxical one is one that is unprovable. It paradoxical sentence is NOT true like you said. It is a self-referential or a back-referential sentence that is neither true nor false.
It is a variation of the liar's paradox, like the sentence "I am lying". This is an unprovable statement that is neither true nor false. It is a paradoxical statement. It is NOT like you said, it is NOT a true statement.
Clearly you haven't actually understood shit from the theory and just took your uni's textbook derivation at face value. You didn't even think beyond what it said, almost like you just memorized the final result and repeat it.
Holy fucking shit.
And I'm sure you'll take this as a personal attack and say some other snarky thing again, or bring up my 1 slip up that I forgot the definitions of 1st order and 2nd order logic and mixed them up.
>and I'm also happy to deride philosophers, though for different reasons than you
And let's not forget, THIS was the where the argument was going. So tell me what are your reasons.

>>18821382
>the only truth is in our Lord and Savior Jesus Christ
can you prove it beyond reasonable doubt?

>>18821619
>>18821612
No anons, both of you clearly haven't actually understood shit from the derivation and the theory. The halting problem has used Godel's theorem as part of its corpus of proofs. It doesn't itself prove anything related to the halting problem. It just created a convenient notation to use previous order operations as symbols in higher order operations. Clearly you are also another one who memorized this stuff from a variety of n-hand sources.
And no, doubling down on what you read about computation doesn't constitute an argument.
And clearly I did mean 2nd order systems because I mention multiple times "self-refernce" and "back-reference" which is only possible in 2nd order systems. See? I knew you would bring this up to discredit and deflect everything else I said. But you didn't even have an argument for everything I said. All you anons have done is some variation of "but what you said is false". Fuck it. Clearly I'm arguing with people who take their text books results and memorize them, only to repeat them endlessly.
My point still stands:
1. Godel's theores are trivial but formalized.
2. Most of what you know about these theorems is cannibalized versions of them, or simplified textbook versions of them
3. Anyone who uses Godel, or any other such result completely outside of the context in which it is defined is retarded.
Cya folks. Hopefully the anon's who haven't understood the first theorem will actually work through them and get its true meaning some day.

>>18821643
Love it, Godel's Incompleteness Theorem is a variation on the Liar's Paradox.

You literally do not understand the definition of completeness if you think the notion that a True statement cannot be provable means that the statement is neither True or False (which, again, is not a paradox).

>>18821710
Oh my fucking God. You fucks really haven't understood shit. You just repeat your uni textbook talking point forever.
Fuck it. I'll try a different approach.
Construct a sufficiently complex system of statements (which Godel doesn't define too well, but a convenient example is a system that allows for self-reference or back-reference). Make it about 10 or so axiomatic statements.
Now try and construct, as per your version of Godel's first theorem, a true statement that is also unprovable.
Next, work through the proof carefully and show where the final unprovable statement is taken to be true. And really work through your uni's textbook derivation, because 100% that the constructed statement isn't assumed or proved to be true, and if it is, one of the previous steps in the derivation wasn't a correct one, but merely a convenient one designed to get students through the course.
But I know you won't do this. You will instead repeat the same think like a retarded pokemon.
Like I said, no skin off my back.

>>18821703
I never claimed the Godel's theorem alone proved the halting problem's undecidability. Just read the Kleene paper and you'll know what I'm saying.

Your statement of "creating a convenient notation to use previous order operations as symbols in higher order operations" is barely coherent.

You can't seriously suggest that computability has nothing to do with the incompleteness theorems, it's just retarded. Read the original Church paper from 36 and tell me computability has nothing to do with those theorems (not from a textbook, the original paper by Church himself).

Ditto for the 43 paper by Kleene.

I've read the original versions of the theorems, but a proof is a proof, and a 'cannibalized version' whatever that's supposed to mean, still proves the theorem.

>>18821758
contd...
A paradox is defined by a self-contradiction. WHICH MEANS NEITHER TRUE NOR FALSE, or both true and false... which means neither true nor false. Again, what the fuck did you actually understand when learning this stuff bro?
Whatever. Cya fucks.

>>18820019
You are the person we're talking about. Nothing Godel did is in any way a reply to OP, and Godel himself would probably agree with OP.

>>18821783
Ok final answer...
I have the kleene paper opened in front of me. It is literally as I described. It used the notation to subsume lower order logic as an operand in higher order logic systems. Which is exactly lambda calculus. The incompleteness proof itself has no bearing on the kleene paper. So what the fuck are you on about bro? What the fuck does this have to do with comparability? Do you even understand these theorems or do you repeat what you memorized for n-ary sources? Ok, i'll go even further this time. Since the second theorem states a system of statements (say A) cannot prove itself, a higher order system (say B) that has A as a subset must be necessary to prove A. So lambda calculus is used to prove a particular mathematical operation by creating higher order mathematical operations and seeing if it provable. Provability isn't computability. Neither does it have anything to do with the halting problem, except maybe being mentioned in passing in literature surrounding it.
I mentioned multiple times what I mean by textbook versions of the proofs.
Ok I'm done. Bai bai.

