Thread 16757409

> We then discuss a 748-state Turing machine that enumerates all proofs and halts if and only if it finds a contradiction.

Suppose this machine halts. That means ZFC entails a contradiction. By principle of explosion, the machine doesn't halt. That's a contradiction. Hence, we can conclude that the machine doesn't halt, namely that ZFC doesn't contain a contradiction.

Since we've shown that ZFC proves that ZFC is consistent, therefore ZFC isn't consistent as ZFC is self-verifying and contains Peano arithmetic.

source: https://www.ingo-blechschmidt.eu/assets/bachelor-thesis-undecidability-bb748.pdf

>>16757409 (OP)
First, I assume what you are doing is starting in ZFC as a formal theory (imagine a formal theory as just a bundled rule set, it can be contradictory or not, its just a list of symbols we're talking about.)

You are encoding a Turing machine enumerating all ZFC proofs.

Now say it halts: recreating the proof in ZFC gives a formal contradiction.

From the outside metalogic so to speak, saying the formal theory of ZFC gives a contradiction isnt itself a contradiction. We just said a formal theory has this property of contradiction, and that isnt itself a contradiction.

What this means is that principle of exclusion from the outside wouldn't apply, so the deduction that ZFC must also make the machine not halt is wrong, and here the turing machine in ZFC eother does or doesnt halt.

>>16757409 (OP)
>By principle of explosion, the machine doesn't halt.
nigga, turing machines can run paraconsistent programs, hence the principle of explosion means fuck all for a busy beaver

all they're saying is ZFC is Godel-complete, i.e. that you can write two consistent but contradictory statements in it
which, you know, no big surprise there
the big surprise is how the fucking ZFC grift just keeps on rolling

>>16757840
what's your theory of choice for doing math in?

>>16757840
>two consistent but contradictory statements

That itself is a contradiction, consistent is by definition something not containing a contradiction.

Or do you mean they are separately consistent with ZFC but contradictory to each other, but that's also functionally impossible if its Godel complete.

Suppose the machine halts. That means ZFC contains a contradiction. Therefore the machine doesn't halt.

Since we can conclude from this argument that the machine doesn't halt, therefore we have a proof that ZFC implies that ZFC is consistent. As a result, we know that ZFC is not consistent.

QED

>>16758216
See first reply to OP. And learn formal logic before talking on it.

>>16758217
I see what you're saying, but I think it's a problem. Let me explain.
We can just dispense with this machine formalism and think about ZFC+FC where FC is the "formal contradiction" axiom that states
FC. There is a formal proof that ZFC is not consistent
We should probably say 2-ZFC to distinguish the ZFC we define in ZFC from the ZFC we use.
FC. There is a formal proof that 2-ZFC is not consistent
Part of the issue here is that ZFC + classical logic is too weak. We have a situation here that should produce a contradiction, but it doesn't, and we lack a proof that ZFC+FC is inconsistent because we don't have a "self-recognizing contradiction promotion" inference rule. If we had a "contradiction lifting" inference rule that states "if a structure simulates formal logic with a subset of the axioms we're using, then it doesn't contain contains a simulated contradiction" then we could use it to prove that ZFC+FC is inconsistent.
Out of curiosity, what does ZFC+FC entail in classical logic? Anything interesting?

I've always wondered how people like OP can be so blind to how wrong they are and how obviously stupid they sound.
OP do you have schizophrenia by any chance?
You're thoroughly confused on the topic. If that's your thesis which it seems to be, I'm sorry you've spent so much time on nonsense.
The fact that Con(ZFC) can be represented as the halting of an n-state turing machine is a triviality and does not in any way imply ZFC is inconsistent.
>That means ZFC entails a contradiction. By principle of explosion, the machine doesn't halt.
That doesn't follow.
>>16758216
> That means ZFC contains a contradiction. Therefore the machine doesn't halt.
That doesn't follow.

Also this doesn't deserve its own thread. It belongs in
>>16724182

>>16758441
Consider this: we don't have a one-line proof that ZFC+FC entails a contradiction because ZFC can't recognize a simulated version of itself.
This strikes me as stupid and inferior. What's the problem? Why can't ZFC recognize a simulated version of itself?

>>16758455
>ZFC can't recognize a simulated version of itself
This is meaningless gibberish. ZFC recognizes sets and first order sentences about sets.
>This strikes me as stupid and inferior
Stupid why? You haven't explained. Inferior to what? Propose an alternative.
>Why can't ZFC recognize a simulated version of itself?
Because that's meaningless gibberish.

>>16758464
> This is meaningless gibberish
lol, logic doesn't care if it's meaningless
lmao
>Propose an alternative.
Alright. Contradiction Lifting axiom (CL).
CL. There are no simulated contradictions.
It'll take like 40 pages or so of dense notes to write out in full, rofl

>>16758455
You seem to be angry at ZFC for not being able to formalize your nonsense gibberish "proof" which only looks right until you think about it for one second and realize it makes no sense. That's not the fault of ZFC, that's your fault. ZFC is perfectly fine with supporting valid mathematical arguments. The issue is that what you're trying to do is nonsense, and it tends to be quite hard to formalize nonsense in ZFC, or in any formal language generally. That's why none of the cranks ever do it.

>>16758467
>It'll take like 40 pages or so of dense notes to write out in full, rofl
Hopefully by page 2-3 you will realize what you're doing is nonsense, since clearly thinking about it isn't enough for you.

>>16757409 (OP)
The true question is "how does a retard on /sci/ end up citing Ingo Blechschmidt?".