>>18821758
Godel defines it extremely precisely, he's talking about Peano arithmetic, which is why the notion of "truth" is relevant here -- in his own paper, the original proof, he applies the provability relation to N (natural numbers, this board doesn't have latex). Truth is a model theoretic concept, and Godel was working within Peano arithmetic when he did the proof. The proof clearly states that there are true statements which are unprovable.

I don't need to do what you described, because Godel himself does so in his proof, along with the famous Boolos version of the proof in 98.

>>18821859
This isn't what the Kleene paper says at all... It also does far more than use Godel's notation -- in fact, it uses a different notation from Godel entirely.

Look at section 3 (starting on page 58) -- you'll have to go through the rest of the paper first, of course. But I doubt you'll understand it, since you don't even understand what completeness is.

>>18821863
>But I know you won't [actually work through the derivation using your own brain]. You will instead repeat the same thing like a retarded pokemon.

>>18821887
>But I doubt you'll understand it, since you don't even understand what completeness is
>>More insults to mask your own ignorance and avoid actually thinking about the shit yourself, because its easier to take the results given by xyz figure of authority at face value and repeat it endlessly like a retarded pokemon.

>>18821890
I'm literally citing the Godel proof itself.
Also, saying you don't understand completeness isn't an insult, you've demonstrated that you don't. The 'results given' by the incompleteness theorem are the same regardless of the proof.

>>18819878
Is Logic even unironically gonna be valid in a million years?

>>18819878
Any instructional books on math logic ? I tried the trivium but someone mentioned on here how outdated it is.

>>18821204
Gotcha.

>>18821907
Not that anon but
>Gödel’s disproof of completeness must be just as incomplete as any other proof. That is to say, the Incompleteness Theorem is itself incomplete, and therefore unprovable. It is useless except as another grand contradiction, and we are not in need of further logical contradictions posing as theorems.
What was meant by this?

>>18822043
Yeah you'll be fine mate; as long as you go easy on yourself you'll come up with your own solutions for getting a bit too spiritually or intellectually high, if you know what I mean. Lots of the "insanity" that folks like Cantor or Dr. Semmelweiss or Nietzsche ended up with could be construed as merely being misunderstood, as they could have been gaslighted into a self-fulfilling prophecy type thing. How that started usually being because they were frustrated at people saying they were crazy when they devised theorems that nobody in their time understood; and lo, their combined brilliance is still being talked about to this day. Not to say that schizophrenia isn't a thing. But the term is thrown around rather loosely around these parts, and, well, everywhere, now that I mention it.

>>18822050
I think this is a Popper quote, but I'm guessing he just didn't understand the proof. Nothing I've read indicates that he was very technically skilled as a logician, so it's probably just there that he has the issue.

>>18822004
There's one linked above, https://www.ibisc.univ-evry.fr/~belardinelli/Documents/Logique/Mathematical-Logic-ChiswellHodges.pdf
You should know a bit of how math works before trying this one, but you could also just dive in and see how it goes. Do the exercises.

>>18822003
Insofar as any math is, yes.

>>18820784
Yes. If God is eternal, then He is also pre-logical

>>18820193
This
I fucking hate faggot peuds like this nigger >>18819943 so much.

>>18822158
Point being that psychotic diagnoses can have just as much to do with feelings and social perception of the subject or patient, if not more so, than it has to do with delusion. The subject matter pertaining to mathematics and whatnot being easy enough to understand, perhaps harder to do in practice.

Anyway. Godspeed anon, happy theorizing.

>>18822460
Good point—it does seem like there’s a certain amount of inner world building with these kinds of thinkers that leaves them at odds with their contemporaries. I think with meditation I’ll try to suspend those patterns of thought which might overwhelm me.

And thank you. Godspeed to you too.

>>18819878
People very much underestimate the fact that philosophy is an actual thing to study and not life advice. Most people don't really want to be a philosopher in the capacity it really is; I know I don't.
>>18819943
He was divinely inspired.

>>18820006
>sent from my iPhone

>>18820884
it never was.

>>18819878
Logic = Sophistry
People that teach it should be hung

>>18822698
Cheers.

Philosophers can't just lay out their writing in simple terms. They have to ramble on, using terms they literally made up to symbolize ideas that aren't even complicated, just abstract. Frankly it's all a magic spell to get retards to think they're smart. A smart man can explain the purpose of the universe in one paragraph

>>18819878
all philosophers incorporate logic when necessary
>"read all written works on logic before proving basic determinism"
no

>>18819943
>>18820015
Gentleman, please use the rope

>>18819878
Just keep fucking going.

Im having a really hard time following the arguments in this thread. Is there a logic reading guide or something? I wanna be smart like you anons

>>18820765
First Theorem
G <-> ~Prov(G)
where G is a closed formula that uses the language of arithmetic (thus the problem is for systems that use such language)
Prov(G) means G is provable (please notice the negation operator ~ in front of the formulation)
From this we conclude the formal incompleteness of arithmetic (not all closed formulas that use the language of (Peano) arithemtic are decidable)
Second theorem
G <-> ~Prov(G) <-> Con(PA)
Con(PA) means the consistency (lack of contradictions) of Peano Arithmetic
G is logically equivalent to Con(PA) thus if one proves Con(PA), one proves a contradiction
Suppose we proved Con(PA)
it follows that G is proved and that ~Prov(G) is proved, from the proof of G it follows that Prov(G) is true, but then both Prov(G) and ~Prov(G) are proved, thus the system is inconsistent.
Thus if PA is consistent, its consistency is not provable (within that system).
□

>>18820971
Basically this, also the famous meme page is about 450 pages into the first volume, as opposed to 800 pages. No real difference, just a paraphrase of the meme. (The entire work runs for about 2000 pages). The comic is meant for a generic normie audience but /lit/ as a group are just patrician enough that they know the context so they jump straight to Godel arguments, a classic internet fight.

>>18819878
Let G = is gay, O = OP
∀x (O(x) G(x))

>>18820884

This author also did a book on elementary analysis. She called it Quackulus

>>18819878
Let G = is gay, O = OP
∀x (O(x) --> G(x))

>>18820295
Those are a lot of words.

How do I into logic, I want to know what truth means in math. This brutal beat down in thread makes me wanna know the concepts.

>>18823224
>>18823381
https://www.logicmatters.net/tyl/
This is what I used to start.

>>18819878
Nietzsche already BTFO'd logic. Sorry.

>>18823381
>I want to know what truth means in math.
A discrete math course would be a good place to start, that's how I grasped a decent amount of what was said here, other than the terms regarding first- and second-order axioms:
>>The formalization of arithmetic (the theory of natural numbers) as an axiomatic theory started with Peirce in 1881 and continued with Richard Dedekind and Giuseppe Peano in 1888. This was still a second-order axiomatization (expressing induction in terms of arbitrary subsets, thus with an implicit use of set theory) as concerns for expressing theories in first-order logic were not yet understood. In Dedekind's work, this approach appears as completely characterizing natural numbers and providing recursive definitions of addition and multiplication from the successor function and mathematical induction.

But that being said, beatdowns can be rather easy to avoid, the easiest way to win is not to play.

If you have the discipline to learn via autodidactism, >>18823422 looks like a decent resource.

>>18823427
The only way to "BTFO" anything is by using logic.

>>18820015
>>18819987
Time to Stop posting Russell

>>18821382
Is this true?

>>18820765
1. [within an axiomatic system] There are infinite true statements that have no formal proof
2. No solution to the entscheidungsproblem

>>18820819
>>18820792
No.
GEB used the Göddel Proof as an analogy to explain epiphenomena, same with Bach and Escher. It’s not really interested in the logical results per se. it’s more in love with the clever method that Göddel used principias system. Basically how he used a self referencing axiom to plug up the system. It’s all meant to explain his view of cognitive science and a future AI. A bunch of seamingly meaningless statement and contradictions produces something on a second order that is ultimately intelligence. Aka, your mushy brain cells all moving sodium’s and calcium ends up reading and comprehending this post.

>>18819943
You guys misunderstanding incompleteness of mathematics aren't being clever. It is dumb to watch.

Gödel himself who found the incompleteness theorem considered both logic and mathematics to be valid and mathematical proofs to be solid and complete. He even proved it in his completeness theorem which does not contradict his incompleteness theorem. It is talking about different things. By

>>18819943
The single most cucked post on /lit/.

>>18820295
AAAAAAAAAAAAAAAAAAAAAA BASED

>>18820006
You're well on your way to adopting the alternative to logic!

>>18823624
Reason ain't logic, pal.

bumps

>>18819943
> We are gathered here today in remembrance of anon, who got butchered by a mob after saying something incredibly stupid.
> Though he wasn't the best of persons (he was stupid, spent all his time on forum boards like 4gag and redditchan and lived in his mom's basement) we all have bad qualities.
> He probably had good qualities too.....
> We must trust his soul to God's mercy.
> May peace be upon him.
> Amen.

>>18819878
I cant tell if fiction is really fictional / made-up and philosophical / supposedly truthful teachings aren't really just fictional either

Everything starts to seem illogical when your thoughts are being broadcast and being communicated back to you non-verbally

damn thots

>>18819878
RIP femanons and niganons

>>18819985
theology is to govern retards, philosophy is to know God

I'm really happy that I stopped torturing myself with this autistic hair-splitting some time ago.

>>18826148
ngmi