>>16758468
> it tends to be quite hard to formalize nonsense in ZFC
lol, that is, itself, utter nonsense
look, you're the schizo here
fuckin' Alice in ZFCland here
Anthropomorphism gone wild
like, 420blazeitfgt lolololololol
formalize crank nonsense
oriental frank conscience
my proof went poof
like Alice through the roof
*ahem*
The point is that ZFC+CL+FC is inconsistent, and that's 100% formal. So, from ZFC+CL we can prove !FC. Do you have some problem with ZFC+CL? Am I rustling your jimmies? Activating your almonds?
By the way, all of this is perfectly easy to formalize and isn't nonsense at all. Unless it's nonsense, of course. I mean, it's meaningful unless it's meaningless.

>>16758474
don't you guys check plebbit?!?! 4chan totally missed this story
you guys are losing out
all of the work formalizing those 40 pages has already been done
>>16758470
check it out for yourself, it's on page 1 or 2 of /r/math, look for "Turing machine with 748 states" or 745, one or the other

>>16758474
it takes many sorts to make a world, and that includes the retarded sorts

>>16758479
you guys think plebbit is retarded, but you don't get an important story like this
reality is you're just missing out
this place is retarded for not picking up the story in the OP
why do I have to go to plebbit to see stories
you guys should be covering the stuff that plebbit covers
if you don't, then you're the retards, not plebbit

>>16758002
all math is rotten to its very foundations, it's why Hilbert and Cantor went bananas
NBG
>>16758046
>that's also functionally impossible
lol. lmao even

https://www.ams.org/journals/proc/1961-012-02/S0002-9939-1961-0126376-6/S0002-9939-1961-0126376-6.pdf
those who don't learn math are condemned to re-invent it

>>16758436
I think even more broadly, a theory T proving in itself 'T does not get a contradiction' does not imply 'T does not get a contradiction'. It's like T lying to you: why believe it from the outside?

You can relate this to the fact that T proving Cons(T) doesn't imply T is consistent, and by the second Godel incompleteness for a sufficiently strong T (like Peano Arithmetic), this isn't possible. I mean trivially, if T is inconsistent, anything can be proven so Cons(T) can be proven, but it's like T says whatever: it doesn't mean anything.

>>16757409 (OP)
The argument is actually way simpler than that:
>Suppose ZFC entails a contradiction
>By principle of explosion, ZFC is consistent
>Therefore ZFC is consistent
you don't need busy beavers at all

>>16758798
>you don't need busy beavers at all
Correct.
>>By principle of explosion, ZFC is consistent
This doesn't follow, idiot.

Crank thread, disregard. OP take your meds.

>>16758953
>This doesn't follow, idiot.
yes it does, dipshit

>>16758798
yah
ZFC falls

>>16759471
F

>>16759471
No it doens't retard.
Here's a proof that you're a faggot:
you disagreed with me, therefore you're a faggot.
This argument is just as robust as the one you gave, idiot.

>>16759537
sucks to be you
ZFC has FALLEN

https://www.youtube.com/watch?v=4UNj-VK43iQ recent video footage of ZFC

A picture of ZFC moments after being proven inconsistent

>C
O
>N
T
>R
A
>D
I
>C
T
>E
D

Fuck off I proved ZFC inconsistent before you did. Here's the proof:
There are infinitely many prime numbers. By the principle of explosion, there's a largest prime number. But that contradicts that there are infinitely many prime numbers. Contradiction.

No need to nominate me for the Fields medal, I already nominated myself ;)

Proof I don't have schizophrenia:
Doctor said I have schizophrenia. By the principle of explosion, the doctor is wrong. Therefore I don't have schizophrenia.
QED

>>16757409 (OP)
>>16758455
>>16758216
Your proof is wrong. Applying the principle of explosion explodes your proof, therefore it's wrong.

>>16759640
see
>>16759558
if a formal proof of a contradiction from ZFC exists, then we have a contradiction, therefore no formal proof of a contradiction from ZFC exists, therefore ZFC proves that ZFC is consistent therefore ZFC is inconsistent
I'd like to thank all of you for your suggestions that have helped the proof evolve to its current state. Today, the ZFC cult has been shaken to its core, its power generating system utterly destroyed, I feel like the hero in a video game. In this moment, I am euphoric.

>>16759745
>if a formal proof of a contradiction from ZFC exists, then we have a contradiction
Why? What's the contradiction?

>>16759805
>What's the contradiction?

>>16759805
ZFC doesn't even know that ZFC has a contradiction
BWAHAAHAHAHAHAHAHAHHA!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
THE MOST ADVANCED AXIOMATIC THEORY
AHAHAHAHAHAHAHAHAHAHA!!!!!!!!!!!!!!!!!!!!

>>16759821
>>16759820
Hopelessly retarded.

>>16760197
keep working with your inconsistent theory, bro

>>16760387
It's not inconsistent though. You're just retarded.

>>16760446
>It's not inconsistent though
lol, you have a proof of that
BWAAHAHAAHAHHAH!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
IT'S JUST YOUR FUCKING OPINION
AAHAHAHAAHAHHAH!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

>>16760459
formalize your shit on LEAN or cope

>>16760939
He's a crank he doesn't know what lean is. None of them do.

>>16761261
i figured as much

>>16757409 (OP)
"ZFC is inconsistent" is consistent with ZFC, and the inconsistency of ZFC wouldn't imply the inconsistency of Turing Machines